Philosophiae naturalis principia mathematica . unBo altquo A, in medto curvatura conti- nu£, tangatur a reBa utrtnque pro- duBa A D ^ deinpunBa A, B adinvi- R cem accedant ^ coeant; dico quodan- gulus BAD, [uh chorda ^ tangente contentusy minuetur in infinitum &* ulttmo evanefcet. Nam fi angulus ille non evanefcit, continebit arcus ^B cum tan-gente AT> angulum redilineo aequalem, & propterea curvatura adpunftum A non erit continua, contra hypothefin. L E M M A VII. Ttfdem pofitis; dico quod tdtima ratio arcus, chordae ^ &^tangentis ad invicem efi ratio aqualttatts. Nam dum pundlum B ad punf

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Philosophiae naturalis principia mathematica . unBo altquo A, in medto curvatura conti- nu£, tangatur a reBa utrtnque pro- duBa A D ^ deinpunBa A, B adinvi- R cem accedant ^ coeant; dico quodan- gulus BAD, [uh chorda ^ tangente contentusy minuetur in infinitum &* ulttmo evanefcet. Nam fi angulus ille non evanefcit, continebit arcus ^B cum tan-gente AT> angulum redilineo aequalem, & propterea curvatura adpunftum A non erit continua, contra hypothefin. L E M M A VII. Ttfdem pofitis; dico quod tdtima ratio arcus, chordae ^ &^tangentis ad invicem efi ratio aqualttatts. Nam dum pundlum B ad punftum yfaccedit, intelligantur fem-per A & Al^ ad punfta longinqua b ^z d produci, & fecanti BT)parallela agatur bd. Sitque arcus Ab femper fimilis arcui punftis A^ B coeuntibus, angulus dAb., per Lemma fuperius,evanefcet; adeoque reftae femper finitae Ab, Ad & arcus interme-dius Ab coincident, & propterea aequales erunt. Unde & hifcefemper proportionales reds AB, AD, S>l arcus intermedius ^5 D X eva-. a8 NATURALIS

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