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Such are their sentiments, I assure him; such is their language, when they dare to speak; and such are their proceedings, when they have the means to act. Their geographers and geometricians have been some time out of practice. It is some time since they have divided their own country into squares. That figure has lost the charms of its novelty. They want new lands for new trials.
Must we admit that emanations which reflect white light, and seem to have some analogy with the tails of comets, are less abundant at certain periods? Researches on the zodiacal light have acquired a new degree of interest since geometricians have taught us that we are ignorant of the real causes of this phenomenon.
But so many limitations were necessary to justify this new rule, that it would have been better, in my opinion, to enounce it at the outset with a reservation, by saying, Si similibus similia addas similiter, tota sunt similia. Moreover, geometricians often require non tantum similia, sed et similiter posita. This difference between quantity and quality appears also in our case.
Thence I went in search of other Truths; and having proposed Geometry for my object, which I conceived as a continued Body, or a space indefinitely spred in length, bredth, height or depth, divisible into divers parts, which might take severall figures and bignesses, and be moved and transposed every way. For the Geometricians suppose all this in their object.
It is she that made the Chinese geometricians find out much of the same truths with the Europeans, whilst those nations so very remote were unknown one to another. It is she that makes people in Japan conclude, as in France, that two and two make four; nor is it apprehended that any nation shall ever change their opinion about it.
This idea causes the rejection of many a diamond with a flaw by girls who, as women, fall in love with paste. Now, Celeste had seen in Felix, not irreligion, but indifference to matters of religion. Like most geometricians, chemists, mathematicians, and great naturalists, he had subjected religion to reason; he recognized a problem in it as insoluble as the squaring of the circle.
True, he said. Then if geometry compels us to view being, it concerns us; if becoming only, it does not concern us? Yes, that is what we assert. Yet anybody who has the least acquaintance with geometry will not deny that such a conception of the science is in flat contradiction to the ordinary language of geometricians. How so?
Practical arithmetic extends further than is usually supposed if you would attain exact precision. There are operations of extreme length in which I have sometimes seen good geometricians lose themselves.
And I am not in the least deceived as to the purpose of these confidences on his part. I know perfectly well that he is only making his little financial statements in order to persuade me that he is comfortably circumstanced, steady, fond of home, comparatively independent or, to put the matter in the fewest words possible, able to marry. Quod erat demonstrandum, as the geometricians say.
As for ideas or notions, I call real all those the possibility of which is certain; and the definitions which do not mark this possibility are only nominal. Geometricians well versed in analysis are aware what difference there is in this respect between several properties by which some line or figure might be defined.
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