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Number of Parts, suppose first with Sir [[underline]] Isaac Newton [[/underline]] of 4,196, &c. Parts, whose Logarithm is 0,6228760; to TS, or to the corresponding Distance between the Centers of the Sun and of the Earth, independently from any common Center of Gravity. But that common Center of Gravity shall make hereafter another Branch of our Inquiry. And so the Logarithm of the Distance TS comes out first equal to 2.8738392; and TS equal to 747,8925 Parts.
12. And as this TS, is to LT; that is in Logarithms, as 2.8738392, is to 2.000 &c. So is the Radius of the Tables, to 9,1261608. And this is the Sine of 7˚.41'.2" 1/2; which would be the greatest Elongation of the Center of the Moon from the Center of the Earth, as seen from the distance ST which is betwixt the Center of the Sun and of the Earth; supposing the Angle TLS to be changed into a right Angle; and LT to remain of 100 Parts as before.
13. Having now proceeded thus far; we may find the Length of TY as follows. Let FZ parallel to SL cut the Radius LT in Z. As ST, is to LT: So is FT, to TZ, or 100 FT; to 100 TZ. Thus TZ whose logarithm is 1.7490368, is found of 0.5610955 Parts. And LZ is found of 99,4389045 Parts; whose Logarithm is 1.99755642. And as LZ, is to ZF or FT: So is LT, to TY of 4,220071 Parts whose Logarithm is 0.6253196.
14. As TY of 1 Part; is to TS of 178,22278 Parts, whose Logarithm is 2.2509632; so is y [[superscript]] t [[/superscript]] other TY of 4,220071 Parts, whose Logarithm is 0.62531965 to the corrected Distance TS, of which the Logarithm is 2.8762828.
15. And as this TS, is to LT; so is the Radius of the Tables, to the Sine of 7˚ 38' 26"; which would be the greatest Elongation once corrected, of the Center of the Moon from the Center of the Earth, as seen from the Distance ST, which is betwixt the Center of the Sun and of the Earth; sup'