“Useful Things, though Mechanical, are justly preferable to useless Speculations in Geometry”

— Isaac Newton, book Arithmetica Universalis

Arithmetica Universalis (1707), p.248

Adopted from Wikiquote. Last update Oct. 1, 2023. History

Help us to complete the source, original and additional information

Do you have more details about the quote "Useful Things, though Mechanical, are justly preferable to useless Speculations in Geometry" by Isaac Newton?

Isaac Newton171

British physicist and mathematician and founder of modern c… 1643–1727

Related quotes

“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.”

Isaac Newton book Philosophiae Naturalis Principia Mathematica

Preface (8 May 1686)
Philosophiæ Naturalis Principia Mathematica (1687)

“Present action, though futile, is preferable to passive acceptance of such a fate as awaits us.”

Michael Shea (1946–2014) writer

Source: A Quest for Simbilis (1974), Chapter 6, “The House on the River” (p. 112)

“Though a state of affairs that would contravene the laws of physics can be represented by us spatially, one that would contravene the laws of geometry cannot.”

Ludwig Wittgenstein (1889–1951) Austrian-British philosopher

3.0321
Original German: Wohl können wir einen Sachverhalt räumlich darstellen, welcher den Gesetzen der Physik, aber keinen, der den Gesetzen der Geometrie zuwiderliefe.
1920s, Tractatus Logico-Philosophicus (1922)