Tuesday, 5 December 2017

Abraham von Franckenberg - The Key to the House of David (1646) [beta]

This is an Appendix of Abraham von Franckenberg's publication [1646] of Guillaume Postel's 'Absconditorum clavis, ou La Clé des choses cachées et l'Exégèse du Candélabre mystique dans le tabernacle de Moyse' [The Key of Secrets, or, The Key of Hidden Things and the Exegesis of the Mystic Candelabra in the tabernacle of Moses.], first published by Postel in 1547. Franckenberg served as the Editor, and added several appendixes, of which "The Key of David" is one. In the text below, Franckenberg is the "Editor", and Postel is the "Author". 

In latin, the opening greeting is "Salve Philomysta". Philomysta doesn't seem to exist elsewhere, and is probably a combination of Philo (philosophy) and "mysta", which translates to "deacon", "priest", and other variations through it's connection to "magister sacrorum". A more literal translation would be "Officiating Priest of Philosophy".

Translation and diagram are my own. 


The Editor’s Key
The Author’s Key

Greetings Master of Philosophy.

I. We give you the Key to enter the Sanctuary; receive it with purified hands, and do not enter with unclean feet, for it is necessary to go chastely to the Gods; it's the law. For if you attract beforehand (by the Decrees and Secrets of the Initiates) the Universal Sapience, and if you know in advance the Tetrachord or Quadriga of Apollo, then you will understand more easily and more happily without doubt, the science of  מרכבה (Merkabah), the Chariot of Isra-El, with the Sefirot and the other wheels [spheres] of the Cherubic or Biblical Sapience. By this fight, sometimes Poetic, sometimes Prophetic, penetrated and anointed by the breath of the Holy Spirit, touched and drawn by his attendance, you will escape Divinely from the fortress where you are a prisoner.

II. This is the goal that our Initiate pursued in Chapter 15 when he showed the Spirit contemplating the magnificences and wonders of God and nature that must be known and sought in the interior of the veil. Eternal truth. And it is by this mystical artifice that the three straight lines or three points of the Circle or Triangle of the sacred mono-triad are united and sealed by the fourth or Radical center of this Divine science in the Unity or Sacred Sanctuary Deification.

Table which holds the keys to understanding Chapter 15, abbreviated to make it easier to learn.

III. Collect more grain of the same meal, and chew deeply, if you wish to thoroughly understand the Holy Bible (the doctors of the soul, τα τής ψυκής φάρμακα): the abbot Joachim, Giovanni Pico de Mirandola, Jean Reuchlin, Henry Corneilus Agrippa, Francois Georgius, Paulus Schalichius, Paulus Brunus, Jacob Brocardus, William Ouciacus, Giordano Bruno, Peter Bongus, Jules Sperterus, Philip Zigler, John Bureus, and the other initiates of the greatest peoples, Greeks, Chaldeans, or Hebrews. right here; and listens to and observes what they have taught in writing about the mysteries and the Arcana of names, powers and sacrosanct numbers and not temporal riches (Lat Nomino, Numina, Numeri and Nummi) and more that they have revealed and verbally entrusted to their truly worthy listeners, that is, to their Faithful and their {attachés}.

IV. Seriously apply your spirit to what our author [Postel] has exhibited according to his time and his genius, to be admired, sought after, applied and properly explained according to our way of seeing and our century; believe it and be firmly convinced of it. Collect thus and understand Scripture with Nature and Nature with Scripture united in a sweet and blessed union by the infinite mysteries of innumerable numbers and senses (because the word of God is infinite) and that they are not proposed and faithfully and piously exhibited only in one sense and perpetually similar to himself in all and everywhere, and only one mystery predestined and hidden from the constitution of ages, that is, Jesus Christ, savior of the world, and who is really the Incarnate, Crucified, Risen and Exalted God for Us, and, according to the Mystery and Analogy of the King, who must be spiritually Incarnate, Crucified, Risen and Exalted every day in each of us, believers, and in all until the consumption of the centuries. So finally, that all testimonies or Gentiles or Christians and all nature and writing concordant together, be applied to this one Unique and True and Living God and that every language and Spirit admits and acknowledges that it is necessary that H I C Jesus is the Christ, Ha immanu Æl, the true God and the Eternal life that is in all and in whom are all Beings. May he be blessed in the centuries.


Tuesday, 21 November 2017

The Hunting of the GREENELYON


ALL haile to the noble Companie
Oftrue Students in holy Alchimie,
Whose noble practise doth hem teach
To vaile their secrets with mistie speach;
Mought yt please your worshipfulnes
To heare my silly soothfastnes,
Of that practise which I have seene,
In hunting of the Lyon Greene:
And because you may be apaid,
That ys truth, that I have said;
And that you may for surety weene,
That I know well thys Lyon greene:
I pray your patience to attend
Till you see my short writt end,
Wherein Ile keepe my noble Masters rede,
Who while he lived stoode me in steede;
At his death he made me sweare hym to,
That all the secrets I schould never undoe
To no one Man, but even spread a Cloude
Over my words and writes, and so it shroude,
That they which do this Art desire,
Should first know well to rule their Fyre:

For with good reason yt doth stand,
Swords to keepe fro mad Mens hand:
Least th'one should, kill th'other burne,
Or either doe some sore shroud turne:
As some have done that I have seene,
As they did hunt thys Lyon greene.
Whose collour doubtles ys not soe,
And that your wisdomes well doe know;
For no man lives that ever hath seene
Upon foure feete a Lyon colloured greene:
But our Lyon wanting maturity,
Is called greene for unripenes trust me,
And yet full quickly can he run,
And soone can overtake the Sun:
And suddainely can hym devoure,
If they be both shut in one towre:
And hym Eclipse that was so bryght,
And make thys redde to turne to whyte:
By vertue of hys crudytie,
And unripe humors whych in hym be,
And yet wythin he hath such heate,
That whan he hath the Sun up eate,
He bringeth hym to more perfection,
Than ever he had by Natures direccion.
This Lyon maketh the Sun sith soone
To be joyned to hys Sister the Moone:
By way of wedding a wonderous thing,
Thys Lyon should cause hem to begett a King:
And tis as strange that thys Kings food,
Can be nothing but thys Lyons Blood;
And tis as true that thys ys none other,
Than ys it the Kings Father and Mother.
A wonder a Lyon, and Sun and Moone,
All these three one deede have done:

The Lyon ys the Preist, the Sun and Moone the wedd,
Yet they were both borne in the Lyons Bedd;
And yet thys King was begott by none other,
But by Sun and Moone hys owne Sister and Brother.

O noble Master of pardon I you pray,
Because I did well-neere bewray
The secret which to me ys so deare,
For I thought none but Brothers were here:
Than schould I make no doubt
To have written plainely out,
But for my fealty I must keepe aye,
Ile turne my pen another way,
To speake under Benedicite
Of thys noble Company:
Wych now perceives by thys,
That I know what our Lyon ys.

Although in Science I am noe Clerke,
Yet have I labour'd in thys warke:
And truly wythouten any nay,
If you will listen to my lay:
Some thing thereby yow may finde,
That well may content your minde,
I will not sweare to make yow give credence,
For a Philosopher will finde here in evidence,
Of the truth, and to men that be Lay,
I skill not greatly what they say.
For they weene that our Lyon ys
Common Quick silver, but truly they miss:
And of thys purpose evermore shall fayle,
And spend hys Thrift to litle availe,
That weeneth to warke hys wyll thereby,
Because he doth soe readely flie;
Therefore leave off ere thou begin,
Till thow know better what we meane;

Whych whan thow doest than wilt thou say
That I have tought thee a good lay,
In that whych I have said of thee before,
Wherefore lysten and marke well my lore.

Whan thow hast thy Lyon with Sol and Luna well fedd,
And layd them clenly in their Bedd;
An easie heate they may not misse,
Till each the other well can kisse;
And that they shroude them in a skin,
Such as an Egg yelke lyeth in:
Than must thow draw from thence away,
A right good secret withouten any nay:
Wych must serve to doe thee good,
For yt ys the Lyons Blood:
And therewith must the King be fedd,
When he ys risen from the dead:
But longe tyme it wilbe,
Or ere his death appeare to thee;
And many a sleepe thow must lack,
Or thow hym see of Collour black.
Take heede yow move hym not with yre,
But keepe hym in an easy fyre;
Untill you see hym seperate,
From hys vile Erth vituperate;
Wych wilbe black and light withall,
Much like the substance of a fusball:
Your magnet in the midst wilbe,
Of Collour faire and white trust me;
Then whan you see all thys thing,
Your fire one degree increasing;
Untill yow well may se thereby,
Your matter to grow very dry:
Then yt ys fit wythout delay,
The excrements be tane away;

Prepaire a Bed most bryght and shine
For to lodge this young Chylde in:
And therein let hym alone lye,
Till he be throughly dry;
Than ys tyme as I doe thinke,
After such drouth to give him drinke:
But thereof the truth to shew,
Is a greate secret well I know;
For Philosophers of tyme old,
The secret of Imbibition never out tould;
To create Magnesia they made no care,
In their Bookes largely to declare;
But how to order it after hys creacion,
They left poore men without consolacion;
Soe many men thought they had had perfeccion,
But they found nothing in their Projeccion:
Therefore they mard what they had made before,
And of Alchimy they would have no more.
Thus do olde Fathers hide it from a Clearke,
Because in it consisteth the whole subtill warke;
Wych if ye list of me to know,
I shall not faile the truth to shew.
Whan your pure matter in the glasse is fitt,
Before that you your vessell shitt;
A portion of your Lyons sweate
Must be given it for to eate:
And they must be grounded so well together,
That each fro other will flee noe whither;
Then must you seale up your Glasse,
And in hys Furnace where he was,
You must set them there to dry.
Which being done then truly,
You must prepare like a good Phisitian,
For another Imbibition:

But evermore looke that you dry
Up all hys drinke, that none lye by,
For if yow make hym drinke too free,
The longer will your workeing be,
And yf you let hym be too dry,
Than for thirst your Child may dye;
Wherefore the meane to hold is best,
Twixt overmoyst and too much rost;
Six tymes thy Imbibitions make,
The seaventh that Saboath's rest betake:
Eight dayes twixt ilke day of the six,
To dry up moist and make it fix;
Then at the nynth tyme thy Glasse up seale,
And let him stand six weekes each deale:
With his heate temperd so right,
That Blacknes past he may grow white;
And so the seaventh weeke rest him still,
Till thow Ferment after thy will;
Which if thow wilt Ferment for Whyte,
Thereby thow gainst noe greate profitt;
For I assure thee thow needest not dred,
To proceede with fire till all be Redd;
Than must thow proceede as did Philosophers old
To prepaire thy Ferment of peure Gold,
Which how to doe though secret that it be,
Yet will I truly teach it thee.

