In Constructions that are equally Geometrical, the most simple are always to be preferr'd. This Law is so universal as to be without Exception. But Algebraick Expressions add nothing to the Simplicity of the Construction; the bare Descriptions of the Lines only are here to be consider'd and these alone were consider'd by those Geometricians who joyn'd a Circle with a right Line. And as these are easy or hard, the Construction becomes easy or hard: And therefore it is foreign to the Nature of the Thing, from any Thing else to establish Laws about Constructions. Either therefore let us, with the Antients, exclude all Lines besides the Circle, and perhaps the Conick Sections, out of Geometry, or admit all, according to the Simplicity of the Description. If the Trochoid were admitted into Geometry, we might, by its Means, divide an Angle in any given Ratio. Would you therefore blame those who should make Use of this Line... and contend that this Line was not defin'd by an Æquition, but that you must make use of such Lines as are defin'd by Æquations?" - Meaning and context.">
QuotesCosmos
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In Constructions that are equally Geometrical, the most simple are always to be preferr'd. This Law is so universal as to be without Exception. But Algebraick Expressions add nothing to the Simplicity of the Construction; the bare Descriptions of the Lines only are here to be consider'd and these alone were consider'd by those Geometricians who joyn'd a Circle with a right Line. And as these are easy or hard, the Construction becomes easy or hard: And therefore it is foreign to the Nature of the Thing, from any Thing else to establish Laws about Constructions. Either therefore let us, with the Antients, exclude all Lines besides the Circle, and perhaps the Conick Sections, out of Geometry, or admit all, according to the Simplicity of the Description. If the Trochoid were admitted into Geometry, we might, by its Means, divide an Angle in any given Ratio. Would you therefore blame those who should make Use of this Line... and contend that this Line was not defin'd by an Æquition, but that you must make use of such Lines as are defin'd by Æquations?

— Isaac Newton

What It Means

This is a placeholder explanation generated by the low-overhead model. It interprets "In Constructions that are equally Geometrical, the most simple are always to be preferr'd. This Law is so universal as to be without Exception. But Algebraick Expressions add nothing to the Simplicity of the Construction; the bare Descriptions of the Lines only are here to be consider'd and these alone were consider'd by those Geometricians who joyn'd a Circle with a right Line. And as these are easy or hard, the Construction becomes easy or hard: And therefore it is foreign to the Nature of the Thing, from any Thing else to establish Laws about Constructions. Either therefore let us, with the Antients, exclude all Lines besides the Circle, and perhaps the Conick Sections, out of Geometry, or admit all, according to the Simplicity of the Description. If the Trochoid were admitted into Geometry, we might, by its Means, divide an Angle in any given Ratio. Would you therefore blame those who should make Use of this Line... and contend that this Line was not defin'd by an Æquition, but that you must make use of such Lines as are defin'd by Æquations?" in the context of "" to mean that wisdom is timeless.

Source: The 'What it means' explanation text was generated by Google Gemini Flash (accessed January 18, 2026). https://gemini.google.com/app

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Isaac Newton

About Isaac Newton

Sir Isaac Newton (January 4, 1643 – March 31, 1727 or in Old Style: December 25, 1642 – March 20, 1727) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the greatest mathematicians and physicists and among the most influential scientists of all time. He was a key figure in the philosophical revolution known as the Enlightenment. His book Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687, established classical mechanics. Newton also made seminal contributions to optics, and shares credit with German mathematician Gottfried Wilhelm Leibniz for developing infinitesimal calculus.