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# Title: [Vera Circuli Et Hyperbolae Quadratura] Vera Circvli Et Hyperbolæ Quadratura (shelfmark Leibn. Marg. 98)
# Folio 19, page id 834940469:0027
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 31 lines, status machine
# Lines: 31 recognised, mean confidence 0.89
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imaginane hanc seriem in infinitum concinuari, possumus
imasnari vlcimos terminos couergentes esse equales, quos
terminos equales appellamus seriei termimationem
PROP. VIP PROBLEMA.
Oporret pradicta serici terminationem invenire
T huic problemati laristat, oporret primo invenire
quantirarem que eodem modo componitur ex termi
nis conversentibus a, b. quo exi terminis conversencibus
ca + bd- ad, bc be t ac hoc gurem Facile tir hoc modo: inue-
niatur quancitas quae mulciplicata in a ec addica b mulcipli-
caca in quanciearem dacam in eandem quantitatem Facie ac
Si mulciplicaretur in caibd ad _E AddCrCTUX bC-bCHL2C Mys
ciplicara etii in eande quanritarem daram m. Tc quanticas il
la 2, _ proinde 2a bm squatur 20a if. 2bd - 2ad F mbc mberi mac
d aequatione reducta invenitur = mac - mbe; quae quanti-
ad - bd
eas tiue mulciplicara in a X addita mb, sue mulciplicara in
cait bd - ad e dddita mibc-mbeir mac efficir candem in veroque
calu quancitarem nempe maac-mibas rf. mbad- mobd: X proin:
cd- bd
de predicta quantiras eodem modo componitur excerminis
convergentibus a, b, quo componitur ex terminis conuer-
Bentibus carsi bd ad, bc - ber ac arque a _ b quoniam LunE
quantieares indeAnitae possunr esse quiliber torius seriei Eer-
mini conuersences, modo termini conuorsences immediare
SequenEeS SnE Catf bd - 2d _ bc = ber F 2c; _ PrOInde quanCICAS
manemmbae is mbad-mbbd eodem modo coponirur ex quibul-
cd. Bd
libetrorius seriei terminis conuergentibus quo componicur
exterminis conversentibus ab; ec isitur praedicta quancitas
eodem