In the next Chapter as erst I did say,
That soe the truth finde yow may,
Therefore of Charity and for our Lords sake,
Let noe man from my writings take
One word, nor add thereto,
For certainely if that he doe,
He shall shew malice fro the which I am free,
Meaning truth and not subtilty;

Which I refer to the Judgement
Of those which ken the Philosophers intent:
Now listen me with all your might,
How to prepare your Ferment right.

O noble Worke of workes that God has wrought,
Whereby each thing of things are forth aye broght;
And fitted to their generacion,
By a noble fermentacion;
Which Ferment must be of such a thing,
As was the workes begyning;
And if thow doe progresse aright
Whan thow hast brought the worke to whight;
And than to stay is thy intent,
Doe after my Comandement;
Worke Luna by her selfe alone,
With the blood of the greene Lyon:
As earst thow didst in the begining,
And of three didst make one thing,
Orderly yeilding forth right,
Till thy Magnet schew full whyte;
Soe must thow warke all thy Ferment,
Both White and Red, else were yt shent.
Red by yt selfe and soe the White,
With the Lyons Blood must be deight;
And if thow wilt follow my lore,
Set in thy Ferment the same houre,
Of Sol for Redd, of Luna for White,
Each by himselfe let worke tight;
Soe shall thy Ferment be ready edress,
To feede the King with a good mess
Of meates that fitt for his digestion,
And well agreeing to his Complexion;
If he be of Collour White,
Feed hym than with Luna bright;

If his flesh be perfect Red,
Than with the Sun he must be fedd,
Your Ferment one fourth parte must be,
Into your Magnet made evenly,
And joyne hem warme and not cold,
For raw to ripe you may be bold
Have disagreement soe have heate and cold:
Therefore put hem warme into thy Glasse,
Then seale it up even as it was:
And Circle all till yt be wonne,
By passing degrees every each one:
Both black and whyte, and also redd,
Than of the Fire heere have noe dread;
For he will never dreade the fyre,
But ever abide thy desire.

And heere a secret to thee I must shew,
How to Multeplie that thow must know,
Or else it wilbe over micle paine
For thee to begin thy worke againe:
I say to thee that in noe fashion,
It's so well Multeplied as with continuall Firmentation:
And sure far it wilbe exalted at the last,
And in Projeccion ren full fast:
There for in fyre keepe Firment alway,
That thy Medicine augment mayst aye;
For yf the maid doe not her leaven save,
Then of her Neighbours sche must needs goe crave;
Or sche must stay till sche can make more,
Remember the Proverbe that store is no sore:
Thus have I tought thee a lesson, full of truth,
If thow be wicked therefore my heart is reuth:
Remember God hys blessing he can take,
Whan he hath given it, if abuse any you make,
For surely if thow be a Clerke,

Thow wilt finde trewth in thys werke:
But if so be that thow be lay,
And understond not what I say,
Keepe Councell then and leve thy Toy,
For it befitts no Lymmer loy,
To medle with such grete secresie:
As ys thys hygh Phylosophye.
My Councell take, for •how schalt finde it true,
Leave of seeking thys Lyon to pursue,
For hym to hunt that ys a prety wyle,
Yet by hys Craft he doth most Folke beguile,
And hem devour and leave hem full of care,
Wherefore I bidd thee to beware.
And Councell give thee as my frend,
And so my Hunting here I end.
Praying God that made us we may not myss
To dwell with hym in hys Hevenly blyss.

The Geometrical Order of the World - beta

This was originally going to be a post of the diagrams from Otto Van Veen's "Physicae et Theologicae Conclusiones" (1621), but I found an old paper, "The Geometrical Order of the World: Otto Van Veen's Physicae et Theologicae Conclusiones" by Christoph Geissmar (known nowadays as Dr. Christoph Geissmar-Brandi), published in Journal of the Warburg and Courtauld Institutes, Volume 56, 1993. The author notes that the "conception of this paper was made possible by a Frances A. Yates fellowship at the Warburg Institute."

In the paper, Geissmar-Brandi provides a paraphrasing of the latin text that accompanies each diagram (each considered a "chapter"). This is this basis for the english explanations included below - they have only been slightly edited to fit this format. After the 20 chapters, Geissmar-Brandi provides some comparisons to other works of Van Veen, and those of Kepler and Jacob Boehme, parts of which I will include at the end as well.


Physicae et Theologicae Conclusiones (1621)

The small folio book consists of a title-page, tabic of contents, list of errata, prologue (addressed, unusually, to the Viewer as well as the Reader: 'Lectori & Spectatori') and a note by the anonymous printer.

In the prologue Van Veen refers in general terms to the Platonic tradition of diagrammatic explanation in mathematical figures which he wishes to revive and apply to theology. His central concern is the problem of predestination and free will: if man partakes in the nature of God and therefore has a capacity for free action, how can this be reconciled with his falling into sin? The question is to be addressed and demonstrated in the illustrations. For Van Veen the deity in man (deitas hominis) is the original cause of justification and condemnation; man’s separation from God entails damnation and his conjunction with him brings salvation. Applying the alchemical theory of Paracelsus (and his supposed predecessor Isaacus Hollandus) that all entities are composed of three substances, he aims to show the triune nature of body (salt), spirit (mercury) and soul (sulphur). Despite his assurance at the outset that he is convinced that his conclusions are in perfect conformity with the teaching of the Catholic Church, it is clear that the material was controversial. For a note appended by the printer to the author’s preface seeks to relieve Van Veen of responsibility for the publication: it maintains the pictures were engraved and the work was then published without the author’s knowledge.

Chapter 1

The book opens with God, designated appropriately by the letter A: ‘God the ineffable, of one being yet three, eternal, embracing everything' ('Deus Ineffabilis, Ens unicum, Trinum, Aeternum, omnia continens A'). The corresponding picture (PI. 22a) consists solely of a capital A at the centre of a white square of ground. The letter both represents and signifies the space entirely occupied by God. 

Chapter 2
Being (Ens) and Nothingness (Nihil)

This chapter concerns the nihil at the centre of ens which causes light, life, intelligence and other qualities of ens to be pushed into the central abyss of darkness, death, confusion and other things opposed to being. This is illustrated in the letter B bounded by a circle, with A—the sign of God or ens unicum —shifted to the middle of the upper edge, so that it is directly above B and if joined to it would form a vertical line. In the figures which follow this line constitutes the compositional basis, with B remaining the centre of a circle. The circle is essential to most of the later figures and is generally interpreted as a sphere. 

Chapter 3
Being Seperated from Nothingness

In the illustration to this chapter A appears with B within the central circle while B accompanies A at the top of the page: this is because the separation of ens and nihil cannot be absolute, since ens embraces everything. Thus even in the depths of being nothingness remains, and in the depths of nothingness is infinite being. Darkness is not the privation of light hut a true entity. Here, as often elsewhere in the book, Van Veen cites an apposite scriptural passage, in this case referring to Exodus 10.21 on the darkness that was thick and palpable.

Chapter 4
The Creation of the Universe

God creates the entire universe (BB). with its natures and created things and its spirit (AAA), from ens universi and its prima materia by means of his word (ens potentissimum). In the view of some the universe consists of eleven spheres (rather than the nine of the ancients); it is not to be excluded that there may be infinite worlds, but given that there is no way to demonstrate this, humans should not seek such knowledge (cf. Romans 11.20).

Chapter 5 
The Creation of Man 

The account of the creation of man in this chapter is based on the assumption of Man’s formal likeness—as a composite of body, spirit and soul—to the triune God. By his free will, given solely to him by God, he is distinguished from other creatures. Man is therefore possessed of a freedom which in this respect makes him the equal of God. Therefore divine foreknowledge and predestination are not definite and determined, since they can be obstructed (impediri possint) by workings of the deity in man. Man is illustrated in the picture's centre by three intersecting circles and the triangle or letter A, which represents the deity in man, inscribed within them. This motif will recur throughout the book.

Chapter 6
The Fall of Lucifer

Here Van Veen explains in cosmological terms the fall of Lucifer (CCC) and his followers which occasioned God's first act of judgement.

Chapter 7
The Working of the Deity in Man 

This operation is nothing other than free will. Man's passions (EEE) incline him either towards God the creator (A) or towards creation (BB). It is on this basis that God will eventually judge him, leading to his damnation or salvation. God, by contrast, as infinite being (H), can neither fall nor be moved by passions; however, in sphere G, which exists between God and the created universe, the deity, in whom all time, motion and change exist, 'is moved in stability' (in stabili movetur). The illustration attempts to represent these complex ideas. The standard image of the triunity of creatures, the three circles, has been shifted to the picture's centre, with DDD representing man and EEE standing for his passions.

