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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 457, page id 175905688X:0479
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=479
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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 0.85
# 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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vol
DE REDRCFEOHE AE QUATIONRM. 457
coonitam quantitarem habences, quaerendoque per
carum communem dirilorem valores iplius y vel Z.
eodem modo quo in Parte q dictum eAt.
2. Si primo per capitales A, B exam en AaC, eum ex2-
men per reliquas e et E superAuum habendum est, sect
nOM ViCCVeESA.
Exempli gratia, proponatur haec aequatio
∞6- L X5, -  4 X =-  8 ∞ 3 - 5 X X L TEX L 6∞0.
Ouoniam nulli cermini delune. Reductio eric centanda per
A, B, C, E; incipiendoque a minusculis, ac primum ab c, habe-
bItuT Z∞ 9∞ 4, e W ∞ = ∞ 5, adeoque pIO ∞ 3.  y X X  Z X
I W ∞ O, Het ~3 X f + x - f 5 ∞0. Cum vero Propolica xe qua-
tio ver hanc diridi nequeat, transeo ad F, obtineoque y ∞ P ∞ L;
W ∞ = ∞ +; Z ∞ O; de In lOCuM X3 L y X X L Z X -F w ∞0 obti-
neOx3 LLNx F = ∞ 0. Eccum Propolita per hanc quoquenon
dirisibilis existat, eran seo ad A, et P1O 2Z3 - 3922 rpZ 59∞0
+PP + 25 L tP
+99
Obtineo 223 - 22ZZ- F 182=9 ∞ 0, cujus radices (unE. L 3.
 F, d-  12. Ouia aurem omnes hae radices sunt rationales.
ac aouatio Propolita Fractis numeris carer, non poterit nobis
haec ulcima radix inserrire. UInde explorandum tantum reltat per
Z ∞ 3, ee Z ∞ I. Sumendo autem Z ∞ r, reperitur divitionem tic-
rinon posse, ac idcirco sI (UMaEUEZ ∞ 3, Fet W ∞ S + 2 2- 42 ∞2
Ouoniam vero y est ∞ O, Pro ~3- L yXX -L Z X - L v ∞0 obci-
nebitur x3 X-  3x- f 2 ∞0, per qua si diri (Io PropOlItae ten
cetur, comperietur ipsam tieri polle, acque oriri x 3 L LX X- 
TX f 3 ∞0. Sed locorma aequationis juxta A lumere poruisse-
inus 2dam, una dimentione deprectiorem, pro qua obtinuissemus
23ZZ  60Z  6330. Oux unam tantum radicem racio
nalem absolutam admictie, qua, uc supra, clt . 3.
Eenocandum, quod, inventis duabus aequationibus, (quae Pem-
per, Si per communem dirilorem Ouxlitum obtinere velimus,
inveniri debent;) quaeri pocelt radix alteruerius aequationis, sI
nempe ea Facitis sic inrentu, atque explorari, num ex altera ae qua-
Mmm