Philosophiae naturalis principia mathematica . coefficientem ipnus-^,)in^~, hoc eft, in i; & prodit ^i, numeralis coefficiens termini proxime inferioris: dein duco hunc ^^ in i^% five in ^, hoceft, in?; &pro- dit -A numeralis coefficiens tertii termini in illacolumna. Atqueiftai;! X fc f^^i^ 3ji numeralem coefficientem quarti termini; & 7, >^ -g— facit -^, numeralem coefficlentrm infi ni rermini. Idem in aliis ad in-finitum uique coluronis praeftari poteft : Adeoque valor ipfiui DGper hanc Regulam pro lubitu produci. Adhsec, ti BF dicatur^, fitque r lacus reftum EUipfeos, &ff— — • Erit Arcu
Philosophiae naturalis principia mathematica . coefficientem ipnus-^,)in^~, hoc eft, in i; & prodit ^i, numeralis coefficiens termini proxime inferioris: dein duco hunc ^^ in i^% five in ^, hoceft, in?; &pro- dit -A numeralis coefficiens tertii termini in illacolumna. Atqueiftai;! X fc f^^i^ 3ji numeralem coefficientem quarti termini; & 7, >^ -g— facit -^, numeralem coefficlentrm infi ni rermini. Idem in aliis ad in-finitum uique coluronis praeftari poteft : Adeoque valor ipfiui DGper hanc Regulam pro lubitu produci. Adhsec, ti BF dicatur^, fitque r lacus reftum EUipfeos, &ff— — • Erit Arcus Ellipticus BG zz^^rx inT+ ^\^~ ^^ ^+ 4^1 — 10 ^ -77 ^\e] + ^e^ I — >.v% + &c. Quare, fi ambitus totius Ellipfeos defideretur; Bifeca CB in F,& quaere Arcum X)G, per prius Theorema, & Arcum BG perpof-terius. D a 6. Si 48 EPISTOLARUM 6. Si, vice verfa, ex dato arcu Ellipko DG, quaraturSinusejusCF; tum diao CDzir, ^ZIf, & arcu illo DGzz^; Erit CF_«2;—•^•3 —,o„3^ —r^^-^ ? & 504OC* Quse autem de Ellipfi difta funt, omnia facile accommodanturad Hyperbolam ; mutatis tantum fignisipforum f & ^ ubi funt imparium di-menfionum. 7. Praeterea, fi fit CE Hvperbola, cu-jus Afymptoti AD, AF reftum angulumFAD conftituant; & adADeriganturut-cunque perpendicula BC, DE occurren-tia Hyperbolse in C & E: & ABdicatura, BC^, &area BCED2;; Erit BD:rf -t- ,^+ ^, + .-^.+ ji^, + &c. Ubi coefficientes de-nominatorum prodeunt multiplicando terminos hujus Arithmeticaeprogreflionis, i, ij 3 » 4» 5» &c- in fe continuo. Et hinc ex Lo-garithmo dato potefl numerus ei competens invenire. 8. Ello VDE^Wr-iZ^r/.v, cujus vertexefl: V, exiiknte A centro& AE iemi-diametro Circuli ad quemaptatur, &anguloVAEreflo:Demiflbque ad AE perpendiculo quovis DB, & adla QuadratricisTangente DT occurrente axi ejus AV in T:Dic AV = ^, & AB zi ^;Eritque DB iz ^ — f^ _j:l_^_&c. Et VT=:: + &C. Et Area AVDBr:^A?—^-i- —&c. EtArcusVD = ^ + ^^.-H,l
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