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Now, whenever he perceives, believes, or supposes such a kind of divisibility to agree or disagree to his idea of that line, he, as it were, joins or separates those two ideas, viz. the idea of that line, and the idea of that kind of divisibility; and so makes a mental proposition, which is true or false, according as such a kind of divisibility, a divisibility into such ALIQUOT parts, does really agree to that line or no.
And as respects aliquot parts, four shares among three persons are as incommensurable as a guinea is against any attempt at giving change in half-crowns. However, this was all the preservation that the horse found. No saltpetre or sugar could be had: but the frost was antiseptic. And the horse was preserved in as useful a sense as ever apricots were preserved or strawberries.
The corporation may be immortal, and its powers, as well as its acquisitions, increase forever. Men are liable with all their estates for their contracts and obligations. Men in corporations are only liable to the amount of their aliquot share of stock, or often not at all. Corporations may dissolve, and be reborn, divide, and reunite, swallow up other corporations or often other persons.
Nor must the child pass abruptly from measurement to judgment; he must continue to compare the parts when he could not compare the whole; he must substitute his estimated aliquot parts for exact aliquot parts, and instead of always applying the measure by hand he must get used to applying it by eye alone.
This bold act gave the instrument many sympathetic strings free to vibrate from the bridge when the rest of the instrument was played, each string, according to its length, being an aliquot division of a lower string. This gave the instrument a certain brightness or life throughout, an advantage which has secured its universal adoption.
Yet the child ought not to pass too soon from measuring to estimating. It will be better for him, after comparing by parts what he cannot compare as wholes, finally to substitute for measured aliquot parts others, obtained by the eye alone. He should train himself in this manner of measuring instead of always measuring with the hand.
As this is too large a quantity for convenient titration, an aliquot portion of the solution is measured off, representing one fifth of the entire quantity. This is accomplished as follows: Weigh out on an analytical balance two samples of soda ash of about 5 grams each into beakers of about 500 cc. capacity.
But the offended philosopher had departed, and being well wound up could not, any more than any other member of the academies, cease from spouting; so that King Philip was intolerably aggravated to hear him as he waddled down the Palace stairs still declaiming in a loud tone: "And, sixteenthly, the thruppenny bit has about it this noble quality, that it represents an aliquot part of that sum which is paid to me daily from the Royal Treasury in silver, a metal upon which we have always insisted.
Now, allowing the tax to be an aliquot part one-fourth for example of the income derived from each piece of property, it is clear on the one hand that the proprietor would not, in order to lighten his share of the tax, underestimate the value of his property; since, house and farm-rents being fixed by the value of the capital, and the latter being measured by the tax, to depreciate his real estate would be to reduce his revenue.
Rursus cum plana aquæ Superficies non nisi ex una parte eam reflexionem faciat: si contigerit tamen illam in aliquot bullas intumescere, bullam unamquamque reflectionem facere, & candoris speciem creare certa Superficiei parte.
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