This text is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

Images made available for download are licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License (CC BY-NC 3.0)

If several bodies revolve about a common center & the

ecenter: the orbs

~~wil~~ described by the bodies will be all of one & the same kind but may differ from one another in species; & such

are the Conic Sections. And if the

~~f~~ as the cube of the distance the Orbs described will be all of another

kind but differ

from one another in species, such as are the Logarithmica

And if in either case a man should shew how to describe the

Curve which a body shall describe when projected from any given

place with any given velocity in any given determination of motion:

he would

~~shew how to~~ at the same time shew how to describe all the curves in

chr Newton in the XVIIth Proposition of his first Book of Principles has done this in the first

case, that is, when

edistance, & has found that the Curve is always one of the three

Conic Sections. If M

r ernulli& found that the Curve described will be always a Logarithmic Spiral

& will not comprehend all the Curves which can be described by such