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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 45, page id 1041163592:0079
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M
N
M
est
LACIAOCLTA MAETTEMATICA
Scholium.
Ec simili argumento corpus morebitur in Ellipsi vel etiam in
Arperbola vel Parabola, vi centripeta qux SIE RCCIPROCC UE CU-
bus ordinacim applicaca ad centrum virium maxime longinquum
cendentis.
PROEOSITIO IX. PROBLEMA WV.
Oyretur corpus in Spirali P OS secante radios omnes SP, SC, C.
in angulo dato: requiritur L. ex
vis centripetae tendentis ad
centrum Spiralis.
Detur angulus indehnite par-
rus FS∞ ec ob datos omnes
angulos dabitur specie AOuTASP ZRT. Ergo datur rario
eT quad
eAtque
R Ut Q T, hOc CsFUES. P. Mutetur jam utcunque angulus P5B
ec recta e R angulum contactus _ P R subtendens mutabitur (PCF
Lemma XI.) in duplicaca ratione iphus P R vel 9T. Ersomanebit
DT quad.
X
eadem quae prius, hoc est ut SP. Ouare
l9. 25F9
3
CA uE SP cub. adeoque (per Corol. L _E5 PFOP. VL.) vis centripeta eA
reciproce uc cubus distantia SP. 8. F. I.
Idem aliter.
Perpendiculum SY in tangentem demissum; ec circuli Spiralem
cansentis chorda P V sune ad alcicudinem SF in datis rationibus;
ideoque SP cub. eA ucSZgX P V, hoc eA (per C orol. 3ec 5 PrOP. VI. )
reciproce ut ris centripeta.
L E MIMI A ZII.
Paralleloeramma omnia, circa datae F. lipseos vel Fyperbolae diametros
quasvis conjuratas descripta, esse inter se aequalia.
Constat ex Conieis.
L.tBF
PRLMDS
LRC