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

 f il13l from' this caue, are interini'Xt  the other much greater variations, ariing from the eccentricity of the orbit.. T H E angle of the Moon's elongation H3 from the center, deigned by B T N, is properly the variation or reflection of the Moon. The properties  which are evident from the decription F IR T, It is as the line of the double ditance of the Moon from the quadrature or conjunction with the Sun: For 'it is the difference of the two angles BTA -and N TA, whoe 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 ynodical 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 ynodicaltinie of revolution, , 1 ' i A ' V T H E greatet variation is an angle, whoe fine is to the radius, as the 'difference of the greatet and leat ditances fl' Q, and 'T L, that is 3./1€2, to their um. -According to the proportion of the lines before decribed, this rule makes the elongation near 29 minutes; which would f p bc