Newton's principia, first book sections I, II, III, with notes and illustrations and a collection of problems, principally intended as examples of Newton's methods (1900)
. 13. A number of bodies which describe ellipses about the centreof force as centre in the same periodic time, are projected from agiven point with a given velocity in different directions in a plane.Prove that their paths will all touch a fixed ellipse with the givenpoint as focus. SECTION in. ON… … Let B be the focus to which the force tends, P theposition of the body at any time, PCG., DCKconjugate diameters, Q a point near P, QT., PFperpendiculars on SP, DCK, from Q, P respectively,PR a tangent at P, QR parallel to SP, Qxv parallelto PR, meeting SP in x, and P C in v, and let >SP,Z>C^…
Mechanics · Celestial mechanics
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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-319-211.webp)
![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-391-272.webp)
