Titulus, Dedicatio, Præfatio, Carmen

Preface
to the
Reader.

Since the ancients (as Pappus tells us) held mechanics in the highest esteem in the study of nature, and the moderns, setting aside substantial forms and occult qualities, have undertaken to bring the phenomena of nature under mathematical laws, I have decided in this treatise to develop mathematics so far as it bears on natural philosophy. Now the ancients divided mechanics into two kinds: the rational, which proceeds exactly by demonstrations, and the practical. To practical mechanics belong all the manual arts, and it is from them, indeed, that mechanics borrowed its name. But because craftsmen usually work without much exactness, mechanics as a whole has come to be distinguished from geometry in such a way that whatever is exact is assigned to geometry, and whatever is less exact to mechanics. Yet the errors belong not to the art but to those who practise it. Whoever works less exactly is a less perfect mechanic, and if anyone could work with perfect exactness, he would be the most perfect mechanic of all. For the drawing of straight lines and of circles, on which geometry is founded, is itself a matter of mechanics. Geometry does not teach us how to draw these lines; it postulates it. For it requires that the beginner have learned to draw them exactly before he reaches the threshold of geometry; then it teaches how problems are solved by means of these operations. To draw straight lines and circles are problems, but not geometrical ones. Their solution is demanded of mechanics, and geometry teaches the use of them once solved. And geometry prides itself on achieving so much from so few principles, borrowed from elsewhere. Geometry, therefore, is founded on mechanical practice, and is nothing other than that part of universal mechanics which sets out and demonstrates exactly the art of measuring. But since the manual arts are chiefly concerned with moving bodies, geometry is commonly associated with magnitude and mechanics with motion. In this sense rational mechanics will be the science, exactly set out and demonstrated, of the motions that result from any forces whatever, and of the forces required to produce any motions whatever. The ancients cultivated this part of mechanics in the five powers that belong to the manual arts, and they considered gravity (since it is not a manual power) scarcely otherwise than in the moving of weights by those powers. But since I write with philosophy in view rather than the arts, and of natural rather than manual powers, I deal chiefly with what concerns gravity, levity, elastic force, the resistance of fluids and other such forces, whether attractive or impulsive: and for that reason I offer this work as the mathematical principles of philosophy. For the whole difficulty of philosophy seems to lie in this: to discover the forces of nature from the phenomena of motions, and then from these forces to demonstrate the other phenomena. The general propositions worked out in the first and second books are directed to this end. In the third book I have given an example of this by explaining the system of the world. For there, from the celestial phenomena, by means of propositions proved mathematically in the earlier books, are derived the forces of gravity by which bodies tend toward the Sun and toward each of the planets. Then from these forces, again by mathematical propositions, the motions of the planets, the comets, the Moon and the sea are deduced. Would that the rest of the phenomena of nature could be derived from mechanical principles by the same kind of reasoning. For many things lead me to suspect that they may all depend on certain forces by which the particles of bodies, for causes not yet known, are either driven toward one another and cohere in regular figures, or are repelled and recede from one another: and because these forces have been unknown, philosophers have so far made their attempts on nature in vain. But I hope that the principles set down here will throw some light either on this way of doing philosophy or on some truer one.

In the publishing of this work Edmond Halley, a man of the sharpest mind and learned in every branch of letters, gave his help: he not only corrected the printers’ errors and had the figures engraved, but was also the one who persuaded me to undertake its publication. For when he had obtained from me my demonstration of the shape of the celestial orbits, he never stopped asking me to communicate it to the Royal Society, which then, by its encouragement and kind patronage, led me to begin thinking of making it public. But after I had taken up the inequalities of the Moon’s motions, and had then begun to try other things as well (the laws and measures of gravity and of other forces, the figures described by bodies attracted according to any given laws, the motions of several bodies among themselves, the motions of bodies in resisting media, the forces, densities and motions of media, the orbits of comets and the like), I thought the publication should be put off to another time, so that I might search out the rest and bring it all before the public together. What concerns the Moon’s motions (being incomplete) I have gathered together in the corollaries of Proposition LXVI, so as not to be obliged to set out and prove each point separately by a longer method than the subject deserves, and so break the sequence of the remaining propositions. Some things found late I preferred to insert in less suitable places rather than change the numbering of the propositions and the cross-references. I earnestly ask that everything be read with good will, and that its shortcomings, in so difficult a subject, be not so much faulted as investigated and kindly made good by the fresh efforts of readers.

ON THIS
MATHEMATICO-PHYSICAL WORK
OF THE MOST EXCELLENT MAN
MR ISAAC NEWTON

The outstanding glory of our age and nation.

Behold the rule of the heavens, the balances of the divine mass,
and the reckoning of Jupiter: laws that, as he framed the first beginnings
of things, the Creator who brings forth all would not
break, and that he set as the foundations of his eternal work.
The inmost chambers of the conquered sky lie open,
and the Force that wheels the outermost orbs is hidden no more.
The Sun, enthroned, commands all things to tend towards him
in downward descent, and does not let the chariots
of the stars move in a straight path through the vast void,
but sweeps each one round in unmoving circles, himself the centre.
Now the curving road of the dreadful Comets is plain;
now we no longer marvel at the apparitions of the bearded Star.
From this we learn at last why silver Phoebe
walks with unequal steps; why, subject until now to no
astronomer, she has refused the reins of number;
why the Nodes go back, and why the Apsides advance.
We learn too with what great forces wandering Cynthia drives the ebbing Sea,
when, its waves broken, it leaves the sedge
behind, and bares the sands that Sailors dread,
beating by turns upon the highest shores.
Things that so often racked the minds of the ancient Sages,
and vex the Schools in vain with hoarse dispute,
we see plainly before us, now that Mathematics drives away the cloud.
Error no longer weighs down with any darkness the doubters
to whom the keenness of a lofty Genius has granted to enter the homes of the Gods
and to climb the heights of Heaven.

Rise, Mortals, cast away your earthly cares,
and learn from this the powers of a heaven-born Mind,
far and wide removed from the life of beasts.
He who by written Tables bade men curb Murder,
Theft and Adultery, and the crimes of perjured Fraud;
or he who first taught wandering peoples to ring their Cities with walls,
or blessed the nations with the gift of Ceres;
or he who pressed from the Grape a solace for our cares;
or he who showed how, with the reed of the Nile, painted
sounds are joined, and Voices set before the eyes:
each raised the human lot less high, since he looked
only to the few comforts of a wretched life.
But now we are admitted as guests of the Gods; we may handle
the laws of the high heavens; now the hidden vaults of the dark
Earth lie open, and the unmoving order of things,
and all that lay hidden from the ages of the world gone by.

Join me in singing, with the Camenae, the one who shows us such things,
you who delight to feast on heavenly nectar:
NEWTON, who unlocks the coffers of hidden Truth,
NEWTON, dear to the Muses, in whose pure breast
Phoebus dwells, whose mind he has entered with all his Godhead:
nearer the Gods no Mortal may approach.

EDM. HALLEY.