Philosophiae naturalis principia mathematica . ora urgenturfunt aequales fub initio & fpati-is defcrib ndis TR^ GL fem-per proportionales, atq^ adeo, (iaequantur 7 K ad L G,aequales inlocis TSc L; patet corpora iiladefcriberefpatia ST^HL sequa-lia fub initio, adeoqi fubinde per-gere aequaliter urgeri,& aequalia fpatia defcribere.Quare,per Prop.XXXVIII., tempus quo corpus defcribit arcum S7 eft ad tem-pus oicillationis unius, ut arcus HI ( tempus quo corpus H per-veniet ad L ) ad femicirculum HKM ( tempus quo corpus Hperveniet ad M.) Et velocitas corporis penduli in loco T eft advelocitatem ipl
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Philosophiae naturalis principia mathematica . ora urgenturfunt aequales fub initio & fpati-is defcrib ndis TR^ GL fem-per proportionales, atq^ adeo, (iaequantur 7 K ad L G, aequales inlocis TSc L; patet corpora iiladefcriberefpatia ST^HL sequa-lia fub initio, adeoqi fubinde per-gere aequaliter urgeri, & aequalia fpatia defcribere.Quare, per Prop.XXXVIII., tempus quo corpus defcribit arcum S7 eft ad tem-pus oicillationis unius, ut arcus HI ( tempus quo corpus H per-veniet ad L ) ad femicirculum HKM ( tempus quo corpus Hperveniet ad M.) Et velocitas corporis penduli in loco T eft advelocitatem iplius in loco infimo K, ( boc eft velocitas corporisH in loco L ad velocitatem ejus in loco G, feu incrementum mo-mentaneumlinex HL ad incrementum momentaneum lineaHG, arcubus H /, HK aequabili fluxu crefcentibus J) utordinatim ap- plicata LI ad radium GK, five ut V S K q. — T K q. ad SR. Unde cumin Ofcillationibus inaecjualibus defcribantur aequalibus rtmporibusarcus totis Ofcillationum arcubus proportionales, habentur ex datis W tem-. C 54].temporibus & velocitatcs & arcus defcripti in Ofcillationibus uni-verfis. Quae erant primo invenienda. Ofcillentur jam funipendula duo corpora in Cycloidibus inx-qualibus & earum femiarcubus aequales capiantur redtae GH, gb, centriiq, G, g 8c intervallis GH, gh defcribantur femicirculiHZKM, h%-m. Jn eorum diametris HM, hm capiantur li-neolae aequalesHT, hy, & erigantur normaliter 7~Z, ^xcircum-ferentiis occurrentes in Z & %. Quoniam corpora pendula fubinitio motus verfantur incircumferentia globi 00S, adeoq; a vi-ribus sequalibus urgentur in centrum, incipiuntq; dire£re verfuscentrum moveri, fpatia fimul confe&a aequalia erunt fub initio.Urgeantur igitur corpora H, h a viribus iiidem in H & h, fmtq;