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# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 26, page id 175906937X:0050
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=50
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 54 lines, status machine
# Lines: 54 recognised, mean confidence 0.82
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

de
a5  a a b3
P X I N C I P L A
aaca = aa d d relInquCEu 25 = a a b3 - b+ d
125.
∞ = 25
b4A
aacd aadd:
aac d - a ad a. SiC de CITollatur
23- - 30 X ∞ - 625
∞3 = 25 ∞ _ N - 10∞ f2,  LCMaNCDIL ∞4 - + 5 ∞3- 25 ∞ N - 125X
Fadem racione ad subducendum aa = ab
a. + 3 dea, reducta quanti-
tate a ad denominatorem a = b, demiptoque 2a = ab  a a + ab
2ab
a + b
het reliquum a. +. 8. Non secus si Cubrrahatur b. ,
relinquetur a - b + d
De Mulciplicatione fractionum.
2b
a + B3
de a - f b.
D multiplicandum = per =X mulciplico numeratorem ab
per numeratorem de, ut ee denominatorem cper denomi-
natoremf (ad modum tractionum rulgarium), ticque productum
abde.
aa- bb
multiplicatum per 2ac
 diC d
b. Fc
producie 243b -- 2 ab3
60 +cc
Ad Faciliorem autem operationem non raro convenit abbre.
viare quantitates per crucem. Cr ad mulciplicandum
aac = aad -- bbc + bbd a3 - a bb
aa + 2ab F bb Per Ca = da: Quoniam A AC = a a d =- bbc
 bbd _ cd - d d reducuntur ad limpliciores a a -- bb de d, ut &
a3 = a bb _ aa + 2 a b f bb adt a a = a b X a j b; hinc loco1muI-
tiplicandi a ac - a a d -- bbc. + bb d per a = abb mulciplico aa bb
per aa - ab; ee loco mulciplicandi aa- + 2 a b - F bb per c d - d d
multiplico a- L b per d: eritque productum -= a3b - aabb. +- ab3
ad = bd
Porro ad muleiplicandum a a - bb pcr 2 a = a b
a + B: Substituto F
pro denominatore ipsius a a = b b, GuOnIAII NUMIETATOF A a -bb
e denominator a L b reduci polune ad a - b e Z, hinc multi-
plicatis numeratoribus inter se, ut a denominatoribus, Hec pro-
duCtum 23 = 2a ab + abB
(eu a3 = 2 a a b F a b b.
Eademratione cum mulciplicatur a. L
aa = ab + bb aa - 2ab + bb
BPeFa- 2b. + =, hOC
: Quoniam a a - 2 4b f bb
80