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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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Arithmetica Infinitorum.
PrOP. 182
Oux estigitur summa Ceriei Mmartanorum cujuo terminus
ulcimus eA lE numerus cerminorum l F T.
Vel, si pro numero terminorum lF 1, Tubsticuatur n, a
provcerea Ceries r qualium n1o; erit series Ouareanorum Znl
15n1 + 30nt= = 26RI. (Einempe terminus primus HC O,
Eccundus 1:) vel.
nIL
n12
101 = 3012
30t
9. Adeoq; Peries finica Ouartanorum ad seriem coridem max-
EMO AE qualium eAUC Z X
rac inquirendum.
101 + 301= 3015 ad T. Ouod e.
Ecpari modo, his cognicis, ratio quam habet ad seriem A-
qualium Peries Ouincanorum, inremietur ope characteris in
proxima praelentis cabellae serie: PF deinde, quam habec feries
Sexcanorum, opc characteris seriei proxime sublequencis in hac
eabella; ee hc deincepe quoulq: libet.
Ouo melius aurem hoc intelligarur, operae Forcasse prerium
eric, qua jam cradica lunc, paulo distinctius aperire: Elcuc enim
ea Caris aperee rradidisse nos nobis videamur, heri tamen porest
uc leccor illis minus assuecus nonnunquam Corlan hxelitet.
Nocandum ixicur eA, nos hic (ut de alibi Ccmper, ubi de A-
nita Cerie rerba hiune, ) numerum cerminorum altienare l+ L
(nempe literminus primuso, sccundus dicatur L, 3 nimirum
unicare majorem quam eAt numerus parricularum ex quibus
conslacur cerminus maximus, hoc es, omnium differentiarum
terminorum continue policorum, quarum omnium agpresaro
terminus maximus aequacur; sire differencix illae sinc aequales,
ue in serie primanorum, (DUTA L, F, F, T, _C, differencire nume-
rorum arichmecice proportionalium,) sire crescentes, ut in le-
rie lecundanorum, cerrianorum, _C. (PUta T, 3, 5, 7, dec. dit-
terencix numerorum quadracieorum, vel 2,7, 19, 37, _c, ditte.
rentia numerorum cubicorum; _C:) sire eciam decrelcentes,
ut in Cerie subsecundanorum, Cabcertianorum _C; (nam verbi
sracia, difterencia N3- N2 minor est quam ~2 = ~ T, 219:
baeC minor quem VFi VO; e sic in caeceris.) Harum omni-
um differenciarum (in qualibet Perie) numerust, unitate min
nor ell quam numerus terminorum, uc paree; carumq; omnium
dexresacum (proprer cermini primio nullitarem) cs Ip(e rer-
inus
asrue