Chapter 8
God’s Omnipresence

God permeates the entire universe with his life, intelligence and substance which are inseparable one from another. He directs his divine powers towards whatever he wishes to happen, with the sole exception of the deity in man (A), which, since it is free (libera), cannot be compelled by God either towards or away from him.

Chapter 9
The Fall of Adam

Adam (DDD), as a creature of the lower world, succumbed to the natural infiu-ences of the universe BB and, being deficient in his deity (delta), inclined (E) towards the created world. Consequently, he was the second, after Lucifer, to meet with God’s judgement and suffer damnation.

Chapter 10
The Coming of Christ through the Virgin Mary 

God (A), however, saves Adam and his progeny from Lucifer’s fate by sending his son (A), through the Holy Spirit (A), to the Virgin Mary (GGG), and through her the entire universe is filled with his divine and corporeal being (cross). Under the new׳ dispensation all of nature is under Christ’s control, so that prediction of human events through the stars is no longer valid (except by explicit divine ordinance). Moreover, it is to be understood that although the Fall of Man was not predestined, in the course of time God ordained the advent of Christ for human salvation.

Chapter 11

Even though each man has a predestined disposition to good or evil, depending on the seeds which are sent from heaven to him (H, from God’s right and HH from his left), man still retains free will. For just as one should not blame the potter for making 'one vessel unto honour and another unto dishonour' [Romans 9.21], man’s free will allows him to be turned from bad to good or vice versa. All justification depends on the deity in man, not on man’s disposition: a man with a bad nature who turns to God receives a new and better ‘ray of predestination’ (I) and is saved, whereas someone who does not attribute his good nature to God is damned. God’s free will to predestine is not, however, diminished; for the first rays of predestination remain even though (in cases where the deity in man A is properly disposed towards God) he can send another better ray (I) to counteract the effect of the first.

Chapter 12
The Source of Evil

Evil is an inclination of the deity in man away from the creator and towards the created world; it is thus the deity in man. being free, which generates both good and evil. Man has in and around himself God (A) and the universe (B); hence in Pl. 23c, AB is shown within the triangle. Evil comes into being when man’s free disposition towards God and the universe is wrong. A well-disposed will, on the other hand, is given to man by God as a gift of grace. But the free will of the deity in man always precedes the grace which brings the new predestination of God (M). God has mercy only on those whose deity already tends towards him and hardens the heart of those whose deity constantly turns away from him towards the created world. Consequently, there is no question of God saving one man and damning another without cause.

Chapter 13
Grace and Good Works 

Good works that come about through the first predestination arc not meritori-ous but can move the deity in man to incline (F) to the creator (A), who, in turn, through the new predestination (K) gives meritorious works as a gift to man. These are ascribed to man as if they were his own and therefore earn him salvation. If he then attributes them to the grace of God, he constantly receives and does more and better works (L). But if he believes that these come through his own powers, he loses whatever good he has. Therefore, men should not be judged by their works because we cannot know which are meritorious and which not* since the judgement of God is hidden from our eyes.

Chapter 14
The Reality of Man’s Imagination 

Imagination, like all created things, is real and constant in its body, spirit and soul. Just as God (AAA) through his imagination or verbum (NNN) has created the universe (B). so the imagination of man (O) creates real beings (entia realia) (P) which act corporally on things and bodies. If imagination or thought in the natural, rational spirit is accompanied by faith it extends itself marvellously. The state of the deity in man, when with faith it soars upwards supernaturally by means of the imagination, cannot be understood by natural reason; knowledge of it is for God alone.

Chapter 15
Death and Purgatory 

Death destroys man’s triunity and returns soul to an upper sphere, spirit to a middle level and body to the earth (DDD). Yet the three remain connected. If they are pure, they rejoice together; if impure, they will be purified by the particular fire of the orbs to which they adhere until the last day when the world will be consumed by fire and the three parts will recombine for the Last Judgement. (This circumstance accounts lor the way in which magicians—whether by the power of the imagination or with the help of a demon, or in another way entirely—know how to separate spirit and body, so that the spirit takes on the appearance of the body to do wicked things in another place, and one body is perceived in two places; and if the spirit is too slow in returning to the body, or if something untoward occurs to it, then the three parts of man can remain separated until his death.) Of course it is not the gross, earthly body that will be finally reunited with soul and spirit, but rather a more subtle, spiritual one, such as will be able to ascend, purified and distilled, leaving its lower parts in the earth to nourish the process of generation.

Chapter 16
The Last Judgement and Resurrection 

On the last day a sort of magnetic attraction will recombine the three parts of man. This can he demonstrated physically: for if some plant or body is divided by art and fire (i.e. alchemically) into its three parts, salt, sulphur and mercury, and these three parts are then combined again, one body results; and if there are three separate bodies (i.e. nine parts), the three recombine by a secret sympathy. So on the last day man (if only he is purified) will be reconstituted gloriously, along with his actions, thoughts and imaginations, and through the virtue of the body of Christ will ascend from clarity׳ to clarity (AAA) the way prepared by Christ. Man will then be united with God on high, while still remaining a created being (ens creatum); but those who are impure will descend to the abyss.

Chapter 17
On the Virtue and Presence of God in the Eucharist 

Our Saviour with all the realities (enlia realia) of his actions and words (of which the prime reality, ens primarium, is the crucified Christ) united himself with a good man. Thus he ordained that union of man with the Trinity (AAA) would be effected in an external and corporeal manner, and that the deity in man should be promoted and man should be united with the Saviour through the Eucharist (regardless of whether under one species, or otherwise, since the part contains the whole), although without the virtue of Faith (Q) of Hope (R) and of the most essential, Charity (S), no union comes about, but Christ’s being and its consecrated substance remain ineffective. But if the Eucharist cannot be taken, but is desired by someone who sees it, or even is not seen but simply desired, then it also has its effect through the virtue of Faith. Hope and Charity. Again, if some accident befalls the host its consecrated substance and effective virtue still remains within it.

Chapter 18
How the Gentiles and Pagans may be Saved

Since Christ’s coming filled the whole world with his body, spirit and soul, then he must be within pagans and infidels, even if this is not manifested in a Christian way of life. Since Christ is the supreme good from which alt good things (W) proceed, the deity even in a pagan man, moved by the influence of the virtue of Christ (X) and by the holy spirit (A), will incline him to virtue (TT) and indeed he may become an unwitting and hidden Christian and might immediately and invisibly enjoy the benefits of the sacraments and other things essential to salvation. By con-Hast there are those who are nominally and externally Christians who arc judged deficient in virtue by pagans; they will be damned. Pagans can receive the word of God internally, rather than externally, and thus be united to Christ who through his death saved all mankind without exception.

Chapter 19
The Church

The Church (Y) is the community of people who embrace Scripture as the word of God and the traditions of the fathers. She is governed by the holy spirit, and in pronouncements relating to salvation she cannot err. As far as her external organisation is concerned all pious Christians should accept the authority of the pope. The Church is distinguished by three principal features: antiquity, universality׳ and apostolic succession. Thus no credence is to be given to those who say that the signs of the true Church consist of doctrine alone, since this would impose on everyone the necessity׳ of consulting Scripture on every point of controversy. Nor is the inference correct that the Church is an invisible body of the elect, for it is difficult to distinguish good individuals from wicked ones. But the Church has both soul and body, and while the understanding of her soul—that is the good who have received grace —is God’s concern, man needs to recognise the visible and corporeal Church and submit to her authority and to the pope. As for those born outside Christianity, the Church commands that we treat them as heretics and infidels, and avoid them accordingly, even if we should not condemn them, since they may be part of the invisible Church, so that we must leave it to God to judge them; similarly it is absurd to suppose that unbaptised infants cannot be saved.

Chapter 20
How Corporeal Things and External Ceremonies Promote the Deity in Man

Various forms and species of the soul are presented through the bodily senses and through the natural rational spirit which is said to come from the stars or the firmament. These then prompt the deity in man to incline either towards the Creator (B) or away from him, which leads to a new predestination [cf. above, chapter 11] which is either good or bad. Images, ceremonies and pious signs relating to the coming, the life and the death of Christ can enable these entia realia [cf above, chapter 17] to enter the soul through the body and spirit of the ray Z, and thus prompt the deity in man to incline towards the saviour; vanities and the temptation of the devil do the contrary. Thus the Church has established external and corporeal aids to piety, which one should beware of spurning. It is wrong to deny the teaching of the Church and the pope on good works and their heavenly rewards, for the pope finds appropriate paths to piety for different people, God using as many means are there are men. Many are motivated by the desire for rewards or by fear; few are virtuous through love of virtue. The pope’s aim is to render as many as possible better in their mode of life. External ceremonies and the promise of rewards are the only ways to keep some people from behaving like the brute beasts. Since everything is in everything, natural things have access to the supernatural and can move the mercy and grace of God towards man.



Friday, 19 May 2017

Zeus and the Sky-Pillar (The Elysian Way)

The word elysion, which thus signifies both the spot struck by lightning and the abode of the divinised dead, is presumably related to elysie, a ' way' The term is remarkable, and its applicability is not at once clear. We must suppose that the Greeks recognised a definite ' way ' from earth to heaven, along which those honoured by the summons of Zeus might pass. This conception would at least square with certain Pindaric phrases. In a context of Pythagorean import the poet tells how —

Souls that thrice on either side
Free from evil can abide
Travel the road of Zeus to Kronos' tower,
Where round islands of the blest
Ocean breezes lull to rest
And forth there flashes many a golden flower.

