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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. GEOMDL LICA
Primo) aequacur illorum indicibus simul
lumpeis. Sic enim, verbi pracia, cermi-
norum invicem mulciplicatorum unius in-
dex m, alcerius n: erune ergo cermini illi
A AM eC ARN; per proP. 2. horum erso
rectangulum A Rm X A R. = A~ Rn Fn,
quod per A dirisum, extribet A sem +n
AR R R = A B3
XARR = A R2
RARRRRR = N R
hoc est (per prop. 2.) cerminum illum cujus index est n f n, indicum illorum
288rC8at0 aequalis.
22. Eodem modo; Si cermini cres, quacuOr, quinque, aut plureS, concinne
mulciplicentur, productum eoc vicibus una minus diritum per cerminum primum
(sirc ea primi pocellate dirilum quae uno gradu minor est qua nuIerUS termi-
norum sic continue mulciplicatorum,) exhibet terminum cujus index illorum
indicum agBrCgaTO aequatuT. Puta, li continue mulciplicatorum indices (inc L, M, u,
TETMINI CTUNE ARI, ARm, A Rn qui invicem ducti FaCICNE A A A RIFM FN
quodti diridantur per A A, vel A2, prodibir ARIFmFn, cerminus nempe cujus
index l. F m Y n. Der PEOP. 2
23. Si itaque concinue proporrionalium primus cerminus sit F; (quod in ca
bulis Losarichmieis ponicur;) duobus, pluributre, continue mulciplicatis, pro-
veriet cerminus cujus incex illorum indicum aggresatO aquatuT. SequitI ex
PrOP. 21, X 22. Ouia nempe qua illic imperatur divisio per cerminum primum
(sire semel sire laepius tacienda) hoc calu (CUM PTIUS TETHINUS DONITUE L,)
nihil immurabit. NIaM LXLXZXR = FXZXR = TXR = R
24: Icem; numerorum ab 2 concinue proporcionalium; erie quilibet terminus,
ipsa poceltas racionis communis, quae cermini illius indici est cognominis. per
DEOP. 2. Nam (I A == F, exit A Rd =- = Rd = Ra
Acque hinc pender Regula de Mulciplicatione L osarichmica. Nempe Darorum
numerorum Foearithmi simul addici, aequantur Zocarichmo numeri ex datorum
invicem multiplicatione producti. Per pE. 23. Sunc enim Logarichmi, numero-
rum ab E concinue provorcionalium Indices.
25. Continne proportionalium; si duorum alter per alterum diridatur, de quo-
tiens in cerminum primum ducatur; prodibis cerminus cujus index aequatur disse
rentia indicum cerminorum expolitorum. Sit majoris index m L n, minoris m
adeoque eorum difterentia n; Crunt per pr. 2. ipE termini ARm F2, d A Rm
facta itaque divitione, A Rm) ARm Fn (Rn, Si quoriens ducatur in A, habecur
A R~, terminus cujus indCX N PEF PF. Z
26. Si iaque concinue proporcionalium primus cerminus sic Y; quoriens cu
jutris cermini per quemris alium dirisi, clt ipse cerminus cujus index aequatur
illorum indicum ditterentix. (Intellise, excestui indieis dirisi supra indicem
dividentis; et propterea si hic major tueric, quorientis index exit negaciruS.) SC
quicur ex praeced. quia ( A == E CxIt R~ = A R
27. Tiem; numerorum ab Z concinue proportionalium; s aller per alcerum
dividatur, eric quoriens, ipsa porestas racionis communis, ditterenciae indicum da-
torum numerorum cognominis. nempe Rn. per Praced.
Acque hinc pender Regula Diritionis Logarichmicx. Nempe Si ex Loga
rithmo Dividendi auseratur Loearichmus Divisoris, quod reliquum est, est Lo
sarithmus Quotientis. Ouippe Logariclimi sunc numerorum ab F continue pro.
vorcionalium indices.
aliae propoliciones de operacionibus Lopprichmicis; pura, de excractione RA
dicis Ouadraticae, per biparcicionem Losarichmi; de Cubica, per ejusdem cripar.
ricionem, ecc. aliaeque consimiles; ex Propoticionibus jam cradies dependent
Nec opS CH l sulio ex prandis jam immorari, ne nimis digresti videamur.
dibus ab unO ExEremO, quoL Lelus a reliquo, distat.) Cum enim sIc termino-
rum alter A R C pet plOB. L. auL R a) V, per prop. 5. Lucque distania D uirobique
eadem:
Susticie dirico foncem indicalle.
28. In quancitatum concinue proportionaliun quoleunque proprectione; Ouod
sit ex ductu cermini primi in ulcimum, aequatur facto ex mucuo ductu duorum
quorumris terminorum ab excremis aequaliter verinque remotorum. Vel, Rectan.
sulum sub excremis, aequatur rectangulo sud cobus Gebustibet incermediis ab ex-
cremis ucrinque aequaliter distancibus. Incellise; quorum unus coc praecise gra