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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 101, page id 1041163592:0135
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PRIMOIPTA MATETEMATTCA
TC+
Duo Facto, capC G K in ratione ad ROEx perimerrum GI F F G, UF
LIBEB
et tempus quo corpus progrediendo ab A descripsit arcum AP, ad P1 1 M Vi
tempus revolutionis unius in EllipIi. Frisatur perpendiculum L L
Occurrens Trochoidi in L, _c acta L. P ip(I R G paraIlela OCCUTEOE
FIlipsi in corporis loco qualto P.
Nam cenero O, intervallo O  describatur Cemicirculus AQB,
dc arcui AQ OCCUTTAE L F produera in Q junGanEUTque S, OL
ArCuI F F C OCCuTraE O Q in P, _ incandem O O deMIETatuIE Per-
pendiculum SR. ArCa A PS CA UE arca AOS, id est, ut dise.
rentia inter sectorem O A e triangulum O e S, sire ut disteren-
tia rectangulorum Z O9) X Ad) ec =O_X SR, hoc clt, ob datam
2O9 uc differentia inter arcum  dc rectam SR, adeoque (0b
aequalicatem datarum rationum SR ad sinum arcUS  G, OS ad O A,
Aad OG, AD 2dG F, ec dirisim AG = S R ad G F = sIn. aEC. AQ)
uc C K difterentia inter arcum C F ec sinum arcus AB. 8. F. D.
Scholium.
Eaeterum, cum difficilis siE hujus Currae deleriptio, praeltat (Olu-
tionem vero proximam adhibere. Inveniatur cum angulus quidam
B, qui sic ad angulum oradtuum 57, 29578. Quem arcus radio equalis
Tubrendit, ut est umbilicorum distantia SII ad Ellipseos diame-
erum AB; cum etiam longitudo quaedam L, quae sE ad radium in
cadem ratione inverse. Quibus semel invencis, Problema deinceps
contit per sequentem Analysin. Per constructionem quamvis (vel
uccunque conscc-
curam faciendo;
CognOlcaEUE COF-
Porislocus P pro-
ximus vero ejus lo-
cop. Demissaque ad
axem LllipscOS Or-
dinatim applicata
P R, CX PTOPOr-
tione diametrorum
FIlipseOS, dabitur
Circuli circumseri-
Dei AQ B ordinatim applicata il Q Gu inus est anguli AO Q exi
tente AO radio. Susticir angulum illum rudi calculo in numeris
Creximis invenire. Cognolcatur etiam angulus tempori propor.
io