Plane and solid analytic geometry; an elementary textbook (1901)
Ashton, Charles H. (Charles Hamilton), 1866- · New York, C. Scribner's sons · leaf 114
It 27. Find the locus of the middle points of chords whichpass through a fixed point Qxv y^) of the circle x2 + y2 = r2. Let P, (V, ?/), be the middle point of any chord throughPv (xv y^). Let (xv y2~) be the coordinates of P2, theother extremity of the chord. From the formulas for bisecting a line… … (1) *: X* -\~ Xn and (2) y = U±±]h. And, since P2 is a point onthe circle, (3) x* + y*=r*.Here are three equationsbetween the variables x and y\ the constants xv yv and r,and the parameters x.2 and y2. It is therefore possible 96 ANALYTIC GEOMETRY [Ch. VIII, § 61 to eliminate the parameters and…
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-332-223.webp)
