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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
# Folio 145, page id 851387705:0165
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Cap. XXV
ARITF
M = A -
A F a = a, A + a = a = L. F c= e; N F. r = n, N F v = n +
43. Sed de idem obcinet in arichmericis proorectionibus concinuis. Ouod limi-
liter probandum eric. Puca, Si cum A, B, C, D, :=, cum an B, 7 8 =; Tum a, B, C, d, 
crunt A. F a = a, B f B = b, C + 3 FC, D = S F
44. Ec quidem, licet alcera proxrestio crescens tuerie, alcera decrescens.
scA + B, A + 2F, A F 3F, A F 4F, :
Puca Z
41, :
Ouippe aggregatorum excetus concinuus elt F. - c.
Acque hujusmodi complures proporcionalium immurationes de comparationes
facile esset cum comminilei cum demonstrare. Verum illud haud est necesse, sed
cujustibet porius arbitrio permictendum, uc id, PrOUT OpUS Fuerit, PrO LC nata Cu-
rec; e cum res postularerit ipse perticiat.
45 In concinua prorrestione Arichmeriea, Ageregatum extremorum (Z. = A
tV) per numerum cerminorum mulciplicatum P, est duplum summae cermi-
norum omnium. IIoc CA YZ = 25. Progrectionis
cermini ordine directo (a primo inchoaci) di. a F a == Z = A f V
CanEUE a, B, C, d, _c. Tidem cermini ordine re- B = B = Z
erogrado (ab ultimo inchoati) diCanEuE a, B, 7, d, dC. c  y = 7
Duoniam isitur, Der prOP. 28. cum a F a, cum d = s = Z = A L V
b = B, cum c f 7, _EC. XGUIaNEIE aBBFCSAIO CXIC.
MOTUI A F V = Z: CEUnE OmnES a, b, C, d, dc
ec
u omnibus en B, 3 5, c. aequales iph L. cocies 5 f 5 = YZ = Y A + ZV
Tumpeo. HOc Ct, omnes cermini bis sumpri (nempe, cum ordine directo, cum
ordine recrogrado,) aequantuE extremorum aercsato Z. rories lumpto quoi sunt
cermini. Hoc est YZ = 25
46 Idem ralet in quacuor discontinue proporrionalibus Arichmetice. Puca
A, M; N, V. Cum enim, per pcop. 30, lic A + Y = Z = M + N, exit 42
47 Daris ipicur, in Arichmetica proprectione concinua, extremorum aeregato
_ LErIMInOTUI HuMETO; Z, F; habetur cocius progrectionis sIVC TETIMOrum
omnium TumMA. S. ReMPC YZ =25, Per PrOD. 45. FrGO = =S
A8 Et DaTO ExTemOTuM aBGregatO, cum progrectionis summa; Z S: habetur
numerus cerminorum. T. Nam, quia 25 = F Z; eric 25 --
+D EC Dato terminorum numero, cum progrestionis summa; F, S; datur ilem
extremorum ageregatuM. Z. Nam quia 25 = FZ; erit = F = Z
50 Dacis cerminorum numero, proereltionis summa, et termino minimo; F, S, A;
habetur maximus. V. EA enim per P. 48. 7 = Z = A + V. F, O = =A - Z
A = V.
SE Dacis iildem; datur extremorum disterencia. X. Nam, per praecedt 23 = A
=V. ErBO = = 2A (= Z - 2A) = Y = A = X
52 Datis numeto cerminorum, proereltionis summa, et cermino maximo;
F, 3, Y, habetur icem minimus. A. Cum enimus per pr. 48.  = Z = A + Y,
etie 2 - V.
33 Datis