Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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& collatis numeratorum terminis, fiet RGG-RFF+TFF
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, ut -FF ad -
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&c. </
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mas quæ prodeunt ubi Orbes ad formam circularem accedunt, fit
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GG ad
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, ut FF ad
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, &
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viciſſim GG ad FF ut
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ad
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Quæ proportio, exponendo altitudinem maximam
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CV
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ſeu T Arith
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metice per Unitatem, fit GG ad FF ut
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b+c
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ad
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mb+nc,
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adeoque ut
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1 ad (
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mb+nc/b+c
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). Unde eſt G ad F, id eſt angulus
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VCp
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ad angulum
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VCP,
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ut 1 ad √(
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). Et propterea cum angulus
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VCP
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inter
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Apſidem ſummam & Apſidem imam in Ellipſi immobili ſit 180
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gr.
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erit angulus
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inter eaſdem Apſides, in Orbe quem corpus vi
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centripeta quantitati (
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A
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/A
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cub.
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) proportionali deſcribit, æqua
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lis angulo graduum 180 √(
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b+c/mb+nc
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). Et eodem argumento ſi vis cen
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tripeta ſit ut (
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/A
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cub.
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), angulus inter Apſides invenietur graduum
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180 √(
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b-c/mb-nc
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). Nec ſecus reſolvetur Problema in caſibus diffi
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cilioribus. </
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ſolvi ſemper debet in Series convergentes denominatorem ha
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bentes A
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cub.
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Dein pars data numeratoris qui ex illa operatione
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provenit ad ipſius partem alteram non datam, & pars data nu
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meratoris hujus RGG-RFF+TFF-FFX ad ipſius partem
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alteram non datam in eadem ratione ponendæ ſunt: Et quantitates
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ſuperfluas delendo, ſcribendoque Unitatem pro T, obtinebitur
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proportio G ad F. </
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LIBER
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PRIMUS.</
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Corol.
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1. Hinc ſi vis centripeta ſit ut aliqua altitudinis digNI
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tas, inveniri poteſt dignitas illa ex motu Apſidum; & contra. </
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Nimirum ſi motus totus angularis, quo corpus redit ad Apſidem
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eandem, ſit ad motum angularem revolutionis unius, ſeu graduum
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360, ut numerus aliquis
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m
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ad numerum alium
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n,
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& altitudo no
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minetur A: erit vis ut altitudinis dignitas illa A
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(
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nn/mm
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)-3
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, cujus In-</
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