Preface (8 May 1686)
Philosophiæ Naturalis Principia Mathematica (1687)
“Geometry does not teach us to draw these lines, but requires them to be drawn; for it requires that the learner should first be taught to describe these accurately, before he enters upon geometry; then it shows how by these operations problems may be solved.”
Preface (8 May 1686)
Philosophiae Naturalis Principia Mathematica (1687)
Context: The ancients considered mechanics in a twofold respect; as rational, which proceeds accurately by demonstration, and practical. To practical mechanics all the manual arts belong, from which mechanics took its name. But as artificers do not work with perfect accuracy, it comes to pass that mechanics is so distinguished from geometry, that what is perfectly accurate is called geometrical; what is less so is called mechanical. But the errors are not in the art, but in the artificers. He that works with less accuracy is an imperfect mechanic: and if any could work with perfect accuracy, he would be the most perfect mechanic of all; for the description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn; for it requires that the learner should first be taught to describe these accurately, before he enters upon geometry; then it shows how by these operations problems may be solved.
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Do you have more details about the quote "Geometry does not teach us to draw these lines, but requires them to be drawn; for it requires that the learner should …" by Isaac Newton?
Isaac Newton 171
British physicist and mathematician and founder of modern c… 1643–1727Related quotes
p, 125
Arithmetica Universalis (1707)
Augustus De Morgan
(1806–1871) British mathematician, philosopher and university teacher (1806-1871)
Advertisement, p.4
The Differential and Integral Calculus (1836)
Arithmetica Universalis (1707)
Context: Geometry was invented that we might expeditiously avoid, by drawing Lines, the Tediousness of Computation. Therefore these two Sciences ought not to be confounded. The Antients did so industriously distinguish them from one another, that they never introduc'd Arithmetical Terms into Geometry. And the Moderns, by confounding both, have lost the Simplicity in which all the Elegancy of Geometry consists. Wherefore that is Arithmetically more simple which is determin'd by the more simple Æquations, but that is Geometrically more simple which is determin'd by the more simple drawing of Lines; and in Geometry, that ought to be reckon'd best which is Geometrically most simple. Wherefore, I ought not to be blamed, if with that Prince of Mathematicians, Archimedes and other Antients, I make use of the Conchoid for the Construction of solid Problems.<!--p.230
Simone Weil
(1909–1943) French philosopher, Christian mystic, and social activist
Waiting on God (1950), Reflections on the Right Use of School Studies with a View to the Love of God
In the meantime, this little is something which mathematics indispensably requires in its application to natural science, which, inasmuch as it must here necessarily borrow from metaphysics, need not be ashamed to allow itself to be seen in company with the latter.
Preface, Tr. Bax (1883) citing Isaac Newton's Principia
Metaphysical Foundations of Natural Science (1786)
Joseph Louis Lagrange
(1736–1813) Italian mathematician and mathematical physicist
Dans Les Leçons Élémentaires sur les Mathématiques (1795) Leçon cinquiéme, Tr. McCormack, cited in Moritz, Memorabilia mathematica or, The philomath's quotation-book (1914) Ch. 15 Arithmetic, p. 261. https://archive.org/stream/memorabiliamathe00moriiala#page/260/mode/2up
“In geometry his greatest achievement was an accurate value of π.”
Aryabhata
(476–550) Indian mathematician-astronomer
His rule is stated as: dn^2+(2a-d)n=2s, which implies the approximation 3.1416 which is correct to the last decimal place.
In, p. 245.
Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures
“Lines should not be drawn simply for the sake of drawing lines”
Felix Frankfurter
(1882–1965) American judge
Dissenting in Pearce v. Commissioner of Internal Revenue, 315 U.S. 543, 558 (1942).
Judicial opinions
Context: The line must follow some direction of policy, whether rooted in logic or experience. Lines should not be drawn simply for the sake of drawing lines.