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# Title: Qua Continentur, Oratio Inauguralis. Mathesis Universalis; sive, Arithmeticum opus Integrum, tum Numerosam Arithmeticam tum Speciosam complectens. Adversus Meibomii, de Proportionibus Dialogum, Tractatus Elencticus (shelfmarks Leibn. Marg. 84:1, Stück 1; Leibn. Marg. 84:1)
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E AP. 440
De Fractionum Reductionibus variis.
Inhis, inguam, aliisque ejusmodi casibus, obi partes deciman
les vel in lonsum nimis, vel in infinicum excurrume; Cufticit vero
Preximum pro vero accipere; adeoq; operatione quoulq: libee
continuata, quod superes negligere. Puta, pro 33 53 12332, _C.
Tumacur 0(3333. 0,8333.0 (90909, 0 0937. Vel etiam
0(333. 0(833.0(909 0,094. Vel Forre 0(33. 0, 83,0(91.
0109. Pront major minorre accoratio requiratur.
Fractiones aurem Decimales, ubi orus elt, eodem plane mo
doad alias reducuncur, quo religuae fractiones ib una ad aliam
denominationem. Puta 0(5, hoc cA 10, ad =, avidendo
cum Numeracorem cum Denominacorem, per maximum com
munem divilorem 5. Sic 0109375 -- 160000 =- 32, nempe
dividendo per maximam communem menturam 3125. Pe sic
in reliquis. Si aucem ea reperiatur mentura quae non quidem
accurace, ac Calcem qua proxime verumq; terminumenturetspo
ceric illius ope allumi srectio ordinaria, quae, licet non accurate.
quam preximé camen aeguabitur exposuex Decimali: adcoque
proliac alsumi posic; praesercim E supponacur Fractio ille de
cinalis c quod nonraro sic, praetertim in cabulis AAronO-
micis, Frigonomerricis, _c.) nen praeclle Geometricam re-
ricatem, sed veco proximum, debenare. Sic, Pro 0 (33333, hoc
cA 1366 allumi pocerieranquam aequalis Z, cum camenhac
aliquanco majortit, (quippe equalis huic 3335,) sed can-
cillo uc ca differencia cuco neplisi possic, ubi scometrica arpi
Bcca non exigitur.
SiFractio ordinaria quaeris, ad parces sexagelimales re. Reductio
ducenda lic: Ducto dumeracore in 60, per Denominacorem. Fractionis
fiac Dirilio; _ Ouoriens indicabie Minuta: Relduum aurem ordinariae,
divitionis, si quod sic, in 60 ductum, _ per Denominarorem ad parres
(tractionis dacxe) dirisum, exhribebic in Ouoriente Minura l0. Sexaersima
cunda: EFsic deinceps minura cerria, quarca, ec. rroctibunt, les. PI con-
si divitionum relidua semper in 60 aucantur, et producta per 1r4.
communem Fractionis dacx Denominatorem dividantur: Onoa
cousq Faciendum erie, donec vel nullum Cuperhic ressduum, vel
quod (ob operationem jam lacis cortinuatam) neplioi postic.
Ouod enim de Decimalibus modo dictum cA, idem _ in SCxa-
genariis tractionibus laepistime tic; nempe nunc in intinicu, nunC
lalcem in nimis lonsum procedendum esse priulguam coca tra.
 C