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39)
[[Right margin]]
My objection to the 1.[[superscript]]st[[/superscript]] account.

A consequence from both, contrary to all Nature.

Gamaches shows that the motion of the Earth & Moon will always be Retrograde upon the Newtonian Principles. 
S.[[superscript]]r[[/superscript]] I. Newton's Projection & Attraction will not account for the motion of Planets & Comets.
[[/margin]]

If the velocity with which a body would describe a Circle at the point of Projection, be an unit, or 1, then the least velocity that would throw a body or a Planet quite off through the ambient space, describing a curve which does not return upon itself, nor inclose Space, but runs out still to a greater distance ^ [[insertion]] will be [[/insertion]] [[strikethrough]] as [[/strikethrough]] as 1,4142 &c. so that with the velocity 1 a body describes a circle, but with more than 1, and less than 1,4142 (or one & nearly an half) it describes an ellipse, and with more than [[strikethrough]] 1,4142 [[/strikethrough]] ^ [[insertion]] 1,4142 [[/insertion]] it flies quite off.
[[underline]] Baxter's [[/underline]] C.P.
Vol. II. p.152. Ed. 12.[[superscript]]mo[[\superscript]]

(*) i.e. [[underline]] the attraction of the ^ [[insertion]] New [[/insertion]] Moon upon the Sun is as (,36)3833076, at Full as (,36)3787915; the attract of the Moon upon the earth is as (,22)4340279, and that of the earth upon the Sun is as (,16)152416. [[/underline]]

I have since very carefully calculated the Attraction of the Sun, Earth, & Moon upon each other, and find them stand thus;

[[Table with three columns, column two headed Logarithms, column three headed Natural Numbers. Each line of column is separated by dash above and below logarithm number]]
[[heading]] Logarithms Natural Numbers [[/heading]]

√S upon E --     89,5400114 = (,10)346746
S upon New M --  89,5425888 = (,10)34881
S upon Full M -- 89,5374416 = (,10)34470024
√E upon S --     84,1830300 = (,15)152416
√E upon M --     89,2395776 = (,10)1736112
Full M upon S -- 64,5784002 = (,35)3787915
New M upon S --  64,5835474 = (,35)3833076
√M upon E ----   78,6375176 = (,21)4340279
                *87, 
[[/table]]
[[curly bracket encapsulating table data, text written sideways]] Supposing each of the same density. but some authors say they all differ very much in density. V. [[underlined]] Prin[[superscript]]c[[\superscript]]ipia [[/underlined]]. [[/curly bracket]]
[[start table]]
^[[The point of equal Attraction between the]]
Miles from the S     Miles from the E [[**transcriber's note: there is a vertical line between the  (neither column has text)]] 
S & E=
S & New M=
S & Full M=
S & N.M+E=
S & F.M+E=
E & M=
[[end table]]

[[start table]]
^[[The Distance of the Center of Gravity between]]
Miles from S     Miles from E [[**transcriber's note: there is a vertical line between the  (neither column has text)]] 
S & E =
S & New M=
S & Full M=
S & N.M with E=
S & F.M with E=
E & M---=

[[margin]] * This is evidently a mistake; for while E goes forward in the order of the signs [[symbols for Aries, Taurus, and Gemini]], &c. from right to left, the earth at [[bold]] a [[\bold]] goes in the same direction from [[bold]] a [[\bold]] to E, and the moon at b, in a contrary direction, from b to M, while the point b from [[bold]] a [[\bold]], or line [[bold]]ab [[\bold]], will appear to pass through all the signs of the ecliptic in a direct order [[/margin]]