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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 PROGRESSTOHL CuPXXV
tur communis esceltus, L. Nempe, cum sic per praeced. X =DH = Y F = F
et
28. Ec Daca exremctum ditterencia, cum communi excelt; X, F: nabetur
terminorum numerus, T. Cum enim sit DE. = X, erit f = D = Y = L. FL
7 = 2
29. Daro termino primo seu minimo, cum communi excessii, et numero termi-
nOruM: A, F, T: habetur terminus ultimus, V. Cum enim, per 16. Z =-V = A
TF = C; erit V = A Y YF - B, vel V = A + DF.
20. Dato termino maximo, cum communi execllii, et numero terminorum, V.
E, F; invenicur minimus, A. Nempe sublata, ex maximo, excremorum ditferen-
tia, manet minimus. CuM erBO Per 16. X =DF =TF =C. Krit V - X =A
=V- TF. F K = V = DF.
2F. In continua progrectione prictmetica, si ex summa duorum quorumvis ter-
minorum auteratur progrestionis terminus primus; quod restat, cst proereltionis
terminus ille cujus a primo distantia Xe quatuF
iplorum d primo dictantiis simul Cimpeis. Sive
cujus Index aequatur corum Indicibus simul
Cumpris. Nam, per prop. 2. quilibet terminus
constat ex primo eum cor exceltibus quoc gradi-
bus a primo diltat: Frgo duo addiri Continent
primum bis, cum cor excessibus quoc lune ueri-
usque distantiae gradus simul additi. Hinc si sc.
= A + 7F = h mel auteratur primus; manet primus terminus
lemel cum roc excessibus quot Cune ucriusque
dictantia flacus uus aetcut, lOC est (per eandem Prop. 2.) cerminus ille cujus
diltantia est eorum distantiis simul additis aequalis. Puta terminus tertius c= A
+ 2. F, sexTIS s = A f S E, horum agoregatum 6 f f = 2 A = 7F; hinc lublato
A, reltat A F y F cerminus octavus, h: cujus d primo distantia7, x qualis est distan-
tis tertii ee lexti Cimul Tumpris 2 4 5.
22. Fodem modo; summa trium, quatuor, quinque aut plurium terminorum;
abjecto primo cor vicibus una minus; aequatur termino illi cujus Index elt corum
omnium indicibus sunul sumpris aequalis. Puta si dist. b + dist. d f dilt. 8 = dist. 1;
eri b + a f c- 2 a =1. Probatr ve pracedens.
dist. B f dilb. d F dist. e = dist. 1.
2
E7. Eq Data extremorum disserentia, cum numero terminorum; X, F: habe
aist: c. f dist: f = dilt: B.
aFC
24 - = +8F. =2
23. ErsO, S primus progrestionis terminus sit o espulaz vel nihil: duorum
plurrute  a aea elF iH Celmo cujus lndex elt corum In-
dicibus limul lumpeis aequalis. Scu Cx pIOP. 21, LL. Gla sublacio primi ter
mini A = 0, nihril immutat. Puta in ProgreltIOnC O, 3, 6, 5, 22, 25, cs6 f 9 = 15
quippe cusu a agua corum Lucicibus limul lumpris, 5 = 2 + 3
quilibet aquatur illi communis excellus mulciplo, quod elt Indici, sire a primo
distancix coenomine. Cum enim Per PrOP. 2. Sic cerminus quilibet A f D F; si
sIC A = O, CxIL A + DF == DF.
25. In concinua Prostemone Mmmetica, auor CeMO MCTentIX.
addacur cerminus primus; emersit cerminus cujus distancia a primo est eorum di-
ctanciarum irem a primo ditferentia aequalis: lire, cujus lndex aequatur indieum il.
lorum
2. Tiem, in ejusmodi progrettione (cujus primus terminus, elt 0) terminus