# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/175906937X:0069
# Permalink to this reading: https://leibnizlegible.com/page/175906937X:0069?run=74
# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 45, page id 175906937X:0069
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=69
# Source image: https://digitale-sammlungen.gwlb.de/content/175906937X/jpgs/default/00000069.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 59 lines, status machine
# Lines: 59 recognised, mean confidence 0.80
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

a, de t
lepucde
10 uuque
aio prO.
Ali
per CM.
NACOLLM
dmInatO.
15ad Can-
omncendo
Deu.
Opetut.
mnacu
educi pot.
inacotm
AC pFOIU
AAZ  
DUmCCa
ote
irest
22-
licandop
sit
MIA TH ESE OS IINLVERSALIS.
22 f a2 ] a =, unde multiplicando per crucem, invenieryr
XquatiO 2 ∞ bZ Z - abZ = a a b.
Ad lXC SI PEOPONatuE V Z ae quari 5: quoniam x qualium a qua-
lia quoque lunt quadrata, cubi, ecc; hinc liutraque pars in le mul-
ciplicetur quadrate, habebitur Z ∞ 25. Sic ee Ci Tuerit V Z ∞ V 5:
dueca utraque parte in se quadrate, fet 2 ∞ 5. Pari ratione (I V Z
XqueTUEY a ab =b, erit Z ∞ a a b - b. FIaud secuS (I FuCrIEV C. 2
∞V C. aa bb - b, tiet, utramque partem in se multiplicando cu-
bice, Z ∞ a abb - b. FFhC de aliis.
De Reductione per Divisionem.
D OAtea Sidetur ZZ ∞ 4 Z: quoniam, aequalibus per requalia vet
L idem dirisis, proveniune aequalia, Fc uE, Si utraque pars diri-
datur per Z, Oriatur Z ∞ 4. Sic ee Cihabeatur 2+ ∞ 4 Z3 - f - bbZ 2, di-
videndoutrinque per Z Z, tiec Z 2 ∞ aZ F b b. Similicer tc, li propo.
RaTUF 3Z ∞ 12: etenim Ci uerobique diridatur per 3, proreniet
2∞ 4. Fodem modo lituerit a Z ∞ ab, diridendo utramque par-
tem pera, Hec Z ∞ b. Nec alicer Ci habeatur a x -- b x ∞ bb, orie-
tuE, dirisA vErAquE PartC PCTA =b, X ∞ =-7. FTaud SeCUS SI pFO- PaB. 143,
PONATUTAZZ F - bZ Z ∞ ab 2 - f bbZ = a bb - b3: quoniam u- 1B. 27.
traque pars diridi potest per a Lb, Orietur ZZ ∞ b Z = bb. Sic 8
SI FICrIEAZZ = bZ Z ∞ a a Z -- bbZ L abc, diridendo utrinque
Per a - b, ACEZZ DaZ F bZ +
abc
abc
= (eu 22∞ + B~ F a b
Fluc reterendum quoque est, cum bina ae quationis parres, juxta
modum p. 34. octenlum, re duci pollunt ad simpliciores terminos.
CE ( Tuerit aquatiO InEEF aZ +- abZ 3 L abbZZ _ = ab2 3. - 2abbZZ
2ab32 F ab: diridendo utram que partem per maximum com
munem dirisorem aZZ- abZ L abb, OriCtUE ZZ ∞ bZ ] bb.
De Reductione per Fxtractionem Radicis.
Enique ad reducendum Z2 ∞ 25: quoniam aequalium qua-
dratorum ac cuborum ec. aequalia quoque lune latera seu
aliteCs,  uC, h ex veraque parre excrahatur radix quadrata, Pro-
venide