Again, in an equally arresting fragment Pindar says 

Themis the wise, the heavenly, afar
From Ocean's founts on golden car
Up the dread stair the Fates first bore
Alon^ the gleaming way to Olympos' height,
That Zeus the Saviour might
Have her to wife of yore :
The mother she of the unerring Hours,
Gold-frontleted, gay-fruited powers 

What was this 'road of Zeus,' this 'gleaming way'? If I am not mistaken, it was the broad path of dim and distant splendour that stretches across the abyss of the midnight skyl Our forefathers  called it ' Watling Streef' or 'London Road'.' We know it as the ' Milky Way.' And a collection of names for it such as that got together by H. Gaidoz and E. Rolland proves that all the world over it has been regarded as a celestial track. Further, as E. B. Tylor observed, this track is often held to be the road traversed by the gods or the souls of men :
"The Basutos call it the 'Way of the Gods' ; the Ojis say it is the 'Way of Spirits,' which souls go up to heaven by. North American tribes know it as ' the Path of the Master of Life,' the 'Path of Spirits,' ' the Road of Souls,' where they travel to the land beyond the grave, and where their camp-fires may be seen blazing as brighter stars l Such savage imaginations of the Milky Way fit with the Lithuanian myth of the ' Road of the Birds,' at whose end the souls of the good, fancied as flitting away at death like birds, dwell free and happy."
Classical evidence of the Galaxy conceived as a Seelenpfad is not wanting Ovid speaks of it as a road leading to the palace of lupiter

There is a road aloft in the clear heaven,
Milk-white and therefore named the Milky Way.
Here go the gods to the great Thunderer's house
And royal home. To right and left the halls
Of high-born deities fling wide their doors.
The populace in diverse spots may dwell ;
But on this front the denizens of heaven
Puissant and proud have pitched their own abode

Ovid's celestial city is doubtless made to the pattern of Rome: 'this front,' as R. Merkel saw recalls the frons Palatii. But the via sublinis of the poet's vision was borrowed from an old-world belief held by certain followers of Pythagoras. The Pythagoreans indeed were much exercised about the Milky Way. Most of them took it to be a ' way' of some sort. One group said that it was the track made by a star, which had fallen from its proper position at the time of Phaethon's catastrophe. Others saw in it a burnt pathway marking the sun's original coursel Others again deemed it a mere reflection of the solar rays. These opinions are duly recorded by Aristotle, Manilius', and the doxographer Actios. But a view ignored by them all is of more interest to us. Three writers steeped in neo-Platonic lore, and drawing perhaps from a single source ascribe to Pythagoras himself the belief that the Milky Way is the road by which souls come and go. Porphyrios {c. 233 — c. 304 A.D.), who penned an allegorical treatise On the Cave of the Nymphs in the Odyssey, remarks-:

"Elsewhere he (Homer) speaks of ' the gates of the Sun,' meaning Cancer and Capricornus ; for these are the limits to which it progresses when descending from north to south and again when ascending from south to north. Capricornus and Cancer are set at either side of the Milky Way, the latter on the north, the former on the south. And ' the folk of dreams ' according to Pythagoras are the souls, which—he asserts—are gathered together in the Milky Way, so called from those that are nurtured on milk, when they fall into birth."

Macrobius (c. 400 A.D.) in his Commentary on the Dream of Scipio says:
"The following order is observed in the descent by which the soul of man slips from heaven to the lower regions of this present life. The Milky Way embraces the zodiac by means of the circular contact of its oblique periphery in such a way that it intersects the zodiac at the points where two tropic signs, Capricornus and Cancer, are said to be. These the physicists have called the gates of the Sun, because both prevent it from further advance when such is forbidden by the solstice and turn it back to the pathway of that zone whose bounds it never quits. It is supposed that through these gates souls pass from heaven to earth and again from earth to heaven. One is called the gate of men, the other that of the gods : Cancer is the gate of men, because through it they descend to the lower regions ; Capricornus, the gate of the gods, because through it souls return to the seat of their own proper immortality and rejoin the company of the gods. This is what Homer, a poet of divine foresight, intended by his description of the cave in Ithake. Hence too Pythagoras holds that from the Milky Way downwards begins the realm of Dis, since souls that have fallen from it seem already to have left the world above. Milk—he says—is the first food offered to the new-born, because their first movement downwards in the direction of earthly bodies begins at the Milky Way. Wherefore also Scipio, pointing to the Milky Way, observed with regard to the souls of the blessed :
'Hence they start, and hither they return!'"
Proklos (410—485 A.D.), after citing from the Pythagorising Platonist Noumenios a somewhat similar account of Capricornus and Cancer as the openings through which souls are sent upwards and downwards, continues:
"For Pythagoras in mystic language calls the Milky Way 'Hades' and 'the place of souls,' since there they are crowded together. Whence sundry nations pour a libation of milk to the gods that purify souls, and milk is the first food taken by souls that fall into birth."
This belief in the Milky Way as a soul-road is found in several authors who, without being definitely followers of Pythagoras, are known to have come more or less under the influence of Pythagorean speculation. Thus Parmenides' in the preface to his great philosophical poem describes how he was conducted in a chariot ' on the far-famed way of the goddess ' (Ananke ?) and ' maidens led the way,' to wit the Heliades, who escorted him towards the light through the portals of Night and Day till he reached the home of the goddess". The 'way' in question is not improbably the Milky Way'. Again, Empedotimos of Syracuse who figures as an adherent of Pythagoras, held ' that the Milky Way is the road of souls traversing the Hades in heaven'.' Platon too is presumably Pythagorising, when in a famous passage of the Phaidros he tells how god-like souls follow the gods round the great arch of heaven and from its summit behold sights of unspeakable splendour in the region beyond the sky:
"Zeus, the great chieftain in heaven, driving a winged car, travels first, arranging and presiding over all things ; and after him comes a host of gods and inferior deities, marshalled in eleven divisions, for Hestia stays at home alone in the mansion of the gods ; but all the other ruling powers, that have their place in the number of the twelve, march at the head of a troop in the order to which they have been severally  appointed. Now there are, it is true, many ravishing views and opening paths within the bounds of heaven, whereon the family of the blessed gods go to and fro, each in performance of his own proper work ; and they are followed by all who from time to time possess both will and power ; for envy has no place in the celestial choir. But whenever they go to feast and revel, they forthwith journey by an uphill path to the summit of the heavenly vault. Now the chariots of the gods being of equal poise, and obedient to the rein, move easily, but all others with difficulty ; for they are burdened by the horse of vicious temper, which sways and sinks them towards the earth, if haply he has received no good training from his charioteer. Whereupon there awaits the soul a crowning pain and agony. For those which we called immortal go outside when they are come to the topmost height, and stand on the outer surface of heaven, and as they stand they are borne round by its revolution, and gaze on the eternal scene. Now of that region beyond the sky no earthly bard has ever yet sung or ever will sing in worthy strains'. 
It can hardly be doubted that the ' uphill path to the summit of the heavenly vault,' a path along which the souls of the blessed go to the fulness of fruition, imphes the Pythagorean conception of the Milky Way as an Elysian road. 

In the Republic the same bright track is compared with 'the undergirders of triremes' ; but the figure is complicated by the addition of ' a straight Hght like a pillar' stretching along the axis of the universe—an idea taken up by the Manichaeans, who spoke of a 'pillar of glory' or a 'pillar of light' filled with souls in process of purification''. This pillar has no counterpart in astronomical fact or, for that matter, in astronomical theory. It would, however, be unwise to assume that it was introduced by Platon merely to facilitate the transition to his ensuing image—the ' spindle of Ananke.' Rather we may surmise that it was based upon popular belief with ritual usage behind it.

- "Zeus, A study in Ancient Religion" by Arthur Bernard Cook

Tuesday, 28 March 2017

Marcus Vitruvius Pollio - Book IX of De Architecture

"Marcus Vitruvius Pollio (born c. 80–70 BC, died after c. 15 BC), commonly known as Vitruvius or Vitruvi or Vitruvio, was a Roman author, architect, civil engineer and military engineer during the 1st century BC, known for his multi-volume work entitled De architectura. His discussion of perfect proportion in architecture and the human body, led to the famous Renaissance drawing by Da Vinci of Vitruvian Man." 


English translation by Morris Morgan (1914).  Headings are changed to reflect the chapters in the Latin versions. Images are from several 16th century Latin publications (1511, 1523, 1567).






1. The ancestors of the Greeks have appointed such great honours for the famous athletes who are victorious at the Olympian, Pythian, Isthmian, and Nemean games, that they are not only greeted with applause as they stand with palm and crown at the meeting itself, but even on returning to their several states in the triumph of victory, they ride into their cities and to their fathers' houses in four-horse chariots, and enjoy fixed revenues for life at the public expense. When I think of this, I am amazed that the same honours and even greater are not bestowed upon those authors whose boundless services are performed for all time and for all nations. This would have been a practice all the more worth establishing, because in the case of athletes it is merely their own bodily frame that is strengthened by their training, whereas in the case of authors it is the mind, and not only their own but also man's in general, by the doctrines laid down in their books for the acquiring of knowledge and the sharpening of the intellect.

2. What does it signify to mankind that Milo of Croton and other victors of his class were invincible? Nothing, save that in their lifetime they were famous among their countrymen. But the doctrines of Pythagoras, Democritus, Plato, and Aristotle, and the daily life of other learned men, spent in constant industry, yield fresh and rich fruit, not only to their own countrymen, but also to all nations. And they who from their tender years are filled with the plenteous learning which this fruit affords, attain to the highest capacity of knowledge, and can introduce into their states civilized ways, impartial justice, and laws, things without which no state can be sound. 

3. Since, therefore, these great benefits to individuals and to communities are due to the wisdom of authors, I think that not only should palms and crowns be bestowed upon them, but that they should even be granted triumphs, and judged worthy of being consecrated in the dwellings of the gods

Of their many discoveries which have been useful for the development of human life, I will cite a few examples. On reviewing these, people will admit that honours ought of necessity to be bestowed upon them.


