102

Sir I s a a c Newton’s Book I.

in the course os the body’s motion; a sufficient power appli-ed to any point os this line will have the fame effect, as thelike power applied to G a : so that as we before shewed thecenter of percussion within the body on its axis; by this meanswe may find this center on the surface of the body also, forit will be where this line HI crosses that surface.

7 6 . I shall now proceed to the last kind of motion, tobe treated on in this place, and shew what line the power ofgravity will cause a body to describe, when it is thrown for-wards by any force. This was first discovered by the greatGalileo, and is the principle, upon which engineersshould direct the shot of great guns. But as in this cafe bo-dies describe in their motion one of those lines, which in geo-metry are called conic sections; it is necessary here to pre-mise a description of those lines. In which I shall be themore particular, because the knowledge os them is not onlynecessary for the present purpose, but will be also requiredhereafter in some of the principal parts of this treatise.

77. The first lines considered by the ancient geometerswere the straight line and the circle. Of these they compos-ed various figures, of which they demonstrated many proper-ties, and resolved divers problems concerning them. Theseproblems they attempted always to resolve by the describingstraight lines and circles. For instance, let a square A B C D( fig. 61.) be proposed, and let it be required to make ano-

a See Method. Increment, prop. 25.

ther