Quaestiones Convivales

After Tyndares, Florus, a companion of his, who always jocosely pretended to be his admirer, said thus: Sir, we are obliged to you for making your discourse not proper to yourself, but common to us all; for you have made it possible to refute it by demonstrating that geometry is not necessary to the Gods, but to us. Now the Deity doth not stand in need of science, as an instrument to withdraw his intellect from things engendered and to turn it to the real things; for these are all in him, with him, and about him. But pray consider whether Plato, though you do not apprehend it, doth not intimate something that is proper and peculiar to you, mixing Lycurgus with Socrates, as much as Dicaearchus thought he did Pythagoras. For Lycurgus, I suppose you know, banished out of Sparta all arithmetical proportion, as being democratical and favoring the crowd; -but introduced the geometrical, as

agreeable to an oligarchy and kingly government that rules by law; for the former gives an equal share to every one according to number, but the other gives according to the proportion of the deserts. It doth not huddle all things together, but in it there is a fair discretion of good and bad, every one having what is fit for him, not by lot or weight, but according as he is virtuous or vicious. The same proportion, my dear Tyndares, God introduceth, which is called δίκη and νέμεσις, and which teacheth us to account that which is just equal, and not that which is equal just. For that equality which many affect, being often the greatest injustice, God, as much as possible, takes away; and useth that proportion which respects every man’s deserts, geometrically defining it according to law and reason.

This exposition we applauded; and Tyndares, saying he envied him, desired Autobulus to engage Florus and confute his discourse. That he refused to do, but produced another opinion of his own. Geometry, said he, considers nothing else but the accidents and properties of the extremities or limits of bodies; neither did God make the world any other way than by terminating matter, which was infinite before. Not that matter was really infinite as to either magnitude or multitude; but the ancients used to call that infinite which by reason of its confusion and disorder is undetermined and unconfined. Now the terms of every thing that is formed or figured are the form and figure of that thing, without which the thing would be formless and unfigured. Now numbers and proportions being applied to matter, it is circumscribed and as it were bound up by lines, and through lines by surfaces and profundities; and so were settled the first species and differences of bodies, as foundations from which to raise the four elements, fire, air, water, and earth. For it was impossible that, out of an unsteady and confused matter, the

equality of the sides, the likeness of the angles, and the exact proportion of octahedrons, icosahedrons, pyramids, and cubes should be deduced, unless by some power that terminated and shaped every particle of matter. Therefore, terms being fixed to that which was undetermined or infinite before, the whole became and still continues agreeable in all parts, and excellently terminated and mixed; the matter indeed always affecting an indeterminate state, and flying all geometrical confinement, but proportion terminating and circumscribing it, and dividing it into several differences and forms, out of which all things that arise are generated and subsist.

When he had said this, he desired me to contribute something to the discourse; and I applauded their conceits as their own devices, and very probable. But lest you despise yourselves (I continued) and altogether look for some external explication, attend to an exposition upon this sentence, which your masters very much approve. Amongst the most geometrical theorems, or rather problems, this is one: Two figures being given, to construct a third, which shall be equal to one and similar to the other. And it is reported that Pythagoras, upon the discovery of this problem, offered a sacrifice to the Gods; for this is a much more exquisite theorem than that which lays down, that the square of the hypothenuse in a right-angled triangle is equal to the squares of the two sides. Right, said Diogenianus, but what is this to the present question? You will easily understand, I replied, if you call to mind how Timaeus divides that which gave the world its beginning into three parts. One of which is justly called God, the other matter, and the third form. That which is called matter is the most confused subject, the form the most beautiful pattern, and God the best of causes. Now this cause, as far as possible, would leave nothing infinite and indeterminate, but adorn Nature with number, measure,

and proportion, making one thing of all the subjects together, equal to the matter, and similar to the form. Therefore proposing to himself this problem, he made and still makes a third, and always preserves it equal to the matter, and like the form; and that is the world. And this world, being in continual changes and alterations because of the natural necessity of body, is helped and preserved by the father and maker of all things, who by proportion terminates the substance according to the pattern. Wherefore in its measure and circuit this universal world is more beautiful than that which is merely similar to it....

WHEN we supped with Ammonius at Athens, who was then the third time captain of the city-bands, there was a great noise about the house, some without doors calling, Captain! Captain! After he had sent his officers to quiet the tumult, and had dispersed the crowd, we began to enquire what was the reason that those that are within doors hear those that are without, but those that are without cannot hear those that are within as well. And Ammonius said, that Aristotle had given a reason for that already; for the sound of those within, being carried without into a large tract of air, grows weaker presently and is lost; but that which comes in from without is not subject to the like casualty, but is kept close, and is therefore more easy to be heard. But that seemed a more difficult question, Why sounds seem greater in the night than in the day, and yet altogether as clear. For my own part (continued he) I think Providence hath very wisely contrived that our hearing should be quickest when our sight can do us very little or no service; for the air of the blind

and solitary Night, as Empedocles calls it, being dark, supplies in the ears that defect of sense which it makes in the eyes. But since of natural effects we should endeavor to find the causes, and to discover what are the material and mechanical principles of things is the proper task of a natural philosopher, who shall first assist us with a rational account hereof?

Boethus began, and said: When I was a novice in letters, I then made use of geometrical postulates, and assumed as undoubted truths some undemonstrated suppositions; and now I shall make use of some propositions which Epicurus hath demonstrated already. Bodies move in a vacuum, and there are a great many spaces interspersed among the atoms of the air. Now when the air being rarefied is more extended, so as to fill the empty space, there are but few vacuities scattered and interspersed among the particles of matter; but when the atoms of air are condensed and laid close together, they leave a vast empty space, convenient and sufficient for other bodies to pass through. Now the coldness of the night makes such a constipation. Heat opens and separates the parts of condensed bodies. Therefore bodies that boil, grow soft, or melt, require a greater space than before; but on the contrary, the parts of the body that are condensed or freeze are contracted closer to one another, and leave those vessels and places from which they retired partly empty. Now the voice, meeting and striking against a great many bodies in its way, is either altogether lost or scattered, and very much and very frequently hindered in its passage; but when it hath a plain and smooth way through an empty space, and comes to the ear uninterrupted, the passage is so sudden, that it preserves its articulate distinctness, as well as the words it carries. You may observe that empty vessels, when knocked, answer presently, send out a noise to a great distance, and oftentimes the sound

whirled round in the hollow breaks out with a considerable force; whilst a vessel that is filled either with a liquid or a solid body will not answer to a stroke, because the sound hath no room or passage to come through. And among solid bodies themselves, gold and stone, because they want pores, can hardly be made to sound; and when a noise is made by a stroke upon them, it is very flat, and presently lost. But brass is sounding, it being a porous, rare, and light metal, not consisting of parts closely compacted, but being mixed with a yielding and uncompacted substance, which gives free passage to other motions, and kindly receiving the sound sends it forward; till some touching the instrument do, as it were, seize on it in the way, and stop the hollow; for then, by reason of the hindering force, it stops and goes no farther. And this, in my opinion, is the reason why the night is more sonorous, and the day less; since in the day, the heat rarefying the air makes the empty spaces between the particles to be very little. But, pray, let none argue against the suppositions I first assumed.