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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)
# Folio 180, page id 824573315:0392
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ed
Arithmetica Infinitorum.
PrOD. 19X.
dem eranicura cH.) Ouod quidem, A opus (E, HC demonttea-
bitur.
Numerorum, ica ac jam dictum est, concinve mulciplicaro.
rum, parium maximus ( nempe, ex denominatoris tactoribus
alcimus) dicacur Z; adcoq; imparium maximus (nempe, ul-
cimus ex Factoribus Numeratoris,) eric 2 = 1, Cquippe qui
ab itto unieace deticic.) Pric isicur (propter cundem ucrobigi
mulciplicacorem compolicum) numerus jutto major ad nu-
merum justo minOrem WE V L Z - i ad V L Z, (nempe, ve
cerminalis numerus Curdus in illo ad cerminalem numierum sur-
∞ F 1
dum in hoc, ) hoc cR, ut ~ Z -  ad V Z 3 hoccA, ut v
2
2  1 ad V: Z + L: hoc eA, WE V Z= = 2 2dV: Z2 - 1. FiC-
ri autem porest (aucta nempe, quancum opus cA, quancitate
2) uc differencia radicum V Z de V: Z 2 = L: BEMDC Z mo
V: 22  T: minor eracae quaris astienanda, Cuc norum cA,
e alibi eriam a nobis dictum ad proP. 39. COn. Sect. ) PC
Dropterea numerus justo major excedat numerum justo mino-
rem, secundum eam racionem quae minor sic quaris astignata.
Ouod erac ocendendum.
Cum aurem, uc ex dictis paret, aucto in infinicum numero Z,
numnecus jacto major numerum jucto minorem ea ratione Cupe-
rec quae minor sic quaris altignaca: cric corum ab inricem dit-
ferencia (_ propierea ucriulvis a ju (0) intinice parra, huc cst,
null2.
Porro; Ouoniam, numero z sic in infnicum aucto, illa II.
nicaci adjuncta pars Cui aliquoca, Fucura est infinice parvaz exie,
liver 1Z, live V 2 Z = 23 cancundem acq; V Y, CIVC L, (PrOP
cer eranescenrem parcem infinire paeram,) quae mulciplican
3X3 R5XGX7. 7 _C.
donihil mucac: Dicimus, Fractionem illam 2 a 4 X 4 C b rb 8, _C.
in intinicum concinuacam, esse ipsissimum quaesicum numeram
e prxcile; ad quem ita Cc habet L, uc circulus ad Ouadracum
diameeri: Vet, (A id magis placcar, ) ut eA istius tractionis
Wenominacor ad Hlumeratorem, AC esse dicimus circulum ad
SismLrrI