Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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mus, ſunt ad invicem ut 1 ad 59,575. Ergo cum motus medius
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horarius Lunæ (reſpectu fixarum) ſit 32′. </
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<
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>56″. </
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<
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>27′. </
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<
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>12
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iv
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1/2, motus
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horarius Nodi in hoc caſu erit 33″. </
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<
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>10′. </
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<
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>33
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iv
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. </
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>12
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v
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. </
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<
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>Aliis autem in
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caſibus motus iſte horarius erit ad 33″. </
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<
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>10′. </
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<
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>33
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iv
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. </
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>12
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v
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. </
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<
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tum ſub ſinubus angulorum trium
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TPI, PTN,
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&
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STN
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(ſeu
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diſtantiarum Lunæ a Quadratura, Lunæ a Nodo, & Nodi a Sole)
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ad cubum Radii. </
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<
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>Et quoties ſignum anguli alicujus de affirmativo
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in negativum, deque negativo in affirmativum mutatur, debebit
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motus regreſſivus in progreſſivum & progreſſivus in regreſſivum
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mutari. </
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<
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>Unde fit ut Nodi progrediantur quoties Luna inter Qua
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draturam alterutram & Nodum Quadraturæ proximum verſatur. </
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<
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Aliis in caſibus regrediuntur, & per exceſſum regreſſus ſupra pro
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greſſum, ſingulis menſibus ſeruntur in antecedentia. </
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DE MUNDI
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SYSTEMATE</
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Corol.
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1. Hinc ſi a dati arcus quam minimi
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PM
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terminis
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P
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&
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M
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ad lineam Quadraturas jungentem
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Qq
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demittantur perpen
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dicula
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PK, Mk,
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eademque producantur donec ſecent lineam
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Nodorum
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Nn
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in
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D
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&
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d
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; erit motus horarius Nodorum ut area
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MPDd
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& quadratum lineæ
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AZ
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conjunctim. </
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<
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>Sunto enim
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PK, PH
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&
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AZ
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prædicti tres ſinus. </
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<
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>Nempe
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PK
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ſinus di
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ſtantiæ Lunæ a Quadratura,
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PH
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ſinus diſtantiæ Lunæ a Nodo, &
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AZ
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ſinus diſtantiæ Nodi a Sole: & erit velocitas Nodi ut conten
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tum
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PKXPHXAZ.
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Eſt autem
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PT
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ad
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PK
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ut
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PM
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ad
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Kk,
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adeoque ob datas
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PT
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&
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PM
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eſt
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Kk
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ipſi
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PK
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proportionalis. </
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Eſt &
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AT
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ad
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PD
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ut
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AZ
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ad
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PH,
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& propterea
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PH
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rectangulo </
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