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# Title: Qua Continentur, Oratio Inauguralis. Mathesis Universalis; sive, Arithmeticum opus Integrum, tum Numerosam Arithmeticam tum Speciosam complectens. Adversus Meibomii, de Proportionibus Dialogum, Tractatus Elencticus (shelfmarks Leibn. Marg. 84:1, Stück 1; Leibn. Marg. 84:1)
# Folio 247, page id 826603459:0293
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C AP. 25.
De Progressione Priihmerica:
nis. CUMMA; V, F, S; dacUr nmerUS TermINOrUM. T. Nam, per
DeOD 20. V = YE F F = A. adc0q; 2V  YF + F = V +
A = Z. ErBO, Per PEOD. 45. 25 =TZ =- ZIV L TGEFTF.
25
adeoq; F. =
+F.
F Y = T q. Et (retolrendo requationem)
V + ZF F V: Z E9F V9+ VE i 2SF
Nocandum aucem eR, hujus xquationis (urpore ambieux)
radicem minorem tunc conrenire, cum A major est quam Z P
(adeoq; radicem unirertalem V: Z F.g _c. afficiendum signo;
majorem vero (adcoq; F V: _c.) quocies a minor cAt quam
B. Sin A = = L: Perinde eric utra eligatur; nam hoc caluro-
cum illud quod noca radicalicacis afficitur, eranelcie.
67 Dacisiildem; dacur cerminus minimus A. NVam, Per Pra
cedentem habetur T. adeogi A Pex PrOD 20.
Vel Ec. Ouoniam (uc in prop. 65.) 25F =-V 9 in Ag f
VF FAF. Transponancur cermini (A sC V gY F. V plus quam
2SE; quodcum contingee, cum A major est quam P;) ad hane
Formam, Ag  F A =-V 9+EV  2SB: cujus fequatio.
nisradix cA = E F V: ZEqZ V9+ EV = 3SF: = A. Vet (A
siE V9 + FV minus quam 2SF; quod cum concinser, cum A
minor est quam P;) cransponantur ad hanc Formam, P. A.
A9 = 2SF =Vq RV; cujus eguacionis radix est ambiona, nem
De ZF  V: aE9tVg FEV = 25B: quarum radicum ma-
jor convenit quories A major quam Z F; minor aurem quocies
A minor est quam = F. Si autem SIC V9 FFV =- 2S F, mani-
Fectum est (urroris modo dilponancur cermini) Aq L P. A =0,
adeoq; A = P.
Si aurem hac methodo reperiarur A; investicabitur Y, pro-
politionis prxecedentis, per PrOP. 48. Nempe
V+ZE = V: ZEgtV9 +EV = 2SB. Ubi non cemere
Factum, quod cum Forma superius cradita, tuerie F, Jam (IC L.
Nam quo calu in illa Forma eligenda erat radix major, in hac
inor eligenda erit.
Acq; hactenus Progressionis Arichmeticae cradicionem Pacis
rideamur absolrille; cujusbreriorem Gynoxlin capice lequente
exhibebimus.
Nocandum