Newton, Isaac - Philosophia naturalis principia mathematica

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1noſcatur quantitas areæ abſcindendæ tempori proportionalis. Sit ea
A, & fiat conjectura de poſitione rectæ SP,quæ aream APS
abſcindat veræ proximam. Jun

77[Figure 77]
gatur OP,& ab A& Pad
Aſymptoton agantur AI, PK
Aſymptoto alteri parallelæ, & per
Tabulam Logarithmorum dabi
tur Area AIKP,eique æqualis
area OPA,quæ ſubducta de tri
angulo OPSrelinquet aream ab
ſciſſam APS.Applicando areæ
abſcindendæ A & abſciſſæ APS
differentiam duplam 2 APS-2 A
vel 2 A-2 APSad lineam SN,quæ ab umbilico Sin tangentem
PTperpendicularis eſt, orietur longitudo chordæ PqueInſcri
batur autem chorda illa PQinter A& P,ſi area abſciſſa APS
major ſit area abſcindenda A, ſecus ad puncti Pcontrarias partes:
& punctum Qerit locus corporis accuratior. Et computatione
repetita invenietur idem accuratior in perpetuum.

LIBER
PRIMUS.

Atque his calculis Problema generaliter confit Analytice. Ve
rum uſibus Aſtronomicis accommodatior eſt calculus particularis
qui ſequitur. Exiſtentibus AO, OB, ODſemiaxibus Ellipſeos, &
L ipſius latere recto, ac D differentia inter ſemiaxem minorem OD
& lateris recti ſemiſſem 1/2 L; quære tum angulum Y, cujus ſinus
ſit ad Radium ut eſt rectangu

78[Figure 78]
lum ſub differentia illa D, &
ſemiſumma axium AO+OD
ad quadratum axis majoris AB;
tum angulum Z, cujus ſinus
ſit ad Radium ut eſt duplum
rectangulum ſub umbilieorum
diſtantia SH& differentia
illa D ad triplum quadratum
ſemiaxis majoris AO.His
angulis ſemel inventis; locus corporis ſic deinceps determinabitur.
Sume angulum T proportionalem tempori quo arcus BPdeſcrip
tus eſt, ſcu motui medio (ut loquuntur) æqualem; & angulum
V (primam medii motus æquationem) ad angulum Y (æquatio
nem maximam primam) ut eſt ſinus dupli anguli T ad Radium;

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