bolicam; ſecunda 1/2SIaream 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, Berige
perpendicula Ll, Aa, Ss, Bb,quo
rum Ssipſi SIæquetur, 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.
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, Berige
perpendicula Ll, Aa, Ss, Bb,quo
rum Ssipſi SIæquetur, 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
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 Pin Sphæræ centrum trahitur, eſt ut (SIcub/PI),id eſt,
reciproce ut PS cubXPI. que E. I.
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 Pin 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.
tra Sphæram, ſed expeditius per Theorema ſequens.
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