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Si Sphaerae in progressu a centro ad circumferentiam sint utcun{que} dis∣similares & inaequabiles, in progressu vero per circuitum ad datam omnem a centro distantiam sint undi{que} similares; & vis attractiva puncti cujus{que} sit ut distantia corporis attracti: dico quod vis tota qua hujusmodi Sphaerae duae se mutuo trahunt sit proportionalis di∣stantiae inter centra Sphaerarum.
Demonstratur ex Propositione praecedente, eodem modo quo Propositio LXXVII. ex Propositione LXXV. demonstrata fuit.
Corol. Quae superius in Propositionibus X. & LXIV. de motu corporum circa centra Conicarum Sectionum demonstrata sunt, valent ubi attractiones omnes fiunt vi Corporum Sphaericorum, conditionis jam descriptae, sunt{que} corpora attracta Sphaerae con∣ditionis ejusdem.
Attractionum Casus duos insigniores jam dedi expositos; ni∣mirum ubi vires centripetae decrescunt in duplicata distantiarum ratione, vel crescunt in distantiarum ratione simplici; efficientes in utro{que} Casu ut corpora gyrentur in Conicis Sectionibus, & componentes corporum Sphaericorum vires centripetas eadem le∣ge in recessu a centro decrescentes vel crescentes cum seipsis. Quod est notatu dignum. Casus caeteros, qui conclusiones mi∣nus elegantes exhibent, sigillatim percurrere longum esset: Ma∣lim cunctos methodo generali simul comprehendere ac determi¦nare, ut sequitur.
Si describantur centro S circulus quilibet AEB, (Vide Fig. Prop. sequentis) & centro P circuli duo EF, ef, secantes priorem in E, e, lineam{que} PS in F, f; & ad PS demittantur perpendicula ED, ed: dico quod si distantia arcuum EF, ef in infinitum mi∣nui intelligatur, ratio ultima lineae evanescentis Dd ad lineam evanescentem Ff ea sit, quae lineae PE ad lineam PS.
Nam si linea Pe secet arcum EF in q; & recta Ee, quae cum arcu evanescente Ee coincidit, producta occurrat rectae PS in T; & ab S demittatur in PE normalis SG: ob similia triangula EDT, edt, EDS; erit Dd ad Ee ut DT ad ET seu DE ad