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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 35, page id 1041163592:0069
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11
PRINCTPTA MATHIEMATICA.
eodem plano cum criangulo ASB. Junge SC; ee criangulum SBC,
LotB b. R
ob parallelas SB, C.6, aequale crit criangulo S’BC, atque adeoetiam earuv
erianoulo SAB. Simili arQUMeNEO EI viS CenEriPCEA LACCCNIre aZ2E
in C, D, F, _C. Faciens ut corpus singulis temporis particulis (in-
sulas describat rectas C D, DF, F F, _C. JacebunE hx omnes in
eodem plano; ex trianoulum SC D criangulo SBC, eE SD F iDl
SCD, e SF F ipsI SD L aequale crit. A. qualibus igitur cempori-
bus aequales arexe in plano immoto describuntur: et componendo,
Tunt arcarum Cummae quaeris S ADS, SAFS INteF CC, UE CUHE TeM-
Pora descriptionum. Augeatur jam numerus de minuatur lacitudo
criangulorum in infinitum; ex corum ultima perimeter AD) H, (per
Corollarium quartum Lemmatis tertii) crie linca curra: adeoque vis
centripeta, qua corpus a tangente hujus currae perpetuo retrahitur,
aset indesinenter; areae vero quaeris descripia S ADS, SAFS
cemporibus descriptionum semper proportionales, crunt iildem tem-
Poribus in hoc casu provorcionales. . P. D
Corol. T. Velocitas corporis in centrum immobile aetracti est in
Spatiisnon resistentibus reciproce ut perpendiculum a centro illo in
Orbis tangencem rectilincam demissum. E s enim velocitas in locis
illis A, B, C, D, E, ut sunc bases aequalium triangulorum AB, BC.
CD, DE, F F; ec hxe bales sunt reciproce ut perpendicula in ip(as
demicta.
Corol. 2. Si arcuum duorum aequalibus cemporibus in spatiis non
relistentibus ab eodem corpore succestire descriptorum chorda AB,
BC compleancur in parallelogrammum ABCV, et hujus diagona
lis BC in ca positione quam ulcimo habet ubi arcus illi in intini-
cum diminuuntur, producatur utrinque; cransibit cadem per cen
erum virium.
Corol. 3. Si arcuum aequalibus temporibus in spaciis non resicten-
cibus descripeorum chordae AB, BC aC D F, F. F compleantur in
Parallelogramma ABCV, D P. PZ; vires in B e P. sunc ad invi-
cem in ultima ratione diagonalium BV, P. Z, ubi arcus icti in infi-
nicum diminuuneur. Nam corporis motus BC ex F. Fcomponun-
cur (per Legum Corol. P.) ex mocibus B5, BV et F. F, F. Z: ac-
qui BV _ P Z, ipsS Cc e Ff aequales, in Demonstratione Pro-
positionis hujus generabantur ab impulsibus ris centripetae in B e
 ideoque sunt his impulsibus proportionales.
Corol. 4. Vires quibus corpora qualibet in spaciis non resistenti.
bus a mocibus rectilineis retrahuntur ac detorquentur in orbes cur-
vos sunt inter se ue arcuum aequalibus temporibus descripeorum la
Sicexe illae quae conversunt ad centrum ririum, ex chordas bisccant
1b
A.1F
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