Philosophiae naturalis principia mathematica . Si reSia AE & Cur-va A C pofitione dat£ fe mutno fecent in angufo dato Ay <& ad reSiam illam in alio dato angulo ordinalim ap- plicentur B Dy E C, curvte oc- currentesjn B, C; dem punSia B, C accedatit ad punSinm A: dico quod area triangulorum ADB, AEC ernnt ultimo ad invicem in cUtplicata ratione la- terum. Etenimin AD producra ca-piantur Ad, Ae ipfis AD, AEproportionalesj Sc erigantur or- dinatas db, ecordinatis DB, EC parallelx & proporcionalesjProducatur AC ad r, ducatur curva Abcipfi ABC fimilis, 8crecla Ag tangatur- ciirva utraq? in A; &f
Philosophiae naturalis principia mathematica . Si reSia AE & Cur-va A C pofitione dat£ fe mutno fecent in angufo dato Ay <& ad reSiam illam in alio dato angulo ordinalim ap- plicentur B Dy E C, curvte oc- currentesjn B, C; dem punSia B, C accedatit ad punSinm A: dico quod area triangulorum ADB, AEC ernnt ultimo ad invicem in cUtplicata ratione la- terum. Etenimin AD producra ca-piantur Ad, Ae ipfis AD, AEproportionalesj Sc erigantur or- dinatas db, ecordinatis DB, EC parallelx & proporcionalesjProducatur AC ad r, ducatur curva Abcipfi ABC fimilis, 8crecla Ag tangatur- ciirva utraq? in A; &fecantur ordinatim appli-catse in F, G, f, g. Tum coeant puncla B, C cum puncro A, &anguloc Ag evanefcente, coincident areae curviliheae Abd, Acecum rectilineis Afd, A^ e, adeoq; per Lemma V, erunt m du- glicata. C v ] plicata rationc laterum Ad, Ae\ Sed-his areis proportionalesfemper funt arcse ABD^ ACE, & his lateribus latera y4 D, & areae ABD, ACE funt ultimo in duplicata ratione late-rumADjAE. Lemma X. Spatia^ qitjc corpus urgente quacitnq\ vi regulari defcribit^ funt ipfomotus initio in duplicata ratione temporum. Exponantur tempora per lineas A D, A E, & velocitates geni-tx per ordinatas D By E (7, & fpatia his velocitatibus defcriptaerunt ut arese ABD, ACE his ordinatis defcriptse, hoc eft ipfomotus initio ( per Lemma IX ) in duplicata ratione temporumAD, Corol. i. Et hinc facile colligitur, quod corporum ftrailes (inii-lium figurarum partes temporibusproportionalibusdefcribentiumerrores, qui viribus sequalibus in partibus iftis ad corpora fimiliterapplicatis generantur, & menfurantur a locis figurarum, ad qusecorpora temporibus ijfdem proportionalibus abfq; viiibus iftis per-venirent, funt ut quadrata temporum in quibus generantur quamproxim
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