Newton, Isaac - Philosophia naturalis principia mathematica

Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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bolicam; ſecunda 1/2SI aream 1/2ABXSI; tertia (ALBXSI/2LDq) are
am (ALBXSI/2LA)-(ALBXSI/2LB),id eſt 1/2ABXSI.De prima ſub
ducatur ſumma ſecundæ & tertiæ, &

123[Figure 123]
manebit area quæſita ABNA.Un
de talis emergit Problematis conſtru
ctio. Ad puncta L, A, S, B erige
perpendicula Ll, Aa, Ss, Bb,quo
rum Ssipſi SI æquetur, perque pun
ctum sAſymptotis Ll, LBdeſcri
batur Hyperbola asboccurrens per
pendiculis Aa, Bbin a& b; & rect
angulum 2ASIſubductum de area
Hyperbolica AasbBreliquet aream
quæſitam ABNA.

DE MOTU
CORPORUM

Exempl.3. Si Vis centripeta, ad ſingulas Sphæræ particulas
tendens, decreſcit in quadruplicata ratione diſtantiæ a particulis;
ſcribe (PEqq/2AScub) pro V, dein √2PSXLDpro PE,& fiet DNut
(SIqXSL/√2SI)X(1/√LDc),-(SIq/2√2SI)X(1/√LD),-(SIqXALB/2√2SI)X(1/√LDqc).
Cujus tres partes ductæ in longitudinem AB,producunt areas tot
idem, viz. (2SIqXSL/√2SI) in (1/√LA)-(1/√LB); (SIq/√2SI)in √LB-√LA;
& (SIqXALB/3√2SI) in (1/√LAcub)-(1/√LBcub).Et hæ poſt debitam redu
ctionem fiunt (2SIqXSL/LI), SIq,& SIq+(2SIcub/3LI).Hæ vero, ſub
ctis poſterioribus de priore, evadunt (4SIcub/3LI). Igitur vis tota, qua
corpuſculum P in Sphæræ centrum trahitur, eſt ut (SIcub/PI),id eſt,
reciproce ut PS cubXPI. que E. I.

Eadem Methodo determinari poteſt Attractio corpuſculi ſiti in
tra Sphæram, ſed expeditius per Theorema ſequens.

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