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# Piece: https://leibnizlegible.com/api/records/595/text
# Catalogue record: 595 — Tentamentum duas irrationales reducendi ad unam sed deprehensum est naturam obstare
# Incipit: m√[x+b, x+c] + n√[x+c, x+d] = y
# Date: 1676
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=595&katnr=58172
# Work: https://leibnizlegible.com/work/00068201
# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folios: Bl. 31 (from the shelfmark LH 35, 14, 1 Bl. 31): 2 pages, canvases 61–62, page ids 00068201:0061 to 00068201:0062
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068201&page=61
# Lines: 51 recognised on 2 of 2 pages, mean confidence 0.74
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# 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, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 31r — 00068201:0061
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000061.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 48 lines, status machine
entamentum duas crrationales
si sed deprehensum est naturam obstared ucendi ad uemetu
M X+b, XtC + B VX+C,X+ d = y
siit inm, X+b. XFC + 2mn X +C Vx+ b. X+dC
nn. X+6. X+C
p. X+ C + 91 x+ b. X+d= Wd
fit + pp X+C
+99 Xtb. x +d
pg mn
sit cdc0  ~ yy. peret O
p9 = mn seu q= mn: p
Mm XX + nm b X + mmbe
un Xx + nnox +un de
C
pP XX + 2pp CX + ppCC
mnan XX + mmnn, b2X + mmunbo
pp
Ha
pp 5d)
pp
ram = mmppmmnn+d) =, 2pC 0O = napp(d + C)
sit nm= 2pC -npP Cd + C), :, pp(b. + C) - nn (b+ d)
m  P = nnpp,: pp = na = pp. nisi pp nn
2
ubi reset
Mm = DCC= nappdE :, ppbc = un bd sed nonnecesse
aquando valores 2 et 2, iter 3 et 2 habetur
nn- p, bis, nam ex 1 e 2 fiel
2Cp 2C = nn (d+ C), : fb+c - na b+d) = 1 -nn : 1 - nn = 1
P
PP
et
pH
Ergo (DC nnd) = nac = b (+9 - na b (= un d). Ergo
 pP
nn c- b = 1 seu nn = pp
pp
c- b
Ex 3 et 2 fit eode modo cc = un dC = bc - nn bd. seu
cc-bc, Dc. nn  cc-dc = C nisi cum
Pp
ubi res etia
voc-db 0, sed tamen
sed quia u necessaro fit 1. ideo vel C = 1 seu C = d) non necessaria
succediti
vel C = b utroque modo alterntra irrationalum una
perit. Itaque propositum consequi non licet
d

## Folio 31v — 00068201:0062
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000062.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 3 lines, status machine
oete oeso
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