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Updated: June 18, 2025
This affair of squaring the circle seems to be peculiarly liable to error; for even an accurate mathematician cannot speak of it without committing something very like a bull. Dr. Hutton, in his Treatise on Mensuration, p. 119, says, "As the famous quadrature of the late Mr.
He was sometimes unluckily engaged in disputes with ladies, with whom algebraick axioms had no great weight, and saw many whose favour and esteem he could not but desire, to whom he was very little recommended by his theories of the tides, or his approximations to the quadrature of the circle.
To vindicate my reputation, and to cry quittance with Naworth, against whom I was highly incensed, to work I went again for Anglicus, 1645; which as soon as finished I got to the press, thinking every day one month till it was publick: I therein made use of the King's nativity, and finding that his ascendant was approaching to the quadrature of Mars, about June, 1645, I gave this unlucky judgment; 'If now we fight, a victory stealeth upon us; and so it did in June, 1645, at Naseby, the most fatal overthrow he ever had.
Many even of the truths of geometry were generalizations from experience before they were deduced from first principles. The quadrature of the cycloid is said to have been first effected by measurement, or rather by weighing a cycloidal card, and comparing its weight with that of a piece of similar card of known dimensions.
Sirene I the innermost planet was plainly close to a transit. II was away on the far side of its orbit. III was also on the far side. IV was in quadrature. There was the usual gap where V should have been. VI it didn't matter. They'd passed VIII a little while since, a ball of stone with a frigid gas-ice covering.
And in another place he thinks that "the site of Eden will ever rank with the quadrature of the circle, and the interpretation of unfulfilled prophecy among those unsolved, and perhaps insoluble, problems which possess so strange a fascination."
For two and twenty years I have been in pursuit of the fixed point; here I miss it, there I get sight of it again, and just when it seems that I am down upon it so that it can by no means escape me, I find myself on a sudden so far away from it that I am utterly amazed. It is just the same with the quadrature of the circle.
First, in a kind of mockery they implore the divine assistance, which they borrowed from the solemn custom of the poets: then if their text suppose be of charity, they shall take their exordium as far off as from a description of the river Nile in Egypt; or if they are to discourse of the mystery of the Cross, they shall begin with a story of Bell and the Dragon; or perchance if their subject be of fasting, for an entrance to their sermon they shall pass through the twelve signs of the zodiac; or lastly, if they are to preach of faith, they shall address themselves in a long mathematical account of the quadrature of the circle.
Whoever, also, should hereunto join the geometrical propositions that, by the certainty of their demonstrations, conclude the contained to be greater than the containing, the centre to be as great as its circumference, and that find out two lines incessantly approaching each other, which yet can never meet, and the philosopher's stone, and the quadrature of the circle, where the reason and the effect are so opposite, might, peradventure, find some argument to second this bold saying of Pliny: "Solum certum nihil esse certi, et homine nihil miserius ant superbius."
Let it be then supposed, the Earth being at B some time before the last quadrature, that one has seen the said Satellite emerge from the shadow; it must needs be, if the Earth remains at the same place, that, after 42-1/2 hours, one would again see a similar emergence, because that is the time in which it makes the round of its orbit, and when it would come again into opposition to the Sun.
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