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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1791 Excerpt: ... that is, Js the sine total is to the fine of the elevation of thepole of the circle GL above the plane of projection, so is the fine of the distance of the lesser circle from the said pole to half the conjugate axis of the ellipsis which is to be described., and whereof the transverse axis is manifestly equal to MN.-The point m might also be found by taking Cm equal to the fine of the difference of the arcs, MG, BG; and consequently the ellipsis sought, described. E. I.. Application of the two last Problems to the projeclions used in the 'Theory of Eclipses. 197. The Earth being situate at a prodigious distance from the Sun, all the rays which come from thence hither may be considered as parallel; and if we imagine a plane perpendicular to the ray which issues from the centre of the fan to that of the earth, this plane (which will cut the sphere into two equal parts) will represent the d slc of the earth as appearing from the sun; also separate the enlightened from the darkened hemisphere, and lastly have all the points of the hemisphere exposed to the sun projected orthographically upon it. This being premised, if, P, p, represent the poles of the world, the line GL will denote the equator; th# little circle MN will be a parallel whereof GM is the Geographical latitude; the circle ABab will be the circle which Astronomers call the universal meridian; the line BC will represent the ray which comes from the centre of the sun to that of the earth, and consequently the arc BG be the sun's declination;. the line ACa will be a line perpendicular to the plane of the circle Bcb, which has the axis of the ecliptic projected upon it at the solstices, and makes with the said axis an angle equal to the obliquity of the ecliptic at the equinoxes-, ACa 02 Will will rep...

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