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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. XLIII. MULTIPLTCATIONE, EEC.
a - b (a  + ac = b2 - bc (a + B +c
Adeoque communis illius Divisoris ope reducentur exposiixe quancitates a2 f ac
bc, e ab + af - b2 -bf, ad cerminos in cadem ratione minores a + b
F6, _B + f. Adeoque a +ac = B2 - bc a + b +c
ab.
5-
b +f
In hujusmodi iiaque casibus, acque hiscetimilibus, Pagacitate opus erit, et con-
tilium in arena capiendum, ul ex posicae quancicases compolicae, ad simplicistimas in
cadem ratione LCdUCaNEuE.
Sed de Addicione de Subductione hactenus.
Gi A P. XL III.
Fractionum Multiplicatio  Divisio: per numerum In-
teerum; per numerum fractum. Multiplicationis, e
Divisionis inversae, aequipollentia. Producti, e Quo-
tientis, in minimis terminis exhibitio. Operationum
praecedentium (Saditionis, Subductionis. Multipli
Fractio-
cationis.  Divisionis) brevis Synopsis.
CEquitur Fractionum Mulciplicatio et D vitio.
D Si Numerus fractus per Inteorum mulciplicandus, Cit, nihil hrie disticulcacis nis per
inest: Ouippe id sola Numeratoris multiplicatione peracitur. Sic 3X 2 = 2. Nam numerum
bis duo sunt quatuor, quaecunque demum ea sint quae numerantur: Sive integea integrum
Sinc, sive partes. Oua enimratione, bis duo homines, lune quatuor homines; bis Multi-
dO COTPOTA, quatHOT COrPOTA; bis duo incegra, quacuor intesra; bis duo millia, plicatio
quacuor millia, ecc. (nempe, quia bis duo Timpliciter, TunE quatIOT:) cadem, de
bis duX PaTLES, quacOT parteS ; bis duo quadrantes, quatuor quadrantes; bis duo
guintances, quacuor quincances, (live partes quinta.) Sec. Sic Z X A, vel ZA, exit
Sic DX =, vel, Z xD, vel Z D, exie =. Et sic in aliis.
Vel etiam, quoties id commodetieri pocest, pro Multiplicatione Numeratoris,
Tublticui porerie Denominatoris Divisio. Ouippe idem ommino sic, quoad tractio.
nis valorem, sire mulciplicemus Numeratorem, sire Denominatorem dirictamus:
e Conra. Si enim verbi gracia, duplandus sic numerus Fractus Z: perinde cst lire
duplicetur numeratOY, ut tatS; Cire denominator bisecetur, uc tiat 3: eadem enim
urrobique prodibie tactionis quancitas, 5 = Z, quoniam eudem est iurobique nu.
meratoris