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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 103, page id 1041163592:0137
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PRINOIPTA MATHEMATICA.
nolcatur quantitas areae ab scindendxe tempori proportionalis. Oit Cd
L. IBCH
A, ex tiac conjectura de posirione rectae SP, qua aream APS Pnimos.
abscindat vera proximam. Jun-
SaCUE OP, et 2b A ec F
ad
AIYMPEOTOn, aganEUE AI, FX
aCrmproco alteri parallelae, ec per
Tabulam Logarichmorum dabi-
Eur ArCa ATR P, eique aqualis
arca O P A, quae subducta de rri-
ansulo O P Srelinquet aream ab-
Scintam AP S. Applicando arCX
abscindendae A d abscina AZ S
differenciam duplam 2 A FS-
vel 2 A = 2 A=S ad lincam SN, quae ab umbilico s’in tangentem
T Derpendicularis eA, orietur longitudo chordae P9. Inseri-
batur aurem chorda illa F Q inter  e P, R arca abscitTa AFS
major sic arca abscindenda A, secuS ad puncti F COnETATIaS PAFECS:
ex punctum e erit locus corporis accuratior. Et computatione
repetica invenietur idem accurarior in perpetuum.
Acque his caleulis Problema generalieer ConAit Analrtice. Ve-
rum ulibus Astronomieis accommodatior eAt calculus particularis
qui sequitur. Existentibus AO, OB, O D Cemiaxibus HIlip(COS, ec
L ipsius lacere recto, ac D disterentia inter semiaxem minorem O D
de lateris recti semissem EL; quaere cum ansulum Y, cujus lInUS.
SIc ad Radtium uc cAt rectangu-
lum Cub differencia illa D, ec
semisumma axium A0 +O D
ad quadratum axis majoris AB;
cum angulum Z, cujus SInuS
sic ad Kadium ut est duplum
rectangulum sub umbilicorum
distantia SFI e differentia
illa D ad criplum quadratum
semiaxis majoris AO. FIIS
ansulis semel invencis; locus corporis sic deincers determinabitur.
Sume angulum T proportionalem cempori quo arcus B P deserip-
cus eAt, Icu motui medio (ut loguuntur) aequalem; dc angulum.
Primam medii mocus aequarionem) ad angulum Y (aequatio.
nem maximam primam) uc est sinus dupli ansuli P ad Radium;
cque
O3