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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. XLIV. REDUCTIONTBNS.
quacuoe denarios, acque intuper ; unius denarii. Sic, fractio , ad aliam rectu-
cenda quae denominatorem habeat c, erit ) ac
Ouae aurem jam cradlica sumc de lractionis ad dacum Denominacorem reductio. Practio
ne; vel eciam plurium tractionum reductione ad Denominatorem communem: num re-
Fadem non disticulcer de reductionibus ad Numeratorem dacum, atque ad numera ductio ad
torem communem, exponi poltune. Vix enim aliud ad hoc tactu opus clt quam
atum
Numera
uc pro Denominatoris roce Tubsticuatur Numeratoris, de contra. Sic Fractiones torem, ve
2, 23 aquipollenc hilcc 5, 5. Irem tractionibus 3, 3, 3, aquivollent 5, 5, 5. Lic tra. Numera
ctionibus =, =, =, aequipollen 2bc abc abc
ab0 BaC rab. dic tractio, ad adiam commu-
reducenca quae numeratorem habeac, c, eric  = . Et sic alibi.
De Fractionum tractionibus, sire minuriarum minuriis, reducendis; nonnihiil De fra-
etiam dicendum elt. Ouippe nonnunquam tractionem aliquam ulcerius trangi ctionum
concingi; cujus, canquam Luccsri, partes, Minuria minuciarum, sive fractionum fractioni
tractiones diei lolene. Puca criemtis lemis, vel bessis dodrans, _cc. quos sic nocare
Tolent 53. 33. 8c. vel lic, : Cx L. 3 Cx Z. _c. Mallem c80 Sic 3 X 5. 3x 3. _c. (quip.
2, vel ZXF, semillis unius incegrI; ZX 2, Semistis duorum; 5X 3, semilsis erium:
Aique hine Racim patet methodus, ejusnodi tractiones compolicas ad simplices
reducendi. Nempe mulciplicatione lola id peragicur. Duca ductis invicem 3 e 3
Crir (per tracica in CUDCrIOTE CApITC) 3X 3 = 15= 3. Sic 3 X3 = 5. c. Similiter
Si pluries adhuc componatur; pura semis dodrancis duarum terriorum, LX Z X3 = 3
4. Ec Sic alibi.
Eodem plane modo reducenda cM, hujusmodi Fcactio =Z, hoc CA 4 5, X 2, sire
24x 2 = 28 = 2. aliaque Similes ubi Pumerator Fractionem adjunctam habet.
in communem muleipliearorem 5, prodibit (non mutata quantitate) 38, vel 3
Nec dissimilis eric reductio tractionis hujusinodi (cujus Denominatori adjun-
Sicur tractio) 3, = - 3: Ductis neMDC CuI NUMETALOTE Cu DEnOminaIOIe,
in communem mulciplicatorem 2, non immutatuE quancitas.
Sic 43 = 18; ductis nemperum numeratore cum denominatore, in 20 = 5 X2.
12
Fademque plane mechodo ucendum eric, in tractionibus (s id obrineat) crjam
adhuc ulterius fractis, sire in Numeratore, Sire Denominatore, live etiam vrro.
que. Vr non lic opus hisce diutius immorari.
Suverest ut de Fractionibus Sexagenariis, et Decimalibus rerba Faciamus: ex.
redu
cndis
De nihul aliud est hujulmodi tractionis tractio, quam tractio ex duabus invicem.
mulciplicaris compolica.) Vri enim = A vel EX A, est semistis quanticatis A; e
ua Z 2 3, est semiltis crienris; 2X3, docrans bestis, sIve ires quarca duarum terrta.
rum, c.
c
Defra-
runque cum ad inricem, cum ad fractiones ordinarias reductione; atque harum nibus
ad illas. Fx omnibus enim tractionum Reductionibus, hae duxe prae reliquis cele sexage-
bres sunc; nempe reductio ad parces Senagenarias, et ad partes Decimales: de nariisés
vice versa. Illa rereribus admodum tamiiaris erat ee Frequens; haec MaXIIe,
Recentioribus.
In tractionibus Sexagenariis, supponitur intesrum quodris in parces 60 diridiu
quas vocant nenia minura prima, lerupulos primos; lt eorum quodlibet in 60
minura secunda; ex quodvis horum in tocidem minuta certia; de lic deinceps,
in concinua ratione sublexasecupla. Sie, rerbi gratia: FTora diridicur in 60 mi-
nura prima, ee quodtibet minutum primum in 60 sccunda; ec quodlibet secun-
dum in cocidem cerria, etc. Irem circuli, sire quadraniis, auc etiam Signi Ciractus
quilibet eadem ratione diridicur in Minuta Prima, secunda, tercia, Cc.
In Receuciorum parcibus Decimalibus, supponicur incexrum quodvis dividi in
TOPaF-
libus.