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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
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74 DE VEREBUS ET MLOTTBUS CORDORUM. LIB. I.
Caeterum, quia generalis haec solutio quadraturas praesupponit ca-
rum etiam currarum, quae quadrabiles non lunt, ideo problema istud
generaliter sumtum est transcendens, nec alsebraicum At, nisi pro
cerris legibus Colicitationum centralium. Ouaenam vero debeant esse
in genere hae leges graritatis rariabilis, ut illis positis currae proje.
ctorum algebraicae cradtant, problema est latis curiosum e clegans,
sed prima Fronte admodum difficile, de quo, quod sciam, nemo ad-
huc cositarit. Ouomodo rero debeat expediri, id in sequenti ap.
Parebit propositione, Post lemma mox afferendum.
PROPOSITIOZZIV. L E M M A.
263. Flementum S5 tansentis L. S arcus circularis L. M est ad ele-
mentum hujus arcus Mm; ut AS quadratum secantis ad AM qua
215. 38. dratum radii, vel etiam, ut AI. quadratum radii, ad AC quadra-
tum sinus complementi arcus L. MI.
Nam, quia triangula SAS _ Mam communem angulum MAm
continent, erit triangulum SAs ad criangulum MAm, ut rec. lum
SA. 5A ad rec. lum M A. mA, id eAt, ut quadratum S A ad quadratum
MA. AC quia trianguli SAS altitudo est AL, existente baII S5, et
trianguli MAm balin Nm habentis alticudo est MA aequalis alteri
AL, liquet triansulum SAs se habere ad triansulum MAm, ut ba-
iS Ss ad batin Mm, ergo etiam Ss ad MM uE AS ad ANI, vel
propter parallelas SI. et MC, sicut AL. ad AC. Quod crat de-
monstrandum.
C OR OL L A R L U M.
266. Tdcirco, s dicantur radius AL, Y, tangenS L S, Y; arCUS
LM, a, erit (CCaNS AS = V (rr + HV), atque adeo da =rrat: rr + It.
Et conversa hac aequatione in Ceriem, singula seriei membra crunt
Cummabilia, adeo ut cummatione eorum actu instituta habeatur ex
pressioarcus circularis a, Serie infinita tansente et radio expresa.
PROFOSTTTOZAV. PROBLEMA.
267. Indm anom tim aterminandae cravitatis varhabi
Fis. 37, 38. lis seu legis soluionum centralium, pro omnibus curvis alcebraicis in
infimtum, quantitatibus finitis expressum.
I. In figura 38. Rac AD aequalis AD in A8. 37, atque in A8. 38.
CIXCA