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Who said: “I have no satisfaction in formulas unless I feel their arithmetical magnitude.”
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Home > Category Index for Science Quotations > Category Index I > Category: Incommensurable

Incommensurable Quotes (4 quotes)

He is unworthy of the name of man who is ignorant of the fact that the diagonal of a square is incommensurable with its side.
Quoted by Sophie Germain: Mémorie sur les Surfaces Élastiques. In Robert Édouard Moritz, Memorabilia Mathematica (1914), 211
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It is probable that two proposed unknown rations are incommensurable because if many unknown rations are proposed it is most probable that any [one] would be incommensurable to any [other].
In De Proportionibus Proportionum (1351).[Note: incommensurable, mathematical term refers to numbers in a ratio that cannot be expressed as a ratio of integers.]
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No sector of a circle is so small that two such [bodies bodies moving with uniform but incommensurable velocities] could not conjunct in it at some future time, and could not have conjuncted in it sometime [in the past].
In Tractatus de commensurabilitate vel incommensurabilitate motuum cell.
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The ancients devoted a lifetime to the study of arithmetic; it required days to extract a square root or to multiply two numbers together. Is there any harm in skipping all that, in letting the school boy learn multiplication sums, and in starting his more abstract reasoning at a more advanced point? Where would be the harm in letting the boy assume the truth of many propositions of the first four books of Euclid, letting him assume their truth partly by faith, partly by trial? Giving him the whole fifth book of Euclid by simple algebra? Letting him assume the sixth as axiomatic? Letting him, in fact, begin his severer studies where he is now in the habit of leaving off? We do much less orthodox things. Every here and there in one’s mathematical studies one makes exceedingly large assumptions, because the methodical study would be ridiculous even in the eyes of the most pedantic of teachers. I can imagine a whole year devoted to the philosophical study of many things that a student now takes in his stride without trouble. The present method of training the mind of a mathematical teacher causes it to strain at gnats and to swallow camels. Such gnats are most of the propositions of the sixth book of Euclid; propositions generally about incommensurables; the use of arithmetic in geometry; the parallelogram of forces, etc., decimals.
In Teaching of Mathematics (1904), 12.
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In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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