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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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PHITLOSOPMILE NATDRALIS
Corol. 5. Fadem ralene ubi attractio oritur a Sphaerae utriusque
vircute actractira, mutuo exercita in Sphaeram alteram. Nam viri-
bus ambabus seminatur atrractio, provortione servata.
Corol. 6. Si hujusmodi Sphaera aligua circa alias quiescentes re-
volvancur, singulae circa singulas, sintque dictantixe inter centra re-
volrencium ec quielcentium proportionales quielcentium diame-
eris; aequalia crunt Tempora periodica.
Corol. 7. FF vicissim, Si Tempora periodica sunt aequalia; dictan-
tiae crunt proportionales diametris.
Corol. 8. Eadem omnia, quae superius de motu corporum circa
umbilicos Conicarum Sectionum demonstraca lune, obtinene ubi
Sphaera actrahens, Formae ec conditionis cujulris jam descriptae, l0.
catur in umbilico.
Corol. 9. VE _ ubi srrantia lune etiam SphXrA aFETAhENECS, COn-
dicionis cujulris jam descripex.
PROPOSITTO LHRVII TTTEOREMA XXXVII.
Si ad sincula Sphaerarum puncta tendant vires centripetae, propor-
tionales distantiis punctorum a corporibus attractis: dico quod
vis composita, qua Sphaerae duae se mutuo trahent, est ut di-
stantia inter centra Sphaerarum.
Cas. 1. Sit AF. BF SphEra, S
centrum ejus, F corpusculum aE-
cractum, P ASB axis Sphaera Per
centrum corpusculi Eran(ICMS, L P,
ef plana duo quibus Sphaera se
catur, huic axi perpendicularia ex
hinc inde aequalicer distantia 2
centro Sphaerae; C e interlectio
nes planorum ec axis, ec II pun-
ctum quodris in plano F F. Pun-
Eti TIvis centripeta in corpusculum P, secundum lineam F IV exer.
cita, est uc distantia PFI; Xc (per Legum C Orol. 2.) Secundum li-
neam F C, Peu vertus centrum S, ut lonsitudo PCF. Igieur pun-
ctorum omnium in plano P F, hoc est plani torius vis, qua corpuI-
culum P trahitur versus centrum S, est ut numerus punctorum
ductus in distanciam PG: id est, ut contencum sub plano ip(0 P F
ec distancia illa PC. Ec similiter ris plani ef, qua corpulculum P
DF MOZV
1. 9 et 
etaltlec