1. First of all, among the many very useful theorems of Plato, I will cite one as demonstrated by him. Suppose there is a place or a field in the form of a square and we are required to double it. This has to be effected by means of lines correctly drawn, for it will take a kind of calculation not to be made by means of mere multiplication. The following is the demonstration. A square place ten feet long and ten feet wide gives an area of one hundred feet. Now it is required to double the square, and to make one of two hundred feet, we must ask how long will be the side of that square so as to get from this the two hundred feet corresponding to the doubling of the area. Nobody can find this by means of arithmetic. For if we take fourteen, multiplication will give one hundred and ninety-six feet; if fifteen, two hundred and twenty-five feet.

2. Therefore, since this is inexplicable by arithmetic, let a diagonal line be drawn from angle to angle of that square of ten feet in length and width, dividing it into two triangles of equal size, each fifty feet in area. Taking this diagonal line as the length, describe another square. Thus we shall have in the larger square four triangles of the same size and the same number of feet as the two of fifty feet each which were formed by the diagonal line in the smaller square. In this way Plato demonstrated the doubling by means of lines, as the figure appended below will show.


1. Then again, Pythagoras showed that a right angle can be formed without the contrivances of the artisan. Thus, the result which carpenters reach very laboriously, but scarcely to exactness, with their squares, can be demonstrated to perfection from the reasoning and methods of his teaching. If we take three rules, one three feet, the second four feet, and the third five feet in length, and join these rules together with their tips touching each other so as to make a triangular figure, they will form a right angle. Now if a square be described on the length of each one of these rules, the square on the side of three feet in length will have an area of nine feet; of four feet, sixteen; of five, twenty-five.

2. Thus the area in number of feet made up of the two squares on the sides three and four feet in length is equalled by that of the one square described on the side of five. When Pythagoras discovered this fact, he had no doubt that the Muses had guided him in the discovery, and it is said that he very gratefully offered sacrifice to them.  This theorem affords a useful means of measuring many things, and it is particularly serviceable in the building of staircases in buildings, so that the steps may be at the proper levels.

3. Suppose the height of the story, from the flooring above to the ground below, to be divided into three parts. Five of these will give the right length for the stringers of the stairway. Let four parts, each equal to one of the three composing the height between the upper story and the ground, be set off from the perpendicular, and there fix the lower ends of the stringers. In this manner the steps and the stairway itself will be properly placed. A figure of this also will be found appended below.


1. In the case of Archimedes, although he made many wonderful discoveries of diverse kinds, yet of them all, the following, which I shall relate, seems to have been the result of a boundless ingenuity. Hiero, after gaining the royal power in Syracuse, resolved, as a consequence of his successful exploits, to place in a certain temple a golden crown which he had vowed to the immortal gods. He contracted for its making at a fixed price, and weighed out a precise amount of gold to the contractor. At the appointed time the latter delivered to the king's satisfaction an exquisitely finished piece of handiwork, and it appeared that in weight the crown corresponded precisely to what the gold had weighed.

2. But afterwards a charge was made that gold had been abstracted and an equivalent weight of silver had been added in the manufacture of the crown. Hiero, thinking it an outrage that he had been tricked, and yet not knowing how to detect the theft, requested Archimedes to consider the matter. The latter, while the case was still on his mind, happened to go to the bath, and on getting into a tub observed that the more his body sank into it the more water ran out over the tub. As this pointed out the way to explain the case in question, without a moment's delay, and transported with joy, he jumped out of the tub and rushed home naked, crying with a loud voice that he had found what he was seeking; for as he ran he shouted repeatedly in Greek, "Ευρηκα, ευρηκα."

3. Taking this as the beginning of his discovery, it is said that he made two masses of the same weight as the crown, one of gold and the other of silver. After making them, he filled a large vessel with water to the very brim, and dropped the mass of silver into it. As much water ran out as was equal in bulk to that of the silver sunk in the vessel. Then, taking out the mass, he poured back the lost quantity of water, using a pint measure, until it was level with the brim as it had been before. Thus he found the weight of silver corresponding to a definite quantity of water.

4. After this experiment, he likewise dropped the mass of gold into the full vessel and, on taking it out and measuring as before, found that not so much water was lost, but a smaller quantity: namely, as much less as a mass of gold lacks in bulk compared to a mass of silver of the same weight. Finally, filling the vessel again and dropping the crown itself into the same quantity of water, he found that more water ran over for the crown than for the mass of gold of the same weight. Hence, reasoning from the fact that more water was lost in the case of the crown than in that of the mass, he detected the mixing of silver with the gold, and made the theft of the contractor perfectly clear.

5. Now let us turn our thoughts to the researches of Archytas of Tarentum and Eratosthenes of Cyrene. They made many discoveries from mathematics which are welcome to men, and so, though they deserve our thanks for other discoveries, they are particularly worthy of admiration for their ideas in that field. For example, each in a different way solved the problem enjoined upon Delos by Apollo in an oracle, the doubling of the number of cubic feet in his altars; this done, he said, the inhabitants of the island would be delivered from an offence against religion.

6. Archytas solved it by his figure of the semicylinders; Eratosthenes, by means of the instrument called the mesolabe. 

Noting all these things with the great delight which learning gives, we cannot but be stirred by these discoveries when we reflect upon the influence of them one by one. I find also much for admiration in the books of Democritus on nature, and in his commentary entitled Χειρὁκμητα, in which he made use of his ring to seal with soft wax the principles which he had himself put to the test.

7. These, then, were men whose researches are an everlasting possession, not only for the improvement of character but also for general utility. The fame of athletes, however, soon declines with their bodily powers. Neither when they are in the flower of their strength, nor afterwards with posterity, can they do for human life what is done by the researches of the learned. 

8. But although honours are not bestowed upon authors for excellence of character and teaching, yet as their minds, naturally looking up to the higher regions of the air, are raised to the sky on the steps of history, it must needs be, that not merely their doctrines, but even their appearance, should be known to posterity through time eternal. Hence, men whose souls are aroused by the delights of literature cannot but carry enshrined in their hearts the likeness of the poet Ennius, as they do those of the gods. Those who are devotedly attached to the poems of Accius seem to have before them not merely his vigorous language but even his very figure. 

9. So, too, numbers born after our time will feel as if they were discussing nature face to face with Lucretius, or the art of rhetoric with Cicero; many of our posterity will confer with Varro on the Latin language; likewise, there will be numerous scholars who, as they weigh many points with the wise among the Greeks, will feel as if they were carrying on private conversations with them. Li a word, the opinions of learned authors, though their bodily forms are absent, gain strength as time goes on, and, when taking part in councils and discussions, have greater weight than those of any living men.
10. Such, Caesar, are the authorities on whom I have depended, and applying their views and opinions I have written the present books, in the first seven treating of buildings and in the eighth of water. In this I shall set forth the rules for dialling, showing how they are found through the shadows cast by the gnomon from the sun's rays in the firmament, and on what principles these shadows lengthen and shorten. 


1. It is due to the divine intelligence and is a very great wonder to all who reflect upon it, that the shadow of a gnomon at the equinox is of one length in Athens, of another in Alexandria, of another in Rome, and not the same at Piacenza, or at other places in the world. Hence drawings for dials are very different from one another, corresponding to differences of situation. This is because the length of the shadow at the equinox is used in constructing the figure of the analemma, in accordance with which the hours are marked to conform to the situation and the shadow of the gnomon. The analemma is a basis for calculation deduced from the course of the sun, and found by observation of the shadow as it increases until the winter solstice. By means of this, through architectural principles and the employment of the compasses, we find out the operation of the sun in the universe. 

2. The word "universe" means the general assemblage of all nature, and it also means the heaven that is made up of the constellations and the courses of the stars. The heaven revolves steadily round earth and sea on the pivots at the ends of its axis. The architect at these points was the power of Nature, and she put the pivots there, to be, as it were, centres, one of them above the earth and sea at the very top of the firmament and even beyond the stars composing the Great Bear, the other on the opposite side under the earth in the regions of the south. Round these pivots (termed in Greek πόλοι) as centres, like those of a turning lathe, she formed the circles in which the heaven passes on its everlasting way. In the midst thereof, the earth and sea naturally occupy the central point.

3. It follows from this natural arrangement that the central point in the north is high above the earth, while on the south, the region below, it is beneath the earth and consequently hidden by it. Furthermore, across the middle, and obliquely inclined to the south, there is a broad circular belt composed of the twelve signs, whose stars, arranged in twelve equivalent divisions, represent each a shape which nature has depicted. And so with the firmament and the other constellations, they move round the earth and sea in glittering array, completing their orbits according to the spherical shape of the heaven.

4. They are all visible or invisible according to fixed times. While six of the signs are passing along with the heaven above the earth, the other six are moving under the earth and hidden by its shadow. But there are always six of them making their way above the earth; for, corresponding to that part of the last sign which in the course of its revolution has to sink, pass under the earth, and become concealed, an equivalent part of the sign opposite to it is obliged by the law of their common revolution to pass up and, having completed its circuit, to emerge out of the darkness into the light of the open space on the other side. This is because the rising and setting of both are subject to one and the same power and law.

5. While these signs, twelve in number and occupying each one twelfth part of the firmament, steadily revolve from east to west, the moon. Mercury, Venus, the sun, as well as Mars, Jupiter, and Saturn, differing from one another in the magnitude of their orbits as though their courses were at different points in a flight of steps, pass through those signs in just the opposite direction, from west to east in the firmament. The moon makes her circuit of the heaven in twenty-eight days plus about an hour, and with her return to the sign from which she set forth, completes a lunar month.

