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# Title: Ad majorem Dei gloriam. Theorema Arithmeticum (shelfmarks Leibn. Marg. 88, Stück 5; Leibn. Marg. 88)
# Folio 3, page id 827668708:0005
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=827668708&page=5
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 51 lines, status machine
# Lines: 51 recognised, mean confidence 0.69
# 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.
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# After the first blank line: the recognised lines in reading order, one per line.

bensoben sobesobe ddben
110 le 6(06106e 6 606O
st os os cto e e
65
60 1000 soet den8060 30610de
6c660606C(6106l0  no 0eeo
l e use esg esg als ess uls eo es ess e ess ils e ese els ess ala plo ese els es d 
e
 ese
D(O esu Ces∞ (D C)C ((C) () (3 ((C (e)C (0)D (0(∞) (D sC )) C(C) Cet
a
e
C6 4
 ose 6 6 6 e e6e  66  6 6 622 6
6090
ARITIIMETTOOM
Macese
on est posibile, tres inaquales numeros assi-
enare: quorum differentia, tres quadrati;
eg differentiae quadratorum, tres quadrati.
s
e
ne
OSSTBTLE CA enim, duos inaquales nume
10s allignare, quorum differentia quadrato.
cum, quadracus: ec primum duos, quorum
differentia quadratorum quadratus impai.
ADumatur enim quodcumque Lacusa: e du-
plum lacus 2 a: ex augeatur rnicare, ve hat 2 a F r. APumatux
ejuldem laceris rriansulus a 2F a (2): e quadruplus criangu
LuS2a2F2a: d mulciplicetur per quemdam imparem nume-
rum b, ve Aac 2 a 2 b F2 a b, numerus minor: qui augeatur iplo
impare b, ve frac 2 a 2b F 2 ab Fb, numerus major. FcaTuman-
cur duorum hujusmodi numerorum quadract, 4 a 4 b 2 + 8 a
b2 + 4a 2b2, minor quadratuS; ec 4 a 4 b 2 F8a 3b 2 + 8 a
2b2t 4 ab 2Fb2, major quadratus: quorum differentia + a
2b2+ 4 ab 2 + b2, quadratus a radice 2 a b t b: quxe producieur
ex 2 a FF, in b.
Irem possibile est duos assignare numeros, quorum difte-
rentia quadtacorum quadracus PaI.
ANumatur enim quodcumque lacus a: ejusque quadratus
a 2: Qui vnITaTe MINUAEIT, VE AAC a 2 = f: de per quemeum
que numerum b, mulciplicetur; ve fiac productus a 2 b - b.
ex minor numerus: cui addaTUF 2b, PaF, ve AaE majOF nu-
merus a 2b F b. Ouorum AanC quodraEt, a A6Z = 2 a 2 b 2 1
r
A
D
2
e
A