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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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CaP. XXXIII. DE PROGRESSFOHE, SEC.
LLL. XXXTII.
Proeressio Geometrica fusuls rcut.
STCUL TUPCrIUS Cap. XZVII C XXVIII, Frogreltionis Prichmeticae doctrinam
DFulius prosecuri lumus, libet eadem Meodo e Prosrectionem Greomecricam
tunco quibus Cum uturus Symbola.
Terminus minimus, quem primum appello, sic A; MaxiuS V; extremorum
rectansulum H == V X A; maximi ad minimum ratio Z: Rcclangutorum (iptiM
aequa) Celnis reciproce sumpeis CompMeMOru ASGrESaTI, Z; mIeTUS
termnorum, T; communis racio R (incellise, Rationis communs xponentem)
ducanlia termini cujutris à dato, D; Lumi progretionis, S. Termini ipli, a mi-
agcredi, sequencibus propolicionibus explicandam. Ouod quo rectius tat, haec
nimo inchoando, dicaneur. a, B, c, a e, _c. d maximo vero inchoando, dicantur
en B, 7, d _C. Numeros qui cujusque termini d primo distanciam indicane Indi-
ces axpello; puta 0, L, 2, 3, dc. LHS praemullis, lequuntur propoliciones.
8
AL
(3T22
L+
AL
30366 AR3 k. 0
T. Si SCa = A, erit B = A R, C = AR2, d = AR3, dc. Ouitibet enim termi-
nus in communem rationem ductus, producit terminum proxime sequencem, per
det. Prosressionis Geometrica
2. Omilibet erso terminus producitur ex mulciplicatione termini primi in
Rationis communis porestatem Indici cognominem; vel (quod idem eAt) cogno.
minem distanciae iptius a cermino primo, iptum primum non compucando. Nempe
ARd. Sequitur ex praeced.
3. Datis igitur Termino primo seu minimo, Racione communi de termini quae-
fici distancia d primo; A, R, D; habEEuE terminUIS quasicuS, nempe ARd. per
praeced. Pura terminus sextuS f, cujus index live distancia a primo 5, fic ex ductu
primi in rationis communis poteltarem sun diltancia D =5 coenominem.
= AR3.
12t 1
4. Si cerminus maximus tire ulrimus lc V, eric pemulrimus  vel R) V; an.
cepenulcimus = L vel R =) V; hinc proxime minor R.) V; de sic deinceps; V = a,
R) V =B, R2) V = y R3) V = 5. Sc. Ouilibet enim terminus per rationem
communem dirisus, dac terminum proxine minorem. Per det. proBr. GeOM.
5. Duilibet isicur cerminus aequalis ell, termino maximo per rationis commu
nis poceltarem distancia ab ultimo cognominem diriso. Nempe R d) V. per praeced.
6. Dato ergo termino Maximo, cum Ratione communi, et Distancia cermini
quaesiti a maximo; V, R, D; habetur terminus quasituS. Puta sextuS a fine, Sive
anee ulcimum quincus, s = R3) V. Per Praced.
7. Daco cermino quovis, (uc f) cumratione communi, de cujusris altienati
majoris distancia a dato; f, R, D; inrenitur terminus altionatus (pura J.) nempe,
mulciplicando terminum dacum in Rationis communis poceltatem distantix cogno.
minem. HOc Ci = fRd = sR3. Nam per det. vel prop. 1. pro fingulis ct
S
Stanciae