Newcomb, Simon, 1835-1909 · New York, H. Holt and company · leaf 159
conjugate axes by a and b, and the co-ordinates of P by x, y. Then (§ 125) the co-ordinates of Dare -p +^• Hence sin Q = ^-; cos u = —,-; • af ^^ cos^= ,,- Substituting in (a), we have bx ,^ ^ = aab + THE ELLIPSE. 143 (10) But since (?/, y) is on the curve, Therefore sm a> = , ,,, = -nr- 128.… … Proof From the last equation we have ab sin (p = ab;but ab sin cp is equal to the area of the parallelogram CPQD,and ab is equal to the area of the rectangle CAEB; thereforethe parallelogram QRST = the rectangle EFGH, which isconstant. Cor. 1. The triangle CPD is equal to the triangle ACB,each…
Geometry, Analytic
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![An illustration from Nicolai Copernici Torinensis De reuolutionibus orbium coelestium, libri VI : Habes in hoc opere iam recens nato, & aedito, studiose lector, motus stellarum, tam fixarum, quàm erraticarum, cum ex ueteribus, tum etiam ex recentibus obseruationibus restitutos: & nouis insuper ac admirabilibus hypothesibus ornatos. Habes etiam tabulas expeditissimas, ex quibus eosdem ad quoduis tempus quàm facillime caculare poteris. Igitur eme, lege, fruere. [Line in Greek] (1543)](https://img.insideoutlibrary.com/img/200/ia-nicolaicopernici00cope-87-64.webp)
