Newton, Isaac - Philosophia naturalis principia mathematica

Corol.1. Eſt igitur Rræqualis (DRXAB/N)-(RDGT/N), ideoque
ſi producatur RTad Xut ſit RXæqualis (DRXAB/N), (id eſt, ſi
compleatur parallelogrammum ACPY,jungatur DYſecans CP
in Z,& producatur RTdonec occurrat DYin X;) erit Xræqua
lis (RDGT/N), & propterea tempori proportionalis.

LIBER
SECUNDUS.

Corol.2. Unde ſi capiantur innumeræ CRvel, quod perinde eſt,
innumeræ ZX,in progreſſione Geometrica; erunt totidem Xrin
progreſſione Arithmetica. Et hinc Curva DraFper tabulam Lo
garithmorum facile delineatur.

Corol.3. Si vertice D,diametro DEdeorſum producta, & La
tere recto quod ſit ad 2DPut reſiſtentia tota, ipſo motus initio,
ad vim gravitatis, Parabola conſtruatur: velocitas quacum corpus
exire debet de loco Dſecundum rectam DP,ut in Medio uNI
formi reſiſtente deſcribat Curvam DraF,ea ipſa erit quacum ex
ire debet de eodem loco D,ſecundum eandem rectam DP,ut
in ſpatio non reſiſtente deſcribat Parabolam. Nam Latus re
ctum Parabolæ hujus, ipſo motus initio, eſt (DVquad./Vr) & Vr
eſt (tGT/N) ſeu (DRXTt/2N). Recta autem quæ, ſi duceretur, Hy
perbolam GTBtangeret in G,parallela eſt ipſi DK,ideoque
Tteſt (CKXDR/DC) & N erat (QBXDC/CP). Et propterea Vreſt
(DRqXCKXCP/2DCqXQB), id eſt, (ob proportionales DR& DC, DV
& DP) (DVqXCKXCP/2DPqXQB), & Latus rectum (DVquad./Vr) prodit
(2DPqXQB/CKXCP), id eſt (ob proportionales QB& CK, DA& AC)
(2DPqXDA/ACXCP), adeoque ad 2 DP,ut DPXDAad CPXAC; hoc
eſt, ut reſiſtentia ad gravitatem. Q.E.D.

Corol.4. Unde ſi corpus de loco quovis D,data cum velocitate,
ſecundum rectam quamvis poſitione datam DPprojiciatur; & re
ſiſtentia Medii ipſo motus initio detur: inveniri poteſt Curva
DraF,quam corpus idem deſcribet. Nam ex data velocitate

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