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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 LROGRESSTOHE CaP. LLX
quatuor laltem terminis constituitur; puta 2. 4.: : 3. 6. Cum enim, ratio quaelibet
duos terminos poltulet, quippe qui invicem comparantur; eademque racio laltem
bis occurrat uc constituatur analosia, quae rationes comparat: si terminus medius
lit utrique rationi communis (Duta prioris consequens, ee polterioris antecedens)
in cribus cerminis eadem bis reperiri porest ratio; sin minus, non nili in quatuor,
cum utriusque rationis duo termini, a duobus reliquis cerminis alii sint. Porelt
aurem rum analogia concinua pluribus adhue quam tribus; ee disjuncta, pluribus
quam quatuor absolri. Puta 2. 4. 8. 16. 32 Tunt continue provortionales; dir-
concinue rero 2. 4:: 3. 6::9. 18:: 5. 10. Vel etiam (nam es sic proporrionales no-
larm
det cciriit
tare licebic) 2. 3. 5: : 4. 6. 10. puta, ut Tunt ad invicem 2, 3, 5; fic X 43 6, +0.
De Progrestione Geometrica concinua, duo praetertim eradi Polent operationum
compendia; duobus Problematis propolica. Primum est; Focius progreltionis lum
mam, sine continua incermediorum additione, inrenire. Alterum est; Termi
rumesti. num ulcimum, aliumre d primo lacis remorum, neolectis intermediis, invenire.
59040
Primum quod atrinet. Concinux Progretionis Tumma Sic
O reperitur. Si terminus ultimus per communis rarionis FX
Donenrem mulciplicetur, (sire, quod cancundem cst, proprel.
2 lio per unum adhuc gradum ContInueTur;) aeque inde au-
teratur terminus primus, es quod reltat per numerum uni-
tate minorem quam elt communis rationis Exponens divi-
datur; prodibir prosressionis lumma. Hloc Clt, E terminus
primus seuminimus dicatur A, maximus V, communis ra-
rionis ExponenS L, e progrectionis LuIa S. CxII
VR - A
nemuS.
= 5. Cujus Regulae demonstrationem infra expo.
Sic in progrestione adjuncta, decem termitorum Fermi.
nus ulcimus 39360 in communis rationis L Xponentemt 3 du-
ctusus tacit 178098; unde dempris 2 (termino. primo) re-
Ctanc F28096. Oui numerus ver 2 (numerum unitare mi-
norem quam clt, 3, rationis communis Exponens) dirisus,
quorientem extibet 59048, tocius progrectionis Tummam.
Oux quidem cadem est ee quae ex terminis omnibus conci.
nue addiris emersit
Cum autem res cadlio plena videri poltic, in prolixiori
bus falcem progrestionibus, lingulos cerminos concinua mulciplicatione sigillatim
invellixare; Hujus iaque operationis compendium quaeric problema illud ale
rum; Nempe
Prosrestionis cujulris inchoacae, terminum ulcimum, aliumre quemvis actisna-
cum, a primo Caris remotum, invenire. Ouod hoc pacto taciendum docent. Pror
srellio expolita, per aliquor taltem gradus inchoecur. F. r linguli cermini nocari
incelligantur coridem numeris naturali serie prosiecliencibus diciptra inchoatis;
DutA O, T, 29. B, 43 _ (rel etiam quibulris aliis, concimta prosreltiono, proceden
tibus, ab oinehoatis:) qui snaices rocari Colent, lire Rxponentes; cailtantiam eus
jusque termini a primo indicances. Hac praeparatione tacta; si terminorum jum
inremcorum quilibet mudciplicetur vel in tervelleorum alium quemtitets edipro-
ductum per terminum primum diridatur: prodibir cerminus iillevenl respondet
Index ex inricem mulciplicatorum Indicibus additis concatus.  Atque hoe, quo
ties opus tuerie, icerandum exis. is Suut  vig SCIO est sristere je
Exempli Bratia. In exposica plogrestione; Ihreniis cerminis primoribuls qua.
tOF, 2, 6, 28, 54, quibus respondent indices 0, 1, 2, 3. Ductis 54 in 54 (ter.
mino quario in sciptum, cujus index 3, 3,) hunt 54 x54 = 2926; quem nu-
merum si per 2 cerminum primum diridamus, proveniet 2) 2926 (2458 termi
nus septius cujus index 6 =3 F 3. Deinde, Si r458 terminus sepeimus jam
inventus, (cujus index 6,) ducatur in 54 terminum quarrum, (cujus index 3)
prodibune 78732, quae per 2 (terminum primum) divila, exhibebine 2) 78732
(39366 cerminum dccimum, cujus index 3 = 6 + 3. Le c deinceps, quoulque
opus tuerit, progressio per Taltus concinuabitur.
1
Summa
investi
ratio ter
rint.
mini ul-
18
5.
16
48
245
43
C3T2
8030
5904
39366
L1069C
2) L18090