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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 397, page id 1041163592:0431
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I1
PRINOIDIA MATHEMATICA.
Tumma senita, id est, ut acceleratio de scriptionis arex CZ P, (CW L LVEK
incremencum momenti. Vis qua Luna circa Terram quiescentem YExxIVS.
ad distanciam F P, tempore suo periodico CAD BC dierum 27.
hor. 7. min. 4.3. rerolvi DoNeE, CHICCrCE UE COrpUS, tempOre CL
cadendo, delcriberet lonsitudinem =C F, e velocicarem simul
aequireret aequalem relocitatis qua Luna in Orbe suO MOVCTUI.
Patet hoc per Corol. 9. Prov. Ir. Lib. l. Cum autem perpen-
diculum Xa in T F demissum (IE ipBUS F L ParS certia, e ip.
AuS TD seu M L. in Octantibus pars dimidia, vis PL. in Octan-
tibus, ubi maxima est, superabie vim MI. in racionc 3 2d 2,
adeoque erit ad vim illam, qua Luna tempore luo periodico circa
Terram quiescentem revolvi posset, ut 100 4d 3X 178722 Peu
TI9T5, et tempore C. F relocitatem generare deberet quae cACE
pars igrs velocitatis Lunaris, tempore autem C F A velociratem
100
majorem generaret in ratione C A ad CF (Cu TP. ExPONatuE
vis maxima F L. in Octantibus per arcam FRX Rk rectangulo
ETPX Pp aequalem. Ec relocitas, quam vis maxima tempore
quoris CF gencrare poslet, erit ad relocitatem quam vis omnis
minor P.L. eodem tempore generat, ur rectangulum 2T PXC P
ad aream RCCF F: TCMPOTE aULEM EOEO C F A, velocitates se-
nicae crune ad inricem ue rectangulum =T P XC A ec triangulum
TCC, Sive ut arcus quadrantalis C A e radius FP. Ideoque
(Per PrOP. IX. Lib. V. Elem.) relocitas PoleriOE, FOtO tempOrO
700
genitas erit pars =19r velocitatis Lune. Hluic Lunae velocitatis
quae arexe momento medioeri analosa eA, addatur e auteratur
dimidium relocitatis alcerius; ec Ei momentum medioere expona-
CuE per numerum 119I5, Tumma 219Y5 + 50 Tcu 11965 exhri-
bebie momentum maximum arex in Syzygia A, ac differentia
21915 = 50 (cu 11865 ejusdem momencum minimum in Ouadra-
curis. Isitur arex temporibus aequalibus in Syzygiis ec Guadra-
curis descripea, sune ad inricem ut 11965 ad 11865. A. d mo-
mencum minimum 17865 addatur momentum, quod sIc ad mo-
mentorum differentiam 100 uc trapezium FKCC C ad triangu-
Jum FCG (vel quod perinde eA, uc quadratum Sinus FR ad
quadratum Radii TP, id eAt, uc Pd. ad ZF) e summa extri-
bebit momencum arexe, ubi Luna est in loco quoris interme-
dio F.
Hxec omnia ita se habene, ex Hypocheli quod Sol et Terra qui-
elcune, et Luna cempore Synodico dierum 27. Bor. 7. min. 43. re-
volvIII. Cum autem periodus Synodica LUnaTIS VerC lC d
rum