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# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 29, page id 175906937X:0053
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=53
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 67 lines, status machine
# Lines: 67 recognised, mean confidence 0.78
# 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.

niIS, I22.
l. 210 2
2t +b
postine
2 ab + bb
etumb
abb. 1
ulciplico
EC
1 X)
CX, Gut
budet
1258
bHicuco1
in nume
aa- bb.
C eAt
eF A F 1,
ud aliiet,
Oret
5.
ex Mm
1n Oua
ali
NIA THE SEOS CIH ZY ERS A L1S.
dix quadrata ex a abb est ab, ee radix quadrata ex cc estc, Pcribo
proradice quae lca
Fodem modo, si exrrathatur radlix quadratL ex 2t = 2 a abb f b4
Aet =a- bb
aa + 4 ab + 4bb3
+ 2b. Pari ratione ad extrahendum radicem quadratam ex
64. de X = 160 ∞
64 X X = 16OX
ee radix quadratA Cx 2OO-- 16O X
L64 Xx est TO = 8X, de radix quadratA ex 25 est 5; erie radix
Non secus radix cubica ex
27Xb --5425- f -17144 - 188.3- f 28542 - 150X F 125 F
23. OXX + 27∞- 27
3X _ - 2∞ f- 5
X-
Ouod si quaesica radix praedicto modo ex numeratore atque
denominatore extratu nequie, praepontur data tractioni lignum
radicale V. Ut ad extrahendam radicem quadratan ex ccxn
Fcribo V cc
+bb
FaCIECCXX = 4 abbB
4bB
4b6
46.
ac in formam tractionis
de ex denominatore + bb extrahi porest ra-
dix, guae est 2 b: ideo quaelita radix sic quoque scribi poterie
V CCXX = 40bbC
Similiter radix quadrata ex
aabb
aa L. b63 eriE Y aa F 6b
Idem de reliquis radicibus est intelligendum.
DE LOCISTLCA OYANTITAEVM SVRDARVM.
Clemadmodum tractiones oriuntur. ex diritione impertecta
Lquanticatum, quarum una per alteram sine reliquo dividi
nequIE: Ita ex excractione radicis quantitatum radicem non ha-
bencium exlursunt quanticates surdae, quarum operationem se-
quentibus exemplis exponere visum fuit.
De Reductione quanticatum surdarum.
Clencu agues guou eul aoperaltonca lacce t
versa denominationis oporter prius iplas ad eundem denomi-
BaL.