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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 176, page id 1041163592:0210
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176
PHIILOSOPMIIH NATORALIS
Ot Moro verse. Sed particulae sunE ut Sphaerae, hoc est, in ratione tripsicgru
conxorom diametrorum, ec distantix sunc uc diametri, et ratio prior directe
una cum ratione posteriore bis inverse est ratio diametri ad diame-
trum. d. F. D.
Corol. T. Fiinc Si corpuscula in Circulis, circa Sphaeras ex materia
aequaliter actractira constantes, revolvantur; sintque distantix a cen-
eris Sphaerarum proportionales carundem diametris: Tempora peri-
odica crune aequalia.
Corol. 2. FF vice versa, si Tempora periodica sune aequalia;
dictantix erune proportionales diamerris. Constane lxec duo per
COrol. 3. PFOP. IV.
Corol. 3. Si ad Solidorum duorum quorumris similium ec aequali-
ter denlorum puncta singula tendane rires aequales centripetae de-
crescentes in duplicata ratione dictanciarum a punctis: vires qui-
bus corpuscula, ad Solida illa duo similiter sicas atcrahentur ab iis-
dem, erunt ad inricem ut diametri Solidorum.
PROPOSITIO LXXIII. THEOREMA XXXIII
Si ad Sphaerae alicujus datae puncta singula tendant aequales vires
centripetae decrescentes in duplicata ratione distantiarum a pun
Etis: dico quod corpusculum intra Sphaeram consticurum attra-
bitur vi proporcionali distantia suae ab ipsus centro.
In Sphaera ABC D, cenero S descripta,
locetur corpusculum P; e centro codem S,
interrallo SP, concipe Sphaeram interiorem
PF. QF describi. Manitectum CA, per PFOP.
EXX, Quod Sphaericae Superticics concentri-
eae ex quibus Sphaerarum disterentia AF. B
componitur attractionibus per attractiones
contrarias destructis, nil agunt in corpus
P. Restat sola acrractio Sphaerae interioris
PF QF. RE PEF PFOD, LXXFT, haeC CA ut
distantia FS. d. F. D.
Scholium.
Superficies ex quibus Colida componuntur, hic non sunt pure
Machemarica, sed Orbes adeo tenues ut eorum crassitudo inctar
ldt