6. The sun takes a full month to move across the space of one sign, that is, one twelfth of the firmament. Consequently, in twelve months he traverses the spaces of the twelve signs, and, on returning to the sign from which he began, completes the period of a full year. Hence, the circuit made by the moon thirteen times in twelve months, is measured by the sun only once in the same number of months. But Mercury and Venus, their paths wreathing around the sun's rays as their centre, retrograde and delay their movements, and so, from the nature of that circuit, sometimes wait at stopping-places within the spaces of the signs.

7. This fact may best be recognized from Venus. When she is following the sun, she makes her appearance in the sky after his setting, and is then called the Evening Star, shining most brilliantly. At other times she precedes him, rising before daybreak, and is named the Morning Star. Thus Mercury and Venus sometimes delay in one sign for a good many days, and at others advance pretty rapidly into another sign. They do not spend the same number of days in every sign, but the longer they have previously delayed, the more rapidly they accomplish their journeys after passing into the next sign, and thus they complete their appointed course. Consequently, in spite of their delay in some of the signs, they nevertheless soon reach the proper place in their orbits after freeing themselves from their enforced delay.

8. Mercury, on his journey through the heavens, passes through the spaces of the signs in three hundred and sixty days, and so arrives at the sign from which he set out on his course at the beginning of his revolution. His average rate of movement is such that he has about thirty days in each sign.

9. Venus, on becoming free from the hindrance of the sun's rays, crosses the space of a sign in thirty days. Though she thus stays less than forty days in particular signs, she makes good the required amount by delaying in one sign when she comes to a pause. Therefore she completes her total revolution in heaven in four hundred and eighty-five days, and once more enters the sign from which she previously began to move.

10. Mars, after traversing the spaces of the constellations for about six hundred and eighty-three days, arrives at the point from which he had before set out at the beginning of his course, and while he passes through some of the signs more rapidly than others, he makes up the required number of days whenever he comes to a pause. Jupiter, climbing with gentler pace against the revolution of the firmament, travels through each sign in about three hundred and sixty days, and finishes in eleven years and three hundred and thirteen days, returning to the sign in which he had been twelve years before. Saturn, traversing the space of one sign in twenty-nine months plus a few days, is restored after twenty-nine years and about one hundred and sixty days to that in which he had been thirty years before. He is, as it appears, slower, because the nearer he is to the outermost part of the firmament, the greater is the orbit through which he has to pass.

11. The three that complete their circuits above the sun's course do not make progress while they are in the triangle which he has entered, but retrograde and pause until the sun has crossed from that triangle into another sign. Some hold that this takes place because, as they say, when the sun is a great distance off, the paths on which these stars wander are without light on account of that distance, and so the darkness retards and hinders them. But I do not think that this is so. The splendour of the sun is clearly to be seen, and manifest without any kind of obscurity, throughout the whole firmament, so that those very retrograde movements and pauses of the stars are visible even to us.

12. If then, at this great distance, our human vision can discern that sight, why, pray, are we to think that the divine splendour of the stars can be cast into darkness? Rather will the following way of accounting for it prove to be correct. Heat summons and attracts everything towards itself; for instance, we see the fruits of the earth growing up high under the influence of heat, and that spring water is vapourised and drawn up to the clouds at sunrise. On the same principle, the mighty influence of the sun, with his rays diverging in the form of a triangle, attracts the stars which follow him, and, as it were, curbs and restrains those that precede, not allowing them to make progress, but obliging them to retrograde towards himself until he passes out into the sign that belongs to a different triangle.

13. Perhaps the question will be raised, why the sun by his great heat causes these detentions in the fifth sign from himself rather than in the second or third, which are nearer. I will therefore set forth what seems to be the reason. His rays diverge through the firmament in straight lines as though forming an equilateral triangle, that is, to the fifth sign from the sun, no more, no less. If his rays were diffused in circuits spreading all over the firmament, instead of in straight lines diverging so as to form a triangle, they would burn up all the nearer objects. This is a fact which the Greek poet Euripides seems to have remarked; for he says that places at a greater distance from the sun are in a violent heat, and that those which are nearer he keeps temperate. Thus in the play of Phaethon, the poet writes: καἱει τἁ πὁρρω, τἁγγυθεν δ εὑκρατ ἑχει.

14. If then, fact and reason and the evidence of an ancient poet point to this explanation, I do not see why we should decide otherwise than as I have written above on this subject. Jupiter, whose orbit is between those of Mars and Saturn, traverses a longer course than Mars, and a shorter than Saturn. Likewise with the rest of these stars : the farther they are from the outermost limits of the heaven, and the nearer their orbits to the earth, the sooner they are seen to finish their courses; for those of them that have a smaller orbit often pass those that are higher, going under them.

15. For example, place seven ants on a wheel such as potters use, having made seven channels on the wheel about the centre, increasing successively in circumference; and suppose those ants obliged to make a circuit in these channels while the wheel is turned in the opposite direction. In spite of having to move in a direction contrary to that of the wheel, the ants must necessarily complete their journeys in the opposite direction, and that ant which is nearest the centre must finish its circuit sooner, while the ant that is going round at the outer edge of the disc of the wheel must, on account of the size of its circuit, be much slower in completing its course, even though it is moving just as quickly as the other. In the same way, these stars, which struggle on against the course of the firmament, are accomplishing an orbit on paths of their own; but, owing to the revolution of the heaven, they are swept back as it goes round every day.

16. The reason why some of these stars are temperate, others hot, and others cold, appears to be this: that the flame of every kind of fire rises to higher places. Consequently, the burning rays of the sun make the ether above him white hot, in the regions of the course of Mars, and so the heat of the sun makes him hot. Saturn, on the contrary, being nearest to the outermost limit of the firmament and bordering on the quarters of the heaven which are frozen, is excessively cold. Hence Jupiter, whose course is between the orbits of these two, appears to have a moderate and very temperate influence, intermediate between their cold and heat.

I have now described, as I have received them from my teacher, the belt of the twelve signs and the seven stars that work and move in the opposite direction, with the laws and numerical relations under which they pass from sign to sign, and how they complete their orbits. I shall next speak of the waxing and waning of the moon, according to the accounts of my predecessors.


1. According to the teaching of Berosus, who came from the state, or rather nation, of the Chaldees, and was the pioneer of Chaldean learning in Asia, the moon is a ball, one half luminous and the rest of a blue colour. When, in the course of her orbit, she has passed below the disc of the sun, she is attracted by his rays and great heat, and turns thither her luminous side, on account of the sympathy between light and light. Being thus summoned by the sun's disc and facing upward, her lower half, as it is not  luminous, is invisible on account of its likeness to the air. When she is perpendicular to the sun's rays, all her light is confined to her upper surface, and she is then called the new moon.

2. As she moves on, passing by to the east, the effect of the sun upon her relaxes, and the outer edge of the luminous side sheds its light upon the earth in an exceedingly thin line. This is called the second day of the moon. Day by day she is further relieved and turns, and thus are numbered the third, fourth, and following days. On the seventh day, the sun being in the west and the moon in the middle of the firmament between the east and west, she is half the extent of the firmament distant from the sun, and therefore half of the luminous side is turned toward the earth. But when the sun and moon are separated by the entire extent of the firmament, and the moon is in the east with the sun over against her in the west, she is completely relieved by her still greater distance from his rays, and so, on the fourteenth day, she is at the full, and her entire disc emits its light. On the succeeding days, up to the end of the month, she wanes daily as she turns in her course, being recalled by the sun until she comes under his disc and rays, thus completing the count of the days of the month.

3. But Aristarchus of Samos, a mathematician of great powers, has left a different explanation in his teaching on this subject, as I shall now set forth. It is no secret that the moon has no light of her own, but is, as it were, a mirror, receiving brightness from the influence of the sun. Of all the seven stars, the moon traverses the shortest orbit, and her course is nearest to the earth. Hence in every month, on the day before she gets past the sun, she is under his disc and rays, and is consequently hidden and invisible. When she is thus in conjunction with the sun, she is called the new moon. On the next day, reckoned as her second, she gets past the sun and shows the thin edge of her sphere. Three days away from the sun, she waxes and grows brighter. Removing further every day till she reaches the seventh, when her distance from the sun at his setting is about one half the extent of the firmament, one half of her is luminous; that is, the half which faces toward the sun is lighted up by him.

4. On the fourteenth day, being diametrically across the whole extent of the firmament from the sun, she is at her full and rises when the sun is setting. For, as she takes her place over against him and distant the whole extent of the firmament, she thus receives the light from the sun throughout her entire orb. On the seventeenth day, at sunrise, she is inclining to the west. On the twenty-second day, after sunrise, the moon is about mid-heaven; hence, the side exposed to the sun is bright and the rest dark. Continuing thus her daily course, she passes under the rays of the sun on about the twenty-eighth day, and so completes the account of the month.

I will next explain how the sun, passing through a different sign each month, causes the days and hours to increase and diminish in length.


1. The sun, after entering the sign Aries and passing through one eighth of it, determines the vernal equinox. On reaching the tail of Taurus and the constellation of the Pleiades, from which the front half of Taurus projects, he advances into a space greater than half the firmament, moving toward the north. From Taurus he enters Gemini at the time of the rising of the Pleiades, and, getting higher above the earth, he increases the length of the days. Next, coming from Gemini into Cancer, which occupies the shortest space in heaven, and after traversing one eighth of it, he determines the summer solstice. Continuing on, he reaches the head and breast of Leo, portions which are reckoned as belonging to Cancer.

2. After leaving the breast of Leo and the boundaries of Cancer, the sun, traversing the rest of Leo, makes the days shorter, diminishing the size of his circuit, and returning to the same course that he had in Gemini. Next, crossing from Leo into Virgo, and advancing as far as the bosom of her garment, he still further shortens his circuit, making his course equal to what it was in Taurus. Advancing from Virgo by way of the bosom of her garment, which forms the first part of Libra, he determines the autumn equinox at the end of one eighth of Libra. Here his course is equal to what his circuit was in the sign Aries.

