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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 243, page id 826603459:0289
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t
De Procressione Priihmerica
M = = + F. 3
a +E:
A +   a AFa  at E +E C; HI+ V n, N+ v LnFF +C Co
13 Sed _e idem obrinet in Rrichmeticis progrestionibus con-
cinuis. Ouod similiter probandum exie. Puca, E cum A, B, C.
D,  CUM a, B3Y, 8,3 CUM a, b, C, d, s. 3 CxUnE At a = a-
B+B = b, C +3 i C, D + st  d, i
44 Ec quidem, licec altera progressio crelcens fuerie, alcera
decrelcens.
EA + C A + ZE, A F 3E, A + 4F, 
Pura
CD  C9 V n 26, V 1 30, v  4D, 
Ouippe axeresatorum excessus continnus eAt P. = e.
Aeq; hujulmodi complures proportionalium immutationes e
comparaciones facile eNer cum comminilei cum demonttrare.
erum illud hand est necesse, sed cujuslibet potius arbierio per-
micrendum, uc id, proue opus Fuerie, Prore nata curce; et eum
res pottularericiple perticiat.
45 In conrinua proprestione Arithmetica, Aggregatum ex-
cremorum (L = At V) per numerum terminorum mulei
plicacum T, cA duplum Cumma terminorum omnium. Hloc cA
TZ = 25. Progrectionis ter-
mini ordine directo Ca primo a + a = Z- A + V
Inchonci) dicancur a, B, C, d, _c. b + B = L
Tidem cermini ordine recrogra c+ 7 = Z
do (abulcimo inchonci) dican- dI5 =-Z = A F V
cur a, B, γ, s, _C. Quoniam igi
EC.
TUE, per PrOP. 28. cum a + a S+S =TL = TA L TV.
cum b+B, cume t Y, _C. X-
QUAnEUE AEBTESATO ExFremOrum A F V =Z: erunt omnes
ag b, C d, _c. cum omnibus a, B, 3, 5, _c. requales iph L tories
sumpro. Hoc est, omnes cerminibis lumpei (nempe, tum or-
dine directo, cum ordine recrogrado,) aequantur extremo ag-
freeaco Z rories sumpro quot sune cermini. HOC eA TZ = 25.
16 Idem ralet in quatuor dilconcinue proportionalibus A-
rithmecice.