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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 239, page id 826603459:0285
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CAP. 25.
De Procressione Arithmerica.
tia, dist. B dist: c = diCt: f, hoc est, dist. B = diA: c Y dist f.
exIE (Per PrOP. 2E. ) B = C + f un a 3 ergo B n C 4 a
26 Siigitur primus terminus sico; duorum quorumvis dit-
Ferencia est cerminus ille cujus index sive dictancia a primo est
llorum indicum differencia aequalis. Ouonium hoc casi.
B  C = B - CF a - f.
27 Irem, hoc casu, cerminus ille, cujus index aequatur eus
rum indicum differenciae, est mulciplum excelsus communis,
andici suo (sire duorum illorum indicum difterentix) cogno-
mine. Cum enim indicum dicterentia oltendar terminorum di-
Rancia; (cq; Per prop. 9. disterencia cerminorum, DF. (mul.
ciplum excellus copnomine distantiae, sire indicum differencise;)
exie cerminus ille, cujus index huic indicum differentiae aequa-
nur, icem D P; quippe quae est cerminorum illorum differencia,
per praeced.
28 In continua progrectione Arichmetica, extremorum ag-
prepacum aequatur aggresaco duorum quorumvis terminorum
aequalicer ab excremis uerinque remocorum; (Incellise, quo-
rum unus a primo eot abest gradibus, quor alter ab ultimo.)
Nam, Per PrOP. 2. _5; canco unus minimum Luperat, quanto
alcer a maximo deficit; propcer aequalem uerobique dictanciam.
PataC = AF 2F, 27 =V  2E; erBo c+ γ =A+ 2F +
V. _ ZF. = A + V. FFHC ubique.
20 Sin cerminus omnium mediis ab utroq; extremo equa-
licer distet, (quod ubi numerus cerminorum cA impar concip.
sic) cerminus ille bis sumprus aequatur extremorum eGGrC-
BacO. PUTa exPOSIEIS a3 B, C, d, e 5 crit a + e = 2c. quia
e a = e nc, propter aequalem verobique distanciam. Ideo
que c +6 = a + e = 26.
+ 2F.