3. When the sun has entered Scorpio, at the time of the setting of the Pleiades, he begins to make the days shorter as he advances toward the south. From Scorpio he enters Sagittarius and, on reaching the thighs, his daily course is still further diminished. From the thighs of Sagittarius, which are reckoned as part of Capricornus, he reaches the end of the first eighth of the latter, where his course in heaven is shortest. Consequently, this season, from the shortness of the day, is called bruma or dies brumales. Crossing from Capricornus into Aquarius, he causes the days to increase to the length which they had when he was in Sagittarius. From Aquarius he enters Pisces at the time when Favonius begins to blow, and here his course is the same as in Scorpio. Li this way the sun passes round through the signs, lengthening or shortening the days and hours at definite seasons.

I shall next speak of the other constellations formed by arrangements of stars, and lying to the right and left of the belt of the signs, in the southern and northern portions of the firmament.


1. The Great Bear, called in Greek ἁρκτος or ἑλἱκη, has her Warden behind her. Near him is the Virgin, on whose right shoulder rests a very bright star which we call Harbinger of the Vintage, and the Greeks,  προτρυγητἡς. But Spica in that constellation is brighter. Opposite there is another star, coloured, between the knees of the Bear Warden, dedicated there under the name of Arcturus.

2. Opposite the head of the Bear, at an angle with the feet of the Twins, is the Charioteer, standing on the tip of the horn of the Bull; hence, one and the same star is found in the tip of the left horn of the Bull and in the right foot of the Charioteer. Supported on the hand of the Charioteer are the Kids, with the She-Goat at his left shoulder. Above the Bull and the Ram is Perseus, having at his right .with the Pleiades moving beneath, and at his left the head of the Ram. His right hand rests on the likeness of Cassiopea, and with his left he holds the Gorgon's head by its top over the Ram, laying it at the feet of Andromeda.

3. Above Andromeda are the Fishes, one above her belly and the other above the backbone of the Horse. A very bright star terminates both the belly of the Horse and the head of Andromeda. Andromeda's right hand rests above the likeness of Cassiopea, and her left above the Northern Fish. The Waterman's head is above that of the Horse. The Horse's hoofs lie close to the Waterman's knees. Cassiopea is set apart in the midst. High above the He-Goat are the Eagle and the Dolphin, and near them is the Arrow. Farther on is the Bird, whose right wing grazes the head and sceptre of Cepheus, with its left resting over Cassiopea. Under the tail of the Bird lie the feet of the Horse.

4. Above the Archer, Scorpion, and Balance, is the Serpent, reaching to the Crown with the end of its snout. Next, the Serpent-holder grasps the Serpent about the middle in his hands, and with his left foot treads squarely on the foreparts of the Scorpion. A little way from the head of the Serpent-holder is the head of the so-called Kneeler. Their heads are the more readily to be distinguished as the stars which compose them are by no means dim.

5. The foot of the Kneeler rests on the temple of that Serpent which is entwined between the She-Bears (called Septentriones). The little Dolphin moves in front of the Horse. Opposite the bill of the Bird is the Lyre. The Crown is arranged between the shoulders of the Warden and the Kneeler. In the northern circle are the two She-Bears with their shoulder-blades confronting and their breasts turned away from one another. The Greeks call the Lesser Bear κυνὁσουρα, and the Greater ἑλικη. Their heads face different ways, and their tails are shaped so that each is in front of the head of the other Bear; for the tails of both stick up over them.

6. The Serpent is said to lie stretched out between their tails, and in it there is a star, called Polus, shining near the head of the Greater Bear. At the nearest point, the Serpent winds its head round, but is also flung in a fold round the head of the Lesser Bear, and stretches out close to her feet. Here it twists back, making another fold, and, lifting itself up, bends its snout and right temple from the head of the Lesser Bear round towards the Greater. Above the tail of the Lesser Bear are the feet of Cepheus, and at this point, at the very top, are stars forming an equilateral triangle. There are a good many stars common to the Lesser Bear and to Cepheus.

I have now mentioned the constellations which are arranged in the heaven to the right of the east, between the belt of the signs and the north. I shall next describe those that Nature has distributed to the left of the east and in the southern regions. 


1. First, under the He-Goat lies the Southern Fish, facing towards the tail of the Whale. The Altar is under the Scorpion's sting. The fore parts of the Centaur are next to the Balance and the Scorpion, and he holds in his hands the figure which astronomers call the Beast. Beneath the Virgin, Lion, and Crab is the twisted girdle formed by the Snake, extending over a whole line of stars, his snout raised near the Crab, supporting the Bowl with the middle of his body near the Lion, and bringing his tail, on which is the Raven, under and near the hand of the Virgin. The region above his shoulders is equally bright.

2. Beneath the Snake's belly, at the tail, lies the Centaur. Near the Bowl and the Lion is the ship named Argo. Her bow is invisible, but her mast and the parts about the helm are in plain sight, the stern of the vessel joining the Dog at the tip of his tail. The Little Dog follows the Twins, and is opposite the Snake's head. The Greater Dog follows the Lesser. Orion lies aslant, under the Bull's hoof; in his left hand grasping his club, and raising the other toward the Twins.

3. At his feet is the Dog, following a little behind the Hare. The Whale lies under the Ram and the Fishes, and from his mane there is a slight sprinkling of stars, called in Greek ἁρπεδὁναι, regularly disposed towards each of the Fishes. This ligature by which they hang is carried a great way inwards, but reaches out to the top of the mane of the Whale. The River, formed of stars, flows from a source at the left foot of Orion. But the Water, said to pour from the Waterman, flows between the head of the Southern Fish and the tail of the Whale.

4. These constellations, whose outlines and shapes in the heavens were designed by Nature and the divine intelligence, I have described according to the view of the natural philosopher Democritus, but only those whose risings and settings we can observe and see with our own eyes. Just as the Bears turn round the pivot of the axis without ever setting or sinking under the earth, there are likewise stars that keep turning round the southern pivot, which on account of the inclination of the firmament lies always under the earth, and, being hidden there, they never rise and emerge above the earth. Consequently, the figures which they form are unknown to us on account of the interposition of the earth. The star Canopus proves this. It is unknown to our vicinity; but we have reports of it from merchants who have been to the most distant part of Egypt, and to regions bordering on the uttermost boundaries of the earth.


1. I HAVE shown how the firmament, and the twelve signs with the constellations arranged to the north and south of them, fly round the earth, so that the matter may be clearly understood. For it is from this revolution of the firmament, from the course of the sun through the signs in the opposite direction, and from the shadows cast by equinoctial gnomons, that we find the figure of the analemma.

2. As for the branch of astronomy which concerns the infiuences of the twelve signs, the five stars, the sun, and the moon upon human life, we must leave all this to the calculations of the Chaldeans, to whom belongs the art of casting nativities, which enables them to declare the past and the future by means of calculations based on the stars. These discoveries have been transmitted by the men of genius and great acuteness who sprang directly from the nation of the Chaldeans; first of all, by Berosus, who settled in the island state of Cos, and there opened a school. Afterwards Antipater pursued the subject; then there was Archinapolus, who also left rules for casting nativities, based not on the moment of birth but on that of conception.

3. When we come to natural philosophy, however, Thales of Miletus, Anaxagoras of Clazomenae, Pythagoras of Samos,Xenophanes of Colophon, and Democritus of Abdera have in various ways investigated and left us the laws and the working of the laws by which nature governs it. In the track of their discoveries, Eudoxus, Euctemon, Callippus, Meto, Philippus, Hipparchus, Aratus, and others discovered the risings and settings of the constellations, as well as weather prognostications from astronomy through the study of the calendars, and this study they set forth and left to posterity. Their learning deserves the admiration of mankind; for they were so solicitous as even to be able to predict, long beforehand, with divining mind, the signs of the weather which was to follow in the future. On this subject, therefore, reference must be made to their labours and investigations. 


1. In distinction from the subjects first mentioned, we must ourselves explain the principles which govern the shortening and lengthening of the day. When the sun is at the equinoxes, that is, passing through Aries or Libra, he makes the gnomon cast a shadow equal to eight ninths of its own length, in the latitude of Rome. In Athens, the shadow is equal to three fourths of the length of the gnomon; at Rhodes to five sevenths; at Tarentum, to nine elevenths; at Alexandria, to three fifths; and so at other places it is found that the shadows of equinoctial gnomons are naturally different from one another.

2. Hence, wherever a sundial is to be constructed, we must take the equinoctial shadow of the place. If it is found to be, as in Rome, equal to eight ninths of the gnomon, let a line be drawn on a plane surface, and in the middle thereof erect a perpendicular, plumb to the line, which perpendicular is called the gnomon. Then, from the line in the plane, let the line of the gnomon be divided off by the compasses into nine parts, and take the point designating the ninth part as a centre, to be marked by the letter A. Then, opening the compasses from that centre to the line in the plane at the point B, describe a circle. This circle is called the meridian. 

3. Then, of the nine parts between the plane and the centre on the gnomon, take eight, and mark them off on the line in the plane to the point C. This will be the equinoctial shadow of the gnomon. From that point, marked by C, let a line be drawn through the centre at the point A, and this will represent a ray of the sun at the equinox. Then, extending the compasses from the centre to the line in the plane, mark off the equidistant points E on the left and I on the right, on the two sides of the circumference, and let a line be drawn through the centre, dividing the circle into two equal semicircles. This line is called by mathematicians the horizon.

