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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)
# Folio 386, page id 826603459:0432
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De Fractionum Reductionibus variis. CAP. 44.
Cui denominatores congrui (modo mox ostendendo) alsump-
ei 20, 15, 8, exhibent expolicis 2, 4,E aquales cognomines
25 325, 25, ee quidem minimum communem denominatorem
habemres. Sic 2, 13, 5; diritis cum 2 _ r0 per communem
MenTuram 23 ProctibunE quociencCS 2, 5; cum iterum 5 (quo-
ciencum jam inrencorum alcero, qui propcerea eciam eliminan-
aus erie, cjalque loconorus per lequenrem divitionem lubsti-
Euendus) S  (denominacore tereio) per communem divilo-
rem 5, unde prodibunt quocientes in 2, _ (ex prioribus duo-
Bus) relumendus x, qui in duos communes dirilores 2, 5, Con-
tinue ducti, dant LXE ~ IX 2X5 = 10 communem denomi
nacorem minimum; quibus relpondent denominatores con-
FruI 5, 3, 8; adeoque tractionibus expotcis 2, 103 5, aqua-
Led TunC, cognomines 18, 253 ad. Sic aB
a35
bas caB
reducuneur ad cognomines minimos à B7 A3 à By s’aBys
Invento autem communi denominatore minimo, Numeratores
consrui invenioneur, hoc eAt, Fractiones expolca ad datum De-
nominatorem reducuneur, hoc modo:
Ad darum denominatorem reducirur data Fractio, (Inovus
ad Denomi altumatur Numeracor, qui, ad dacum Denominaeorem, cam
natorem da habeat racionem, quam habee Fractionis daEx numeracor ad
tenneno denominarorem Cuum. (Rario manifecta cA; quoniam dum
Terracur eadem Numeratoris ae Denominacoremracio, eadem
manectractionis quanticas.) Sic sFractionem Z, reducerere.
lim ad aequale eliam, qua denominatorem habeat 10; Guae-
rendus es Numeratur, qui hcad 10, uc eAt x ad 2. Sire, ad
quem, eam hahear racionem 10, quam 2 ad Y. Qnod per au-
ream resuLA PerABIUE: PUta 2. 1:: 10. 9 = =E =5. A-
deoque 15 im Z. Paricer si ad eundem derDminaEOrEM FO, re-
ducere velim Fractionem E, Sumendus est Numeracor 8: (quia
P. 4:: 10. 8.) Adeogue, S = 8 PF propterea (quod ino
Ao diCium erat) Fractiones Z, 16, 5, ad communem denome
nacorem roreduera, erune 15, 10, 20. Eodem modo, tra-
ctiones.:
20122320: (WVam 2, 2:: 20, 20. ILem 4. 3:: 20, 75.
deem
8
Fractionis