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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 390, page id 175905688X:0412
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=412
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 39 lines, status machine
# Lines: 39 recognised, mean confidence 0.92
# 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.

390
AD B E PIA CNELELN X VV.
V5, 8FEV 242 + 25, deinde ver 2, uejam Factum est, e sc de
CxtCIIS.
Deinde, sineutra pars binomis rationalis suerie, reducendum
Est ver inulciplicationem aue dirisionem ad aliud binomium, cu-
is aleera pars sic racionalis. Id quod per mulciplicationem alter-
uerius partis semper Heri potest; led brerius plerum que per mi
norisnumeri mulciplicationem euc dirilionem. Onemadmodum
V242 = V 243 mulciplicari quidem porest per V 2+2, XAE 242
V58806; sed compendiolius per Y2, e provenit 22 L V 486.
Fodemi modo V 3) 3993. + V (6) 27578+25 pocest bis mulcipli
cari per Y (3) 3093, e producitur aliud binomium, cujus absolu.
tusmumerus est 3973; Sed brevius perv (3)9; et adhuc brerius.
si dividacur per Y (5)3, tierque IY L V 125.
Cibinorandum, postquam habetur binomium, cujus una pars
est rationalis, tunc, quoque quadratum alterius partis rationale
esse debere; aue nullam ex eo radicem, nec etiam ex alio bino.
mio, utramque partem irrationalem habente, a quo permulcipli
cationem auc dirisionem deductum est, extrahiposse.
Tertio, ad extrahendam V 9); oportet primo radicem qua-
dratam extrahere, ee deinde ex haC N (3). Ec ad extrahendam
V9 oporcet bis extrahere Y 3). Fc sic de reliquis radicibus, quae
pernumeros compolitos, hoc est, qui per alios diridi possunt, de
lionantur. Radicem rero quadracam quod actinet, regula ad il.
lam extrahendam latis nota est: quapropter hic tancum opuselti
ut doceam, quo pacto extrahenda sinEV B, V 5, Y E, Y (1I), ee
similes alix, qua pernumeros primos, hoc est, qui per aliosdi
vidinequeunt, denotantui.
Postremo ad extratiendam V 3), V 9, V O, aut similem, per
numerum primum designatam, explorandum primo est, uerum
radix Binomium esse portit, cujus una pars sic rarionalis. Id quod
innocescit subducendo quadrata parrium a Peinvicem, et exreli-
quo extrahendo radicem, nempe cubicam si ex dato binomio
V( Sc exerahenda; aur surdelolidam, si V (5) sit extrahenda, et sic
decaceris. Ouod ita in posterums ubiradix aliqua extrahi debets
intelligendum est, licet expresse non dicatur. Frenim si radix
haec numerus rationalis non fuerit, certo constat, radicem quae-
sitam paste rationali carere. Sed cum binomiumi adhuc esse pol-