*Reference: **A Logical Approach to Theoretical Physics*

This paper presents the preface from the English translation of NEWTON’S PRINCIPIA, American edition, 1846.

The paragraphs of original material are accompanied by brief comments in color based on present understanding. The heading below links to the original materials.

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## THE AUTHOR’S PREFACE

Since
the ancients (as we are told by *Pappus*),
made great account of the science of mechanics in the investigation of natural
things; and the moderns, laying aside substantial forms and occult qualities,
have endeavoured to subject the phenomena 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 phenomena of motions to investigate the
forces of nature, and then from these forces to demonstrate the other
phenomena; 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
phenomena 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 phenomena 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.

*Newton sees mechanics as a practical and universal subject. **According to Newton,**the idea of right (straight) line and circle comes from mechanics; and geometry is that aspect of mechanics that describes what to do with straight line and circle. Geometry is very accurate because it is theoretical and not practical. In other words, geometry is based on certain precise postulates, whereas, mechanics is not. From the postulates underlying geometry (and mathematics in general) mechanics may not appear to be that accurate. But, mechanics is what it is; it is the reality. In other words, geometry is a starting point for understanding of mechanics.*

*The overall concern of mechanics is with
motion resulting from forces, and with forces required to produce any motions.
Geometry commonly refers to their magnitudes, accurately proposed and
demonstrated. Gravity was considered by ancients as one of the powers that
produced motion.*

*The work here is to investigate the forces
of nature from the phenomena of motions, and then from these forces to demonstrate
the other phenomena. In the first two books Newton demonstrates the
propositions mathematically. In the third books he derives the forces of
gravity from the celestial phenomena, and then from these forces he deduces the
motions of the planets, the comets, the moon, and the sea.*

In
the publication of this work the most acute and universally learned Mr. Edmund
Halley not only assisted me with his pains in correcting the press and taking
care of the schemes, but it was to his solicitations that its becoming public
is owing; for when he had obtained of me my demonstrations of the figure of the
celestial orbits, he continually pressed me to communicate the same to the *Royal Society*, who afterwards, by their
kind encouragement and entreaties, engaged me to think of publishing them. But
after I had begun to consider the inequalities of the lunar motions, and had
entered upon some other things relating to the laws and measures of gravity,
and other forces; and the figures that would be described by bodies attracted
according to given laws; and the motion of several bodies moving among
themselves; the motion of bodies in resisting mediums; the forces, densities,
and motions, of mediums; the orbits of the comets, and such like; deferred that
publication till I had made a search into those matters, and could put forth
the whole together. What relates to the lunar motions (being imperfect), I have
put all together in the corollaries of Prop. 66, to avoid being obliged to
propose and distinctly demonstrate the several things there contained in a
method more prolix than the subject deserved, and interrupt the series of the
several propositions. Some things, found out after the rest, I chose to insert
in places less suitable, rather than change the number of the propositions and
the citations. I heartily beg that what I have here done may be read with
candour; and that the defects in a subject so difficult be not so much
reprehended as kindly supplied, and investigated by new endeavours of mv
readers.

*Newton was prescient in admitting that there was a lot more. He knew that the exact nature of all the forces in nature was not known enough to derive all phenomena of nature. He considered his work incomplete.*

*In Newton’s time only matter was known as a substance. Newton was not aware that the dimension of quantization was missing from mechanics and geometry. Quantization was discovered over two hundred years later by Einstein. It showed that light was a substance that quantized to, ultimately, become matter. *

ISAAC NEWTON,

Cambridge, Trinity College May 8, 1686.

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