Newton, Isaac - Philosophia naturalis principia mathematica

Exempl.1. Si vis centripeta ad ſingulas Sphæræ particulas ten
dens ſit reciproce ut diſtantia; pro V ſcribe diſtantiam PE; dein
2PSXLDpro PEq,& fiet DNut SL-1/2LD-(ALB/2LD).
Pone DNæqualem duplo ejus 2SL-LD-(ALB/LD): & ordinatæ
pars data 2SLducta in longitudinem ABdeſcribet aream rectan
gulam 2SLXAB; & pars indefinita LDducta normaliter in
eandem longitudinem per motum continuum, ea lege ut inter mo
vendum creſcendo vel decreſcendo æquetur ſemper longitudini
LD,deſcribet aream (LBq-LAq/2), id eſt, aream SLXAB; quæ
ſubducta de area priore 2SLXABrelinquit aream SLXAB.
Pars autem tertia (ALB/LD) ducta itidem per motum localem norma
liter in eandem longitudinem, deſcribet

122[Figure 122]
aream Hyperbolicam; quæ ſubducta de
area SLXABrelinquet aream quæſitam
ABNA.Unde talis emergit Proble
matis conſtructio. Ad puncta L, A, B
erige perpendicula Ll, Aa, Bb,quorum
Aaipſi LB,& Bbipſi LAæquetur.
Aſymptotis Ll, LB,per puncta a, bde
ſcribatur Hyperbola ab.Et acta chor
da baclaudet aream abaareæ quæſitæ
ABNAæqualem.

Exempl.2. Si vis centripeta ad ſingulas Sphæræ particulas ten
dens ſit reciproce ut cubus diſtantiæ, vel (quod perinde eſt) ut cubus
ille applicatus ad planum quodvis datum; ſcribe (PEcub/2ASq) pro V,
dein 2PSXLDpro PEq; & fiet DNut (SLXASq/PSXLD)-(ASq/2PS)
-(ALBXASq/2PSXLDq),id eſt (ob continue proportionales PS, AS, SI)
ut (LSI/LD)-1/2SI-(ALBXSI/2LDq).Si ducantur hujus partes tres
in longitudinem AB,prima (LSI/LD) generabit aream Hyper-

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