I 
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4 
adding FC?r (found above) the angle FCtf will be 
known ; hence we fhall have the following analogy 
for determining En : As tang./ C» tang. FC n :: 
f n : F /?. 
Now let K/£H (fig. 10.) reprefent the difk of the 
fun, and eD fG that of Jupiter, confidered as a 
circle, whofe diameter is equal to his axis DG, draw 
N pn y the path of the fatelles, making the given 
angle N/>R, with a right light Rg drawn parallel to 
the diameter D G, and let ab be the duration of the 
eclipfe, and V the apex of the fhadow in this hypo- 
thecs ; join V a, V b, and let the plane aV b be pro- 
duced, till it meets the fun’s difk in K and k , it will 
then interfed the diik of Jupiter in the line / tt?, and 
the lines VK, Vb, will alfo touch the circumference 
of the circle eD /G, in the points e and /, draw the 
line SV, and it will be the axis of the fhadow, and 
confequently will pafs through C and M, the centers 
of Jupiter, and the fedion of the fhadow ; join a M, 
£M,/’C, e C, and the triangles abVi y e fD, will be 
fimilar to each other, and, therefore, ab M being 
wholly given, jeQ will likewife be known. Let 
ADBG be the elliptic fedion of Jupiter’s body, and 
produce e n f both ways, till it meets the periphery 
of the ellipfis in the points E and F, draw KF, k E, 
and produce them till they meet with ab y produced 
both ways in N and n, then will N n be the required 
duration of the eciipFe in the true fhadow : Now 
the triangles K/ F, K^N, being fimilar, as are alfo 
the triangles ke E, k b /z, and the fegments F f eE, 
being given by the preceding propofition, the re- 
quired legments N'tf, bn y will alfo become known, 
lor they will be to the former fegments in the given 
ratio of S M to SC. 
It 