4. Then, take a fifteenth part of the entire circumference, and, placing the centre of the compasses on the circumference at the point where the equinoctial ray cuts it at the letter F, mark off the points G and H on the right and left. Then lines must be drawn from these (and the centre) to the line of the plane at the points T and R, and thus, one will represent the ray of the sun in winter, and the other the ray in summer. Opposite E will be the point I, where the line drawn through the centre at the point A cuts the circumference; opposite G and H will be the points L and K; and opposite C, F, and A will be the point N.

5. Then, diameters are to be drawn from G to L and from H to K. The upper will denote the summer and the lower the winter portion. These diameters are to be divided equally in the middle at the points M and O, and those centres marked; then, through these marks and the centre A, draw a line extending to the two sides of the circumference at the points P and Q. This will be a line perpendicular to the equinoctial ray, and it is called in mathematical figures the axis. From these same centres open the compasses to the ends of the diameters, and describe semicircles, one of which will be for summer and the other for winter.

6. Then, at the points at which the parallel lines cut the line called the horizon, the letter S is to be on the right and the letter V on the left, and from the extremity of the semicircle, at the point G, draw a line parallel to the axis, extending to the left hand semicircle at the point H. This parallel line is called the Logotomus. Then, centre the compasses at the point where the equinoctial ray cuts that line, at the letter D, and open them to the point where the summer ray cuts the circumference at the letter H. From the equinoctial centre, with a radius extending to the summer ray, describe the circumference of the circle of the months, which is called Menaeus. Thus we shall have the figure of the analemma

7. This having been drawn and completed, the scheme of hours is next to be drawn on the baseplates from the analemma, according to the winter lines, or those of summer, or the equinoxes, or the months, and thus many different kinds of dials may be laid down and drawn by this ingenious method. But the result of all these shapes and designs is in one respect the same: namely, the days of the equinoxes and of the winter and summer solstices are always divided into twelve equal parts. Omitting details, therefore, — not for fear of the trouble, but lest I should prove tiresome by writing too much,—I will state by whom the different classes and designs of dials have been invented. For I cannot invent new kinds myself at this late day, nor do I think that I ought to display the inventions of others as my own. Hence, I will mention those that have come down to us, and by whom they were invented.


1. The semicircular form, hollowed out of a square block, and cut under to correspond to the polar altitude, is said to have been invented by Berosus the Chaldean; the Scaphe or Hemisphere, by Aristarchus of Samos, as well as the disc on a plane surface; the Arachne, by the astronomer Eudoxus or, as some say, by Apollonius; the Plinthium or Lacunar, like the one placed in the Circus Flaminius, by Scopinas of Syracuse the προς τἁ ἱστοροὑμενα, by Parmenio; the προς παν κλιμα, by Theodosius and Andreas; the Pelecinum, by Patrocles; the Cone, by Dionysodorus; the Quiver, by Apollonius. The men whose names are written above, as well as many others, have invented and left us other kinds: as, for instance, the Conarachne, the Conical Plinthium, and the Antiborean. Many have also left us written directions for making dials of these kinds for travellers, which can be hung up. Whoever wishes to find their baseplates, can easily do so from the books of these writers, provided only he understands the figure of the analemma.

2. Methods of making water clocks have been investigated by the same writers, and first of all by Ctesibius the Alexandrian, who also discovered the natural pressure of the air and pneumatic principles. It is worthwhile for students to know how these discoveries came about. Ctesibius, born at Alexandria, was the son of a barber. Preeminent for natural ability and great industry, he is said to have amused himself with ingenious devices. For example, wishing to hang a mirror in his father's shop in such a way that, on being lowered and raised again, its weight should be raised by means of a concealed cord, he employed the following mechanical contrivance.

3. Under the roof-beam he fixed a wooden channel in which he arranged a block of pulleys. He carried the cord along the channel to the comer, where he set up some small piping. Into this a leaden ball, attached to the cord, was made to descend. As the weight fell into the narrow limits of the pipe, it naturally compressed the enclosed air, and, as its fall was rapid, it forced the mass of compressed air through the outlet into the open air, thus producing a distinct sound by the concussion.

4. Hence, Ctesibius, observing that sounds and tones were produced by the contact between the free; air and that which was forced from the pipe, made use of this principle in the construction of the first water organs. He also devised methods of raising water, automatic contrivances, and amusing things of many kinds, including among them the construction of water clocks. He began by making an orifice in a piece of gold, or by perforating a gem, because these substances are not worn by the action of water, and do not collect dirt so as to get stopped up.

 5. A regular flow of water through the orifice raises an inverted bowl, called by mechanicians the "cork" or "drum." To this are attached a rack and a revolving drum, both fitted with teeth at regular intervals. These teeth, acting upon one another, induce a measured revolution and movement. Other racks and other drums, similarly toothed and subject to the same motion, give rise by their revolution to various kinds of motions, by which figures are moved, cones revolve, pebbles or eggs fall, trumpets sound, and other incidental effects take place.

6. The hours are marked in these clocks on a column or a pilaster, and a figure emerging from the bottom points to them with a rod throughout the whole day. Their decrease or increase in length with the different days and months, must be adjusted by inserting or withdrawing wedges. The shutoffs for regulating the water are constructed as follows. Two cones are made, one solid and the other hollow, turned on a lathe so that one will go into the other and fit it perfectly. A rod is used to loosen or to bring them together, thus causing the water to flow rapidly or slowly into the vessels. According to these rules, and by this mechanism, water clocks may be constructed for use in winter.

7. But if it proves that the shortening or lengthening of the day is not in agreement with the insertion and removal of the wedges, because the wedges may very often cause errors, the following arrangement will have to be made. Let the hours be marked off transversely on the column from the analemma, and let the lines of the months also be marked upon the column. Then let the column be made to revolve, in such a way that, as it turns continuously towards the figure and the rod with which the emerging figure points to the hours, it may make the hours short or long according to the respective months.

8. There is also another kind of winter dial, called the Anaphoric and constructed in the following way. The hours, indicated by bronze rods in accordance with the figure of the analemma, radiate from a centre on the face. Circles are described upon it, marking the limits of the months. Behind these rods there is a drum, on which is drawn and painted the firmament with the circle of the signs. In drawing the figures of the twelve celestial signs, one is represented larger and the next smaller, proceeding from the centre. Into the back of the drum, in the middle, a revolving axis is inserted, and round that axis is wound a flexible bronze chain, at one end of which hangs the "cork" which is raised by the water, and at the other a counterpoise of sand, equal in weight to the "cork."

9. Hence, the sand sinks as the "cork" is raised by the water, and in staking turns the axis, and the axis the drum. The revolution of this drum causes sometimes a larger and sometimes a smaller portion of the circle of the signs to indicate, during the revolutions, the proper length of the hours corresponding to their seasons. For in every one of the signs there are as many holes as the corresponding month has days, and a boss, which seems to be holding the representation of the sun on a dial, designates the spaces for the hours. This, as it is carried from hole to hole, completes the circuit of a full month.

10. Hence, just as the sun during his passage through the constellations makes the days and hours longer or shorter, so the boss on a dial, moving from point to point in a direction contrary to that of the revolution of the drum in the middle, is carried day by day sometimes over wider and sometimes over narrower spaces, giving a representation of the hours and days within the limits of each month.

To manage the water so that it may flow regularly, we must proceed as follows.

11. Inside, behind the face of the dial, place a reservoir, and let the water run down into it through a pipe, and let it have a hole at the bottom. Fastened to it is a bronze drum with an opening through which the water flows into it from the reservoir. Enclosed in this drum there is a smaller one, the two being perfectly jointed together by tenon and socket, in such a way that the smaller drum revolves closely but easily in the larger, like a stopcock.

12. On the lip of the larger drum there are three hundred and sixty-five points, marked off at equal intervals. The rim of the smaller one has a tongue fixed on its circumference, with the tip directed towards those points; and also in this rim is a small opening, through which water runs into the drum and keeps the works going. The figures of the celestial signs being on the lip of the larger drum, and this drum being motionless, let the sign Cancer be drawn at the top, with Capricornus perpendicular to it at the bottom. Libra at the spectator's right, Aries at his left, and let the other signs be given places between them as they are seen in the heavens. 

 13. Hence, when the sun is in Capricornus, the tongue on the rim touches every day one of the points in Capricornus on the lip of the larger drum, and is perpendicular to the strong pressure of the running water. So the water is quickly driven through the opening in the rim to the inside of the vessel, which, receiving it and soon becoming full, shortens and diminishes the length of the days and hours. But when, owing to the daily revolution of the smaller drum, its tongue reaches the points in Aquarius, the opening will no longer be perpendicular, and the water must give up its vigorous flow and run in a slower stream. Thus, the less the velocity with which the vessel receives the water, the more the length of the days is increased.

14. Then the opening in the rim passes from point to point in Aquarius and Pisces, as though going upstairs, and when it reaches the end of the first eighth of Aries, the fall of the water is of medium strength, indicating the equinoctial hours. From Aries the opening passes, with the revolution of the drum, through Taurus and Gemini to the highest point at the end of the first eighth of Cancer, and when it reaches that point, the power diminishes, and hence, with the slower flow, its delay lengthens the days in the sign Cancer, producing the hours of the summer solstice. From Cancer it begins to decline, and during its return it passes through Leo and Virgo to the points at the end of the first eighth of Libra, gradually shortening and diminishing the length of the hours, until it comes to the points in Libra, where it makes the hours equinoctial once more.

15. Finally, the opening comes down more rapidly through Scorpio and Sagittarius, and on its return from its revolution to the end of the first eighth of Capricornus, the velocity of the stream renews once more the short hours of the winter solstice. 

The rules and forms of construction employed in designing dials have now been described as well as I could. It remains to give an account of machines and their principles. In order to make my treatise on architecture complete, I will begin to write on this subject in the following book.