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# Title: Qua Continentur De Angulo Contactus & Semicirculi, Disquisitio Geometrica. De Sectionibus Conicis Tractatus. Arithmetica Infinitorum: sive de Curvilineorum quadraturâ, &c. Eclipseos Solaris Observatio (shelfmark Leibn. Marg. 84:2)
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DE DICATTO.
indicemus, (puta V2, V8, E C:) muliominus sperandumqe
fore judicavi, ut in proeressione magis adhue composeta
Cubi continui multiplicatores sint continue vel crescentes
vel decrescentes; id semper feri possit; adeoq aliuem ali-
quem notationis modum (quam qui adhue recepius est)
inducendum putavi quo numerus ille impossibilis indi-
cetur.
atq: hactenns perveneram istius anni 1652 initio,
tempore (si memini) quadras estmalis quo tempore nempe.
per Academiae nostra constitationes, apoblicis praelectio-
nibusferiari permissum est, adeoq. privatis disquisctioni-
bus magis vacare.
Dum autem hic haerebam, placnit rem aliis quibus fa-
miliariter usus sum viris Mathematieis communicare ut
videam num illi auxilio esse possint in quaesita quantitate
descenanda. Adeoq: ex variis quas. apud me conceperant
ejusmodi proeressionibus, unam selesi, quae omnium vide
batur simplicissima, (ut qua per numeros inteeros proce-
dit:) eam nempe quae jam habetur prop. 192. hujuscetra-
etatus; eamq: ad hanc fere formam (non enim omnibus
illam iisdem plane verbis, sed eodem tamen sen su propo-
sui) problematice concepi; Si aequabilem quandam cur-
vam contingat in vertice rectaunde ad curvam du-
CantuE rectae axi Parallelae, aequalibus ab invicem di-
Rantiis remocae, quarum prima (IC L, Sccunda 6, Ter-
Tia 30, Quarra 140, quinea 630, eC; quanta erit illa
quae interponenda cM media inter 1 8 6. Vel etiam
Arithmetice, In serie numerorum 1, 6, 30, 140, 630, eC.
quaeritur terminus medius ipsis cSC 6 interponendusd
rieri autem hosterminos indicabam, ex continua multi-
plicatione numerorum 2 x 4 2 x 4 = + 4 3 x 4 = _C. Vel etiam
nE + Z = Z~ , = _c. quorum tam numeratores quam de-
nominatores sunt Arithmetice proportionales. Problema
sic conceprum proposui, mensibus sequentibus. (inter alios)
Clarissimis