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Updated: June 19, 2025


And since in any bulk of matter our thoughts can never arrive at the utmost divisibility, therefore there is an apparent infinity to us also in that, which has the infinity also of number; but with this difference, that, in the former considerations of the infinity of space and duration, we only use addition of numbers; whereas this is like the division of an unit into its fractions, wherein the mind also can proceed in infinitum, as well as in the former additions; it being indeed but the addition still of new numbers: though in the addition of the one, we can have no more the POSITIVE idea of a space infinitely great, than, in the division of the other, we can have the positive idea of a body infinitely little; our idea of infinity being, as I may say, a growing or fugitive idea, still in a boundless progression, that can stop nowhere.

In the first place, they have so well got that German lesson! The supply of shell and gun is so abundant, also of fresh troops in reserve thanks to "Papa" Joffre's frugality with human lives; the first, second, third lines on ad infinitum to Paris are so carefully fortified, so alertly held against any "drive"! And the troops are so fit!

When the interest became due, it would, as likely as not, be paid out of the capital just subscribed for the King Solomon's Mines Exploitation Association, the little deficiency in the latter being replaced in its turn, when absolutely necessary and not a moment before, by the transfer of some portion of the capital just raised for yet another company. And so on, ad infinitum.

What she thought she understood of his socialistic scheme was that every poor girl like herself was going to have her limousine and her maid and a couple of footmen. She did not pause to figure out how complicated that would be, since the maid would have to have her maid, and that maid hers, and so on, ad infinitum, ad absurdum.

But can a man of sound sense listen for one moment to such a doctrine? Either predestination admits the existence of free-will, or it rejects it. If it admits it, what kind of predetermined result can that be which a simple resolution, a step, a word, may alter or modify ad infinitum?

I cannot say, "The regress from a given perception to everything limited either in space or time, proceeds in infinitum," for this presupposes an infinite cosmical quantity; neither can I say, "It is finite," for an absolute limit is likewise impossible in experience.

Falkirk. 'Perfectly simple, sir. Of two roads I should always take the most difficult, and so on ad infinitum. 'Perfectly simple, indeed, said Mr. Falkirk. 'Yet it might lead to a complication. I'm afraid it would prove a Western line of travel, my dear end in a squirrel track, and run up a tree. 'What a lookout we shall have! said Wych Hazel. 'But about the dress, Mr.

He there says, that the virtuousness of every virtuous act or choice depends upon its own nature, and not upon its origin or cause. If we must refer every virtuous act, says he, to something in us that is virtuous as its antecedent, we must likewise refer that antecedent to some other virtuous origin or cause; and so on ad infinitum.

So also the lines that are its sides, of what length it pleases, which joining again to other lines, of different lengths, and at different angles, till it has wholly enclosed any space, it is evident that it can multiply figures, both in their shape and capacity, IN INFINITUM; all which are but so many different simple modes of space.

If I ask why you believe any particular matter of fact, which you relate, you must tell me some reason; and this reason will be some other fact, connected with it. But as you cannot proceed after this manner, in infinitum, you must at last terminate in some fact, which is present to your memory or senses; or must allow that your belief is entirely without foundation.

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