[RascalPuff]

In 1959, Truly Yours encountered the following statement by Newton. This post requests that Readers please say what they think of it.

( Google: Preface Principia Mathematica: )

Last sentence of first paragraph, verbatim, translated to English from the Latin (Italicized & underlined in bold):

"Since the ancients (as we are told by Pappas), made great account of the science of mechanics in the investigation of natural things; and the moderns, lying aside substantial forms and occult qualities, have endeavoured to subject the phænomena of nature to the laws of mathematics, I have in this treatise cultivated mathematics so far as it regards philosophy. 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. To describe right lines and circles are problems, but not geometrical problems. The solution of these problems is required from mechanics; and by geometry the use of them, when so solved, is shown; and it is the glory of geometry that from those few principles, brought from without, it is able to produce so many things. Therefore geometry is founded in mechanical practice, and is nothing but that part of universal mechanics which accurately proposes and demonstrates the art of measuring. But since the manual arts are chiefly conversant in the moving of bodies, it comes to pass that geometry is commonly referred to their magnitudes, and mechanics to their motion. In this sense rational mechanics will be the science of motions resulting from any forces whatsoever, and of the forces required to produce any motions, accurately proposed and demonstrated. This part of mechanics was cultivated by the ancients in the five powers which relate to manual arts, who considered gravity (it not being a manual power, no otherwise than as it moved weights by those powers. Our design not respecting arts, but philosophy, and our subject not manual but natural powers, we consider chiefly those things which relate to gravity, levity, elastic force, the resistance of fluids, and the like forces, whether attractive or impulsive; and therefore we offer this work as the mathematical principles of philosophy; for all the difficulty of philosophy seems to consist in this – from the phænomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phænomena; and to this end the general propositions in the first and second book are directed. In the third book we give an example of this in the explication of the System of the World; for by the propositions mathematically demonstrated in the former books, we in the third derive from the celestial phænomena the forces of gravity with which bodies tend to the sun and the several planets. Then from these forces, by other propositions which are also mathematical, we deduce the motions of the planets, the comets, the moon, and the sea. I wish we could derive the rest of the phænomena of nature by the same kind of reasoning from mechanical principles; for I am induced by many reasons to suspect that they may all depend upon certain forces by which the particles of bodies, by some causes hitherto unknown, are either mutually impelled towards each other, and cohere in regular figures, or are repelled and recede from each other; which forces being unknown, philosophers have hitherto attempted the search of nature in vain; but I hope the principles here laid down will afford some light either to this or some truer method of philosophy." - Sir Isaac Newton 1687

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"...particles of bodies... either mutually impelled towards each other... or are repelled and recede from each other..."

Upon having this statement brought to their attention, some people have denied that it exists in the Preface to the Principia. Upon having it proved to them, the same deniers have called it obscure and inconsequential.

Others have said that I have assigned a meaning to it that Newton did not intend...

Some consternated witnesses have described it as being among the most profound revelations they've experienced...

This thread is intended to evoke Reader's responses - regarding, how any published statement by Sir Isaac Newton can be reasonably described as 'obscure'... Particularly when that statement occurs in the 3 page Preface to the Principia Mathematica.

Moreover, what meaning does the Reader assign to (what I call) Newton's 'gravitational alternative' (that gravity may be an impelling or a repelling force, in those words...)?

Is Newton allowing for an opposite vector for the conventionally considered impelling force of attraction, or, is such an interpretation the assignment of a meaning that Newton did not intend; and, if Newton did not intend that gravity may be a repelling force, what did he intend in writing that alternative - in those words - in his Preface to the Principia?

Please tell me what you think of this ('gravitational alternative').

Thank you.
- RP