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# Title: Ad majorem Dei gloriam. Theorema Arithmeticum (shelfmarks Leibn. Marg. 88, Stück 5; Leibn. Marg. 88)
# Folio 6, page id 827668708:0008
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=827668708&page=8
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 38 lines, status machine
# Lines: 38 recognised, mean confidence 0.91
# 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.

paT. Fsob impar. Fric ergo differentia a-b, impar: e dit-
Ferentia quadracorum a 2 -- - b2, impar: e minoris quadraci
lacus b, par, conera hypochelim. Non ergo a, est par, sed
impar: _ reliqui b, c, LUnE ParCS.
EA ergo a --- b, differentia impar, ex quadeacus: cujus
radix dicatur d: critque d2, ipla differentia a - - - b. Pric etiam
a 2, IImp2T, _b 2, Par: _ differentia quadratorum a 2 - - - b 23
ipar, e ipla quadratus: cujus radix impar, ex mulciplex
2d d 2: vnde sublato impare d 2, relinquetur par mulciplex
ad d 2: cujus dimidium dicatur e: exirque lacus a, idem ac-
que 2c2 d2 +2ed 2 + d 2: e minus latus b, idem atque 2 c 2 d
2Y2 ed2, mulciplex ad differentiam d2, Per 2 e2 + 2e, qua
druplum criangulum a latere c.
Acqui b - - - c, est differentia par, e quadratus par: cujus
radix par, de radicis dimidium dicatur f. Prit ergo b - - -c,
idem acque 4f2. Fric quoque radix differentix quadratorum
b2 -- - c2, par, mulciplex ad differentiam 4f2, per numc-
rum, qui dicacur o. Onare 45f2, radix erit disterentix qua-
dratorum: ec eric ipla differentia quadratorum 1682f4: 8
Cumma lacerum 492f2: _ duplum majus latus 48 2f2 F 4f2:
ec majus ipsum lacus b, erir idem atque 28 2 f2 F2 f2: 8t
minuslatus c, idem acque 292f2 ---2f2, mulciplex ad 2f23
per 52--- +, quadracum lateris e, vnicate mulcatum.
Sunt ergo eidem b, cadem, e incer le eadem, 2c2d2 7
2cd2, _ 292f2 72f2: ex est a, idem acque 2 c2 d2 7 2 c d 2 7
d2: ergo a, est idem acque 252f2 F 2f2 + d2: ec idem ac-
que 282f2-- - 2f2: corumque differentia eA 4f2 7 d 2.
Es ec a 2, idem acque 15 +f4 F882f 4 Y 4f4 F 482f2
d2 F 4f2d2 + d4: e c2, idem atque 45 4f4 = 882f 4 Y
4f4: e differentia quadratorum a 2 =c2, eadem acque
1682f47 452f2 d2Y +f2 d2 + d 4: acque ipla est quadratus
2 radice 4f2 7 d 2.
EK ergo radix difterentix quadratorum a2 = c2, ad dit-
ferenciam lacerum a -c, aequalis, e non mulciplex. Atque
ita differentia quadrarorum a 2 = c2, ad differentiam lace-
Tum a =c, CAVE a = c, ad rnitacem: sed eriam est ve a fc,
ad rnitatem: quare a -c. 8 a tc, Cunc aequales. EF hoc est
abCurdum.