Page:Newton's Principia (1846).djvu/482

 The positions of the comet to these fixed stars were observed to be as follow:

Friday, February 25, O.S. at 8½h. P. M. the distance of the comet in p from the star E was less than $3/13$AE, and greater than $1/5$AE, and therefore nearly equal to $3/14$AE; and the angle ApE was a little obtuse, but almost right. For from A, letting fall a perpendicular on pE; the distance of the comet from that perpendicular was $1/5$pE.

The same night, at 9½h., the distance of the comet in P from the star E was greater than $$\scriptstyle \frac{1}{4\frac{1}{2}}$$AE, and less than $$\scriptstyle \frac{1}{5\frac{1}{4}}$$AE, and therefore nearly equal to $$\scriptstyle \frac{1}{4\frac{7}{8}}$$ of AE, or $8/39$ AE. But the distance of the comet from the perpendicular let fall from the star A upon the right line PE was $4/5$PE.

Sunday, February 27, 8¼h. P. M. the distance of the comet in Q from the star O was equal to the distance of the stars O and H; and the right line QO produced passed between the stars K and B. I could not, by reason of intervening clouds, determine the position of the star to greater accuracy.

Tuesday, March 1, 11h. P. M. the comet in R lay exactly in a line between the stars K and C, so as the part CR of the right line CRK was a little greater than ⅓CK, and a little less than ⅓CK + $1/8$CR, and therefore = ⅓CK + $1/16$CR, or $16/45$CK.

Wednesday, March 2, 8h. P. M. the distance of the comet in S from the star C was nearly $4/9$FC; the distance of the star F from the right line CS produced was $1/24$FC; and the distance of the star B from the same right line was five times greater than the distance of the star F; and the right line NS produced passed between the stars H and I five or six times nearer to the star H than to the star I.

Saturday, March 5, 11½h. P. M. when the comet was in T, the right line MT was equal to ½ML, and the right line LT produced passed between B and F four or five times nearer to F than to B, cutting off from BF a fifth or sixth part thereof towards F: and MT produced passed on the outside of the space BF towards the star B four times nearer to the star B than to the star F. M was a very small star, scarcely to be seen by the telescope; but the star L was greater, and of about the eighth magnitude.

Monday, March 7, 9½h. P. M. the comet being in V, the right line Va produced did pass between B and F, cutting off, from BF towards F, $1/10$ of BF, and was to the right line Vβ as 5 to 4. And the distance of the comet from the right line αβ was ½Vβ.

Wednesday, March 9, 8½h. P. M. the comet being in X, the right line γX was equal to ¼γδ and the perpendicular let fall from the star δ upon the right γX was $2/5$ of γδ.

The same night, at 12h. the comet being in Y, the right line γY was