Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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ut 1 ad √
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n.
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Quare cum angulus
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VCP,
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in deſcenſu corporis
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ab Apſide ſumma ad Apſidem imam in Ellipſi confectus, ſit
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graduum 180; conficietur angulus
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VCp,
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in deſcenſu corporis
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ab Apſide ſumma ad Apſidem imam, in Orbe propemodum Cir
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culari quem corpus quodvis vi centripeta dignitati A
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n
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-3
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pro
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portionali deſcribit, æqualis angulo graduum (180/√
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n
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); & hoc angulo
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repetito corpus redibit ab Apſide ima ad Apſidem ſummam, &
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ſic deinceps in infinitum. </
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<
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poris a centro, id eſt, ut A ſeu (A
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4
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/A
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3
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), erit
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n
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æqualis 4 & √
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n
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æqualis 2;
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adeoque angulus inter Apſidem ſummam & Apſidem imam æ
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qualis (180/2)
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gr.
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ſeu 90
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gr.
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Completa igitur quarta parte revolutio
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nis unius corpus perveniet ad Apſidem imam, & completa alia
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quarta parte ad Apſidem ſummam, & ſic deinceps per vices in
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infinitum. </
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>Id quod etiam ex Propoſitione x. </
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>manifeſtum eſt. </
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>Nam
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corpus urgente hac vi centripeta revolvetur in Ellipſi immobili,
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cujus centrum eſt in centro virium. </
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>Quod ſi vis centripeta ſit reci
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proce ut diſtantia, id eſt directe ut 1/A ſeu (A
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2
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/A
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3
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), erit
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æqualis 2, ad
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eoQ.E.I.ter Apſidem ſummam & imam angulus erit graduum (180/√2)
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ſeu 127
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gr.
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16
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m.
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45
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ſec.
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& propterea corpus tali vi revolvens, perpe
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tua anguli hujus repetitione, vicibus alternis ab Apſide ſumma ad
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imam & ab ima ad ſummam perveniet in æternum. </
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<
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>Porro ſi vis
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centripeta ſit reciproce ut latus quadrato-quadratum undecimæ
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dignitatis altitudinis, id eſt reciproce ut A (11/4), adeoQ.E.D.recte ut
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(1/A
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11/4
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) ſeu ut (A
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1/4
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/A
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3
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) erit
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n
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æqualis 1/4, & (180/√
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n
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)
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gr.
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æqualis 360
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gr.
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& prop
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terea corpus de Apſide ſumma diſcedens & ſubinde perpetuo de
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ſcendens, perveniet ad Apſidem imam ubi complevit revolutionem
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integram, dein perpetuo aſcenſu complendo aliam revolutionem in
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regram, redibit ad Apſidem ſummam: & ſic per vices in æternum. </
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DE MOTU
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CORPORUM</
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Exempl.
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3. Aſſumentes
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m
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&
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pro quibuſvis indicibus dignitatum
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Altitudinis, &
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b, c
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pro numeris quibuſvis datis, ponamus vim cen
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tripetam eſſe ut (
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b
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A
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m
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+
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c
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A
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n
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/A
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cub.
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), id eſt, ut (
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b
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in —T-X
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+
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c
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in —T-X
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/A
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cub.
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)
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ſeu (per eandem Methodum noſtram Serierum convergentium) ut
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(
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b
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T
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m
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+
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nc
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XT
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+(
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mm-mb
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/2)XXT
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m
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-2
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+(
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nn-nc
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/2)XXT
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-2
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&c.
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/A
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cub.
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