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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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De Progressione arichmetica.
A, M, 4 - V = 2B = A
 A, V, C
3D N = A L V.
C M, V, d C A = 2M = V.
34 Acq; idem ralet de cribus quatuorre cerminis progressi
onis Arictimeticae, ucur non immediace proximis, modo requa-
libus verobiqi incerrallis distantibus. Puca, I a, b9C, d, e, f, 8,
eric a F e = 2c. ITamm _ a, C, e, si per Prop. 24. Iiem a  f-
c + d. 8 d + e = b + 8. EC AIC alibi. Nam a96; d, fovel a, d; c, f.
_ b, es d, B, Vel b, di ei 8. _C. PerDr. 12.
35 Sed _ praecedentium aliquor converlae paricer demon-
Sraneur. Pura converta pr. 28. In continua progressione Arich.
metica, (excepta tancum progrectione aequalium, abi excecus
est abig; nuHIUS, PACa, 2, L, 2, 2, _C~ 3 quae _ deincepo ali
quocies excepta incellisatur.) Ei duorum incermediorum cer
minorum agereeratum aggregato extremorum aequetur, lunt
illi ab excremis a qualicer ucrinq; remoris (hoc cA, quot pra-
dibus intermediorum alcer ab alcero extremorum, cor reliquus
a reliquo distac.) Puca in progrestione a, b, C, d, C, 5,8,   c + e
= a te, cocidem gradibus distane an cu acque e, e; ICCW a3 e, aC-
quec, p. Cum enim quanto duorum e, e, alcer major eAt quam
a canco alcer minor sE guame, (lecus enim aspregata non
essene x qualia,) distancia urrobique aequolis erit per prop. 13.
36 Ec converla Prop. 29. Si termini alicujus incermedii du-
plum aequetur aggresaco extremorm: Requalicer ille ab ucro-
que excremo distac. Probatur ne prxcedens.
37 lcem converla prop. 33. St unius cermini duplum aeque
cur duorum aggresato, eric ille medius Rrichmericus inter h98.
Nam, nis aequalibus differentiis horum cum alcex maior siccum
alcer minor, quam cM expolicus, non conttaret aequalicas.
38 Similicer _e conver(a prop. 30. Si binibinis simul CIne
requales, crune illi quacuor cermini Arichmetice (ut loguun-
TUT) proporcionales. Puta si A + V = M + N, quanco horum
alcer puca M, Superae alcerum illorum puca A, canco horum
reliquus ab illorum reliquo deticir; (nam nill excesus e dete-
Etus se mucuo perimant non constabic aspresatorum aequali
1a5:) Ideoque M i A = V in Hd = En ErBO R, M i A+ F:
P. 2