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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 236, page id 826603459:0282
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De Propressione Arichmetica.
10 Data vero rerminorum quorumvis differencia, cum
corundem ab inricem dictancia; (puta f L C, D;) datue com-
munis excestus F.. Diridendo scilicet differenciam per distan-
ciam. Nam cum sic, verbi pratia, f c =DF, Per Prace.
dentemi erie p
=r Item data terminorum quorumvis differentia, cum com
muni excessu; (f =c, F:) datur eorundem dictancia D,
Diridendo scilicer differenciam per communem excessum. NVam
Cum (IC (Pex PEOP.D) F _ C =DF; eric H
22 Porro; Termini duo quiliber, cum duobus aliis ejusdem
progressionis quibussibet, in eadem ab invicem dictancia polcis
habene ec eandem differenciam. Cum enim per proD. 9. difse
rencia sir D E; li verobiq: aequalis sic, non modo P communis
excestus, Ced e distantia D; eric eadem urrobiqi differentia D P.
Puca ( a3 b, C, du eg fu 5 CTIEC = a = F  d.
13 Et contra; Si eadem sic verobig; differentia, eadem eAt dt
verobig; distancia. Nam si cum excessus communis P, cum
disferencia DF, st urrobig; aequalis; eric ucrobiqi aequalis D.
Puca a3 b, C, d3 c, f,  e c = a = f = d; CxunCa, C,  f, dd
requalirer remoci.
24. Ergo eciam; Si ex terminis quorvis in continua progres
tione arichmecica consticuris, seligantur quorlibet in eadem
continue ab inricem distantia; erune e hi in concinua pro
prestione arichmerica consti.
rUcI. Puta (I a, b, C, d, C, f, 8, B9 13
R, 5. 9 CrUNEILEM CUM a3C, C,
832, 5. cum b, d, f, B, R0 23
cum a. d, 8. R, s.; Tum a-e
2; in concinua proprestio
ne arichmerica consticuri. Nam
a3 b7 6, lys e3 f383 b 1
23 C9 eg 8
43
du
aqualibus cOn inVE diFFerEMLIIS CONLINUE CTEICUNE, PEr PrOP 12.
15 Ec concra; h ex terminis ita concinue progrediencibus,
Scl. ei quodibet concinue icem proprediuncur; aequalibus ab
haricem dictanciis Tumpei TunE, Per PFOD. 13.
26 Daco excelu communi, cum numer oterminorum, l l.
invenicur excremorum differencia, X. ER enim excremorum
diltamcia unitace minOr, quam numerus cerminorum
13
81
CAP. 27