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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)
# Folio 216, page id 851387705:0236
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DF IRACLION aM
Cap. XLII.
lum sit; divisor ille ultimus, est dator an hamerorum maximus communis divilor.
(Dri ab Fuclide ostensum elt, 2 C7.) Si aurem non prius liltatur quam ad Vni-
esse: quippe T, utrumque diridendo, non minuit. Sic nuerOrUM 12 E 3.
maximus communis divisor (incellise, qui dividendos numeros ita dividat, ut
nullum supersie residuum,) inrenitur 3; quia nempe 3) 22 (4. Tine ullo reliduo.
Sic nUmerOruM 1Z 8 34, maximus communis diritor elt 2: Nam 12 in 34. bis
comtinentur, ee supertunt 10; Deinde r0 in 12 concinencur semel, ee luperlunt
2; Pandem 2 in ro continentur quinquies pracile: poltremus itaque hic diritor
2; est duorum expOlItOrum X2, 34 maximus communis dirisOr. NTUIETOLMI
autem +3 ex 34, maximus communis dirisor est z; (adcoque ipti jam inter le
primi, lire in caclem calione miniril; ) uc ex adjunctis operalionibus patet.
tatem dereniatur; a Dumento Cst CxpOSITOS nUMerOS I CaC TACIBHC MIMMMIOS
X8) LL) 34 (L(+ (5
2∞
R.4
5) 8) 23) 34(2CZCZCLC+ (2
Atque haec ipsa methodus nonnunquam etiam in Symbolicis commode aehihe.
Cur. Fxempli Graria; a = e, _ a = e: li quantitas illa per hane diridatur.
prodibit quociens a (cujus tamen in hoc nesorio nulla racio habetur,) ee reti-
duum ac = e. Si per hoc reliduum dividatur ille Dirisor a = et, prodibit
(quoriens =, _) Retiduum ac =e. Denique si per hoc Reliduum ac = e,
dividacue proximus Divisor av =0, prodibic quoriens e, et nihil restabic. V7
ex adjuncta operatione patet.
acc) ac tbul .
10 - e a = ac a - ac
30.. ac = e. at = c.
Acque hinc aset, poltremum hune diritorem ac = e, expolitarum quantita
tum a =e, a = e communem esse Dirilorem. Ouod es experimento facto
Patebit.
e
0
Adeoque communis hujus divisoris ope, reducuntur expOTita quantitates
a = e, a - e, ad simpliciores in eadem ratione, -- F a f c, = + P; vel etiam
(collendo tractionem) a ut ac + e, a = c. Ft proprerea   1
Acque hujusmodi exempla plurima tacile annecti possunt.
a.
Verum hoc in Synibolis neque ita prompte, nec unirertaliter expediri potest
aeque in numeris. Exempli gracia; quantitatum a f ac - b - bc, _ ab  a)
B- bf, havd ita facile, concinua hac dirisione, communis diritor innotelcit:
cum incerim communem hateant dirilorem a= b; ut ex adjunctis operacionibus
Datet.
Mu
1
e1