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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 391, page id 175905688X:0413
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=413
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 50 lines, status machine
# Lines: 50 recognised, mean confidence 0.84
# 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.

e
breri
cetto
c dlobi
decmuli
EBICCA
c
e
poltone
scoul
A B D E F A I B H X u M.
139. C
SC, cujus veraque pars he irrationalis: hinc ad eam extralendam
datum binomium per differenciam quadratorum parrium erie
mulciplicandum, si de radice cubica extrahenda quaestio fuerit;
aut per quadratum hujus differeneiae, (i de V 5; auc per ejusdem
 
cubum, sider; duxperipsus surdetolidum. S der (F2) qua-
ratur, atque ita de cateris. Oud racione aliud semper binomium
habebicur, in quo radix differentix quadratorum partium erie dit-
terencia quadratorum partium prioris binomii. UEt ad exerahen-
dam radicem cubicam ex 25. F V 968, subduco primum 625,
GuadTatUM ex 25, 2968, dE FEIAHENE 343, cujus numeri radIX
cubica elt7, numerus nimirum rationalis. Id quod arsuie, radi-
cem, modo ex dato binomio extrahi postue, Fore binominim, cu-
jus una pars tutura sic rationalis. Similiter ad extrahendam V (3)
ex 22, = V 406, oporcet 484, quadrarum d 22, Tubdycere ex
486, ec ex reliquo 2 elicere radicem cubicam. Quoniam rero id
tieri non porest, constar radicem cubicam ex 22 + V 486 parre
rationalicarere: ac propterea 22 F V 486 per 2 mulciplicandam
esse, ut habeatur binomium 44 L V 1944, in quo radix ditteren-
cix quadratorum partium est 2. Sic ad extrahendum radicem sur-
Colidam ex YY. F V 125, quoniam subductis 727 a 125, rem2-
nenc 4, quinumerus surdesolidus non est: hinc IY L V 125 muI-
ciplicari debet per 26, quadratum ex 4, ac proreniat 176. f
V32000. In quo radix sursolida differentiae quadratorum par-
tium est 4. Denique ad excrahendam V (D ex 338 = V 1742427
in quo differencia quadratorum partium est 2, quoniam hic nume-
rus B. Curdesolidus non est: ideo datum binomium mulciplicari
debetper S, hoc est, per cubum ex 2, ee hc 2704 + 1 7321488,
in quo r 3) differentix quadratorum parcium est 2.
R F b
420
Pet prxcedende praeparationem semper inrenitur binomium,
cujus una pars, de alcerius partis quadratum, nec non radix diffe-
rencia quadratorum partium, lunt numeri rationales integri; ex
quoV (3, auEV G, aut V ∞, QC. extrati debet.
In quem tinem inveniendus est numerus racionalis, cadice quae.
Sta paulo major; ita uc ditherentia non major sic quam L. Ouod
Facile per rulsarem Arichinericam fieri porett.