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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)
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DE PROGRESSTONE
et te
A, M,
NI, V
7 = 2. M -
A = 2MI - V
34. Acque idem valet de tribus quatuorre terminis progrectionis Arichmeticae
ueur non immediace proximis, modo aequalibus urobique incerralsis distantibus.
Puta, (I a b,6, d, e, 538, 3. Cxit a f e ==26. NTam _Ca, C, C, = Der prOP. 14. Lrem
a +5 = 6 + d. de d. F e = b + 8. FL GC alibi. Nam a,C; a, f. Vel a, d; 6, f. _ b, c:
dy 8, Velb, d; cn 8. etC. Per PF. X2
35. Sed de praecedencium aliquor conversae paricer demonsrantur. Pura con-
verla pr. 28. In concinua proerellione Rrichmerica, (excepta tantum progrestione
aequalium, ubi exceltus ele ubique nullus, puta, 2, 2, E, L, _c. :=; qua _ deinceps
aliquories excepta intelligatur,) Si duorum intermediorum cerminorum asoresatum
acoregato extremorum aequetur, lune illi ab excremis aequaliter uerinque remot:
(hoc est, quoc gradibus intermediorum alter ab alcero extremorum, cor religuus
a religuo distac.) Puta in prosreltione an b, C, du e, f,8, == HIC F e = a L ∞, TOri-
dem gradibus diltanca, c, aique e, s; item an e, aique c, 5. Cum enim quanco duo.
rum C, en alter major elt quam a, tanto alier minor sic quams, (lecus enim agere.
Sata non ellene aequalia,) distantia urobique aequalis crit, Per PFOD. 13.
36. Et converia prop. 29. Si termini alicujus intermedii duplum aequetur 28-
Gregaco extremorum: aequalicer ille ab. viroque extremo diltat. Probatur uE Pra-
Cedens.
27. TIeM COnVerS PrOP. 32. Si uniustermini duplum aequetur duorum agore.
Bato, erit ille medius Rrichnccieus inter hos. Nam, nisi aequalibus disterentiis ho-
rum cum alter major sic cum alcer minor, quam est exposuus, non constaret aequa-
litaS.
38. Similiter et COnVKIa PrOP. 30. Si bini binis cimul sine aquales, crune illi
quacuor termini Arithnerice (ut loguuneur) proporcionales. Puta li A F V =
AI NI, quanto horum alter puta M, Luperar alterum illorum pUTa A, tanCO BO-
rum reliquus ab illorum reliquo deticie; (nam nili excellus et detectus se mutuo
perimane, non constabic asgresatorum aequalicas:) Fdeoque M - A = V --V
F
HrgO A, MI = A F L; N, V =- N V F. Vel lic, quia A. ] V, ==MI F N; crit V =- M
+ N- A, _ V = N = M - - A1 ErGO, per det. A, M; N, V. Sed e codem aro
enEO M, A; V, N. vel V, N; MI, A. Item, cum sic V =M f N - A (uc dictum
CAt) eric cciam V = M = N = A; Ideoque V, M; HI, A, ec M, V; A, N, vet A, B;
M, V. Acque hinc sequicur, non camum 
139. Si quamor termini line arichmerice proporrionales, Tunt ec inverse proPOr-
tionales; (Incellige, si A, M; B, V. vel N, V; A, ML, CUM MI, A; V, N, vel V, N;
M, A.) quod ex ipla detinicione sequitur. Nam S in alteris sE aequalis exceltus,
in alteris erit aequalis detectus; adeoque utrobique prosrestio Arichmetica. Sed e
40. Si quatuor termini sinc Arichmetice proporrionales, sunt e alterne (permu-
cacim, viciltim,) proporcionales. FIoC Ost, s A, ML: N, V, idCOqHC A F V = M f N
eric A, N; M, V, uc ostentum est prOP. 38. Tcem N, A; V, M, ut ilidem, ec prOP. 39.
4T. Tiem si Arichmerice proporcionalium vel primus et cercius, vel secundus et
quarcus, aequaliter vel augeanCuE, vel inuanEuT; manent achue Arichmecice pro
Porcionales. Puta, l A, M, N, V, hoc est A, A ] P; NV, N. Y F; eric cciam A, NI ] B:
NI, V + B, hoc cMt A, A Y R. Y B; N, N. J F J B; Nempe illic communis exceltus
elt k, hic H, F B. Trem A F B, NP = A J Fi; N. F B, V = N + R, ubi commu
nisexcestus elt F =B. FI, pari de cauta, A FB, M + C, N F B, V FC; Ex pariter
in similibus. Ouippe qui pritis etat communis excellus, utrobique vet pariter au-
secur, rel pariter minuitur, adeoque etiamnum urrobique aequalis; et propterea
cermini Arichmeried proporcionale s; ecri CN CssiI
42. Icem, li Arichmeciee proporrionales (INCTM A, MI. N, V. cum aie; v,V; cum
a m; n, un (cum, li placet, quaterni plures:) eryne irem cum aecregaca, tum dit
Ferencia, terminorum respectire sumprorum, termini proporiionales. Puta A F a Fa-
M F e. Fm; N F v Fn V F 0 F u. Nam si in primis excellus sit ubique F, in se-
CunetiSE, In TETEIS =C; erit in quarcis P. + c L e. Or acdirione parebit.
D111