Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/477

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f il13l from' this cauſe, are interini'Xt the other much greater variations, ariſing from the eccentricity of the orbit.. T H E angle of the Moon's elongation H3 from the center, deſigned by B T N, is properly the variation or reflection of the Moon. The properties which are evident from the deſcription F IR ſT, It is as the line of the double diſtance of the Moon from the quadrature or conjunction with the Sun: For 'it is the difference of the two angles BTA -and N TA, whoſe tangents, by the con# fl ruction, are in a given proportion. SECONDL Y, A Tghe variation is, crateris paribus, in the duplicate proportion of the ſynodical time of the Moon's revolution to the Sun. For the variation is in proportion to themean diameter of the epicycle, and that is' in:the duplicate proportion of the ſynodicaltinie of revolution, , 1 ' i A ' V T H E greateſt variation is an angle, whoſe fine is to the radius, as the 'difference of the greateſt and leaſt diſtances fl' Q, and 'T L, that is 3./1€2, to their ſum. -According to the proportion of the lines before deſcribed, this rule makes the elongation near 29 minutes; which would f p bc