The system is evolved in a series of theorems in severely demonstrative order out of the definitions and axioms which we have translated. The existence of substance, he then concludes, is involved in the nature of the thing itself. Substance exists. It does and must.
The God of the heavens and earth has hidden Himself from us since we gave ourselves up to the worship of the false divinities of Phoenicia. No longer can we admire the cosmos; for the cosmos lies beyond a long perspective of theorems and propositions that cross our eyes, like countless bees, from the alcoves of philosophies and sciences.
For these, which are true of all phenomena, or, at least, without distinction of origin, have no connection with laws of Causation, whereas all other theorems asserting resemblance have, being true only of special phenomena originating in a certain way, and the resemblances between which phenomena must be derived from, or be identical with, the laws of their causes.
Assuming that the periodic time of each planet must be equal to that of the portion of the solar atmosphere of which it was formed at the era when it was thrown off, and combining the theorems of Huygens on the measure of centrifugal forces with Newton's law of gravitation, he establishes a simple equation between the time of the rotation of each zone or section of the solar atmosphere, and the distance of the corresponding planets.
"If there is a viva voce, be sure and speak up and give your answers as though you were sure of them. They may be wrong, but on the other hand they may be right. Anyway, the one thing the examiners will not thole is a body that dithers. "Take a last keek at that Proposition they may call them Theorems, though about the Square on the Hypotenuse. It hasn't been set for four years.
Do you also show not your theorems to the uninstructed, but show the acts which come from their digestion. When at a small cost you are supplied with everything for the body, do not be proud of this; nor, if you drink water, say on every occasion, I drink water. But consider first how much more frugal the poor are than we, and how much more enduring of labor.
She craves, if not the gaudy furbelows borrowed from rhetoric's wardrobe, at least a vine leaf. The geometers alone have the right to refuse her that modest garment; in theorems, plainness suffices. The others, especially the naturalist, are in duty bound to drape a gauze tunic more or less elegantly around her waist. Suppose I say: 'Baptiste, give me my slippers.
Grace Harlowe had crammed as assiduously as the rest, for a day or two. She was particularly shaky on her geometry. She went over her theorems until she came to triangles, then she threw the book down in disgust. "What's the use of cramming?" she said to herself.
And did not those very theorems, when carried out to their strict and completing results by the close reasonings of Hume, resolve my own living identity, the one conscious indivisible me, into a bundle of memories derived from the senses which had bubbled and duped my experience, and reduce into a phantom, as spectral as that of the Luminous Shadow, the whole solid frame of creation?
These weighty propositions are, all and singular, true; I can not gainsay them; and truth ever was and will be commendable. But in these three theorems I believe we have exhausted the stock of knowledge as yet accumulated by man on the subject of opium.