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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)
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C AP. 33.
De Proeressione Geometrica.
2) a A R =, 58) aAR3, 5~) aA RL. iUE Pacet quippe cOm
munisratio cAs )R.
Acque hujulmodi complures proportionalium immuracio
nes e comparationes Facile esser cum comminisci cum demon-
Arare. Verum illud haud est necesse, led cujussibet porius arbi-
erio permicrendum, uc id, prour opustuerie, Prore nata curet,
Toilque ulibus accommodet. Oux aurem huc spectane non
pauca deinceps, ubi Fuclidis Elementum quintum explicaturus
Cum, cradentur.
45. In concinue provorcionelibus excremorum Rcctangu
Num ducum in BEMETUM CerMINOTUM, XGUATUT REGFCGaIORC-
etangulorum omniu a qua liu (senlu quo pr. 28) CH enIm PET PE.
28. sICV = a ∞ = bB =  c 7 = = ds = - ec _C. Bncg: haec cocidem
quoccermini; (nam Cnculi cermini ordine directo sumpriin
relpectiros cerminos ordinis retrosradi duci supponuntur; ade-
Oque coc erune rectangula quot rermini;) erit TH = a a F
BBF CY F d5 + eE_C.
Notandum aurem est rectangulum aa, e RK, (A nempe k
Donacur terminus ulcimus) Se in reliquis timilicer, rerera idem
esse rectangulum (nam a _ n, item a  R, Cunt idem cerminus,)
sed cum id non Racim appareac, acque aliis item de causis,
commodius pucarimus tanguam h essene distineta bis numera-
resadeoque toc reputare rectangula quoc lune cermini:) cum
tamen B a a _ Rn (& Timilicer de reliquis) pro codem habea-
musrectanenlo, eric numerus rectansulorum diverlorum = l.
ubi cermini Cunc numero Dares; ac = T + Z, ubi numero in pa-
res; nam hoc catu, ne noatro quidem compuco quadrarum me-
dii bisponicur. Ouod monnisse Cufticiac. Nosicaque priorem
loquendi Formulam porius Celcsimus: quo sensu _ dcincers
loqui incellisamur.
46. Idem vater in quatuor dilcontinue proportionalibye
Puta R. H:: N. V. Nam A V L MN Z NNtVA - qH Per P. 30.
47. Daco icaque in concinue proporcionalibus quortibet.
extremorum rectangulo, e numero terminorum H, T; daiur
Rectangulorum agereeacum. Z. Nempe Z = T I. Per
PFOD. 45.
48. Icem dato extremorum rectangulo, e rectangulorum
ABoreBacO; M, L; dacur numerus terminorum. T. Nam, quia
ETH, eric H)Z ==