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Sphere OLP, having its Cent[[strikethrough]] re [[/strikethrough]]er C upon the prolonged Axis ST, any two Lines LS, LT, drawn from any point L of that Sphere to the Poles S and T of the Projection, are to one another in one and the same Proportion. And by consequence, If the Centers of the Sun and of the Earth be placed in the Poles S and T; and if the Center of the Moon describe any Orbit, either circular [[strikethrough]] or [[/strikethrough]] or more composed, while it moves upon the Surface of the Stereographic Sphere OLP; the Lines drawn from the Center of ^ [[insertion]] the [[/insertion]] Moon to the Centers of the Sun and ^ [[insertion]] of [[/insertion]] the Earth, will be to one another in one and the same Proportion.

 5. [[underline]] Third Theorem [[/underline]]. If, in a Stereographic Sphere OLP, the Gravitations of the Moon towards the Sun and towards the Earth be directly as s the Mass of the Sun and t the Mass of the Earth; and reciprocally as SL [[underline]] quad [[/underline]] and LT [[underline]] quad. that is [[/underline]], if those Gravitations be as 
     s
__________
SL [[underline]] quad [[/underline]] 


and 

   t 
_______
TL quad

, which is the Case in the Solar System: Then, The Direction of the Two united Gravitations of the Moon will tend to one and the same Focus F, or f, placed somewhere upon the Line or Axis ST, or rather upon the Line PT. And, by consequence, equal Areas will be described about that Focus in equal Times.

 6. [[underline]] Fourth Theorem [[/underline]] And in general, If the Gravitations be as s and t directly, and as SL[[superscript]] n [[/superscript]] and LT[[superscript]] n [[/superscript]] directly, taking n for any Index whatsoever, affirmative or negative; [[underline]] that is [[/underline]], If those Gravitations be as sXSL[[superscript]] n [[/superscript]] and tXLT[[superscript]] n [[/superscript]]; The Direction of those Two united Gravitations will tend towards, or [[underline]] in oppositum [[/underline]] to, one and the same Focus F, or f, placed somewhere upon the Axis ST, or rather upon the Line TP.

 7. I communicated also the Sum of these four Theorems to Sir [[underline]] Isaac Newton [[/underline]], in a Letter from [[underline]] London [[/underline]] written before the year 1692. I did hope, even then, that it might serve to find the Sun's

Transcription Notes:
I do not know how to do superscripts or items written as fractions on my computer. Ambrosia:- Superscripts tend to be transcribed as [[superscript]] text [[/superscript]] a bit ugly I know but accurate. As for fractions just do the best you can!