## The System of the World, Demonstrated in an Easy and Popular Manner

**by Isaac Newton**

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*Excerpt:*

The later philofophers pretend to account for it, either by the action of certain vortices, as *Kepler *and 'Des Cartes •, or by fome other principle of impulfe or attraction, as Borelli, Hook, and others of our nation. For, from the laws of motion, it is moft certain that thefe effe&s muft proceed from the action of fome force or other.

But our purpofe is only to trace out the quantity and properties of this force r, *Mt. *from the phenomena, and to apply what we difcoyer in fome fimple cafes, as principles, by which, in a mathematical

way,

- way, we may estimate the effects there-

of in more involved cafes. For it would

be endlefs and impoffible to bring every

particular to direct and immediate ob-

fervation.

We faid, in a mathematical way, to_{#}

avoid all questions about the nature or

quality of this force, which we would

not be underftood to determine by any

hypothecs; and therefore call it by the

general name of a centripetal force, as

it is a force which is directed towards

fome center; and as it regards more par-

ticularly a body in that center, we call

it circum-folar, circum-terreftrial, circum-

jovial, and in like manner in respect of

other central bodies.

T H A T by means of centripetal forces, the Planets may be retained in certain orbits, we may eafily ^{tr}'P^{etal} f°^{rces}understand, if we confider the motions of projectiles. For a ftone projected is P. 4,5. by the prefiure of its own weight forced^{1}^' ^{L} out of the rectilinear path, which by the projection alone it fhould have purfued, and made to defcribe a curve line in the air; and through that crooked way is at left brought down to the ground. And the greater the velocity is with which it is projected, the farther it goes before it falls to the Earth. We may thereB 3 fore

fore fuppofe the velocity to be fo en* creafed, that it would deferibe an arc of i, 2, 5, 10, 100, 1000 miles before it . arrived at the Earth, till at laft exceeding the limits of the Earth, it fhould pafs quite by without touching it.

Let AFB represent the furface of the Earth, C its center, VD, VE, VF, the curve lines which a body would defcribe, if projected in an horizontal diredion from the top of an high mounr tain, fuccefllvely with more and more rid.vol.u. velocity. And, becaufe the celeftial moPrmcip. _{t}j_{ons} _{are} f_{c}arcely retarded by the little or no refiftance of the fpaces in which they are performed; to keep up the parity of cafes, let us fuppofe either that there is no air about the Earth, or at leaft that it is endowed with little or no power of refitting. And for the fame reafon that the body projected with a lefs velocity, defcribes the letter arc VD, and with a greater velocity, the greater arc VE> and augmenting the velocity, it goes farther and farther to F and G; if the velocity was ftill more and more augmented, it would reach at laft quite beyond the circumference of the Earth, and return to the mountain from which it was projected.

And fince the area's, which by this motion it defcribes by a radius drawn

tQ

to the center of the Earth, are (by *Prop. 1 *. Book i. Trincip. Math.} proportional to the times in which they are described ; its velocity, when it returns to the mountain, will be no lefs than it was at first ; and retaining the fame velocity, it will defcribe the fame curve over and over, by the fame law.

But if we now imagine bodies to be projected in the directions of lines parallel to the horizon from greater heights, as of 5, 10, 100, 1000 or more miles, or rather as many femi-diameters of the Earth; thofe bodies, according to their different velocity, and the different force of gravity in different hights, will defcribe arcs either concentric with the Earth, or variouily excentric, and go on revolving through the heavens in thofe trajectories, juft as the Planets do in their orbs.