Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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noſcatur quantitas areæ abſcindendæ tempori proportionalis. </
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<
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A, & fiat conjectura de poſitione rectæ
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SP,
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quæ aream
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APS
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abſcindat veræ proximam. </
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gatur
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OP,
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& ab
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A
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&
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P
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ad
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Aſymptoton agantur
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AI, PK
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Aſymptoto alteri parallelæ, & per
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Tabulam Logarithmorum dabi
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tur Area
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AIKP,
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eique æqualis
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area
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OPA,
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quæ ſubducta de tri
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angulo
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OPS
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relinquet aream ab
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ſciſſam
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APS.
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Applicando areæ
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abſcindendæ A & abſciſſæ
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APS
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differentiam duplam 2
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-2 A
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vel 2 A-2
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APS
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ad lineam
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SN,
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quæ ab umbilico
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S
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in tangentem
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PT
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perpendicularis eſt, orietur longitudo chordæ
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<
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">Pque</
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Inſcri
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batur autem chorda illa
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PQ
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inter
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A
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&
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P,
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ſi area abſciſſa
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APS
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major ſit area abſcindenda A, ſecus ad puncti
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P
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contrarias partes:
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& punctum
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Q
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erit locus corporis accuratior. </
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<
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>Et computatione
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repetita invenietur idem accuratior in perpetuum. </
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LIBER
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PRIMUS.</
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<
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>Atque his calculis Problema generaliter confit Analytice. </
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<
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>Ve
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rum uſibus Aſtronomicis accommodatior eſt calculus particularis
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qui ſequitur. </
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<
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>Exiſtentibus
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AO, OB, OD
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ſemiaxibus Ellipſeos, &
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L ipſius latere recto, ac D differentia inter ſemiaxem minorem
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OD
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<
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& lateris recti ſemiſſem 1/2 L; quære tum angulum Y, cujus ſinus
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ſit ad Radium ut eſt rectangu
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lum ſub differentia illa D, &
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ſemiſumma axium
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AO+OD
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ad quadratum axis majoris
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AB
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;
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tum angulum Z, cujus ſinus
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ſit ad Radium ut eſt duplum
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rectangulum ſub umbilieorum
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diſtantia
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SH
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& differentia
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illa D ad triplum quadratum
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ſemiaxis majoris
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AO.
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His
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angulis ſemel inventis; locus corporis ſic deinceps determinabitur. </
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Sume angulum T proportionalem tempori quo arcus
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BP
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deſcrip
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tus eſt, ſcu motui medio (ut loquuntur) æqualem; & angulum
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V (primam medii motus æquationem) ad angulum Y (æquatio
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nem maximam primam) ut eſt ſinus dupli anguli T ad Radium; </
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