# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068195:0393
# Permalink to this reading: https://leibnizlegible.com/page/00068195:0393?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 197r, page id 00068195:0393
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 198v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068195&page=393
# Source image: https://digitale-sammlungen.gwlb.de/content/00068195/jpgs/default/00000393.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 99 lines, status machine
# Lines: 99 recognised, mean confidence 0.75
# 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.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

Aequationem hanc habemus:
4aarr. 1 90at1 - ari
a an - a = 1 =
d’g alis diga
2d cun +i
20 1 3c0a
da a 3. 1, - d = 1 18 10 i1a 18 184
a + 2aY-dd -d= 4X + 49 +
 a 19d 9d9d a
Reassum am.
srpositae duae aequationes findamentales hae sunt:
264a + 64 a (7 325) vel  1.t
136
18 1B13
32 a + 69 vel  vel
18c,
ee = 16a5 + 32 a + 26 Ergo
+a + 8a  - 44 +1 ) = 16a + 32a + 16
F+F FP Cdd9 = 16a 32 a F 16
Fi
9d2
ut 2 F 1 = 4a +E
a + 1.
A3
9d2 at1
ut 2 = 4a 2 + 4a  - 
odrnat. a +1.
vel 3a +1 = 4a +4a 2 + +a +.
a+d+ +2a3d2 = 4a7 +a + 2X +a) f + 4)7 + 2a3 
4a3d2 - a4d2. 2a2d2, d2
8
16d
4a + 8a3 = 4a +1 = e
ee =
11
aa + ar art
vel a3+1 = 4a +
d’9 d9 d9. = et vel a +1. + a
3a3 H2 - 1 - a = H 4 + 
a = 43-1, - 1 =
e
tiet d’a2 4 d2-
a +2a74 -7 = 4a + 49 + 4 + 1 Y2a + a5
da a +1.
1a2
a A + + a d - ad- d = 4a + 4a + + - a a
d2a
4294
a
942
2a +1. - 4a - 4a + = 4a
+a
4a5 - 44+ 382
n
50
4 +
1esal6
1d5a
1b b
16]4 c6
4
60115, 60. 18
1
5d(20. 170 15
44+8 + 
150
Ergo ddg 16a + 32a + 16 4a + 8a + 4+1.
152 4 a3 8a2 + 4a+ 1  a4 + 2a +44+1 : 9 (a +2074 + 49
gd= i Notundum hic est rem
esse per utilm ab nun parte termiinum,
ab altra raonem habere. Quia ratio
gam per multiplicationes et divisiones a
radicum extractiones tractari poliri re-
duci _ Salva raves identitate, termino
alto intacto Est ergo rad materia aequa-
tronum in aequave. Idque hic egregio
exemplo patet cum enim 4a +8a + 4 suit sequalia od
a2+ 243 +4a + 1.
quadrato Necesser esttrus ravis terminu esse
aequalem cuidam quadrato, neque videndum est
quae quibus divita producant quadratum, et
ante omnia cectum est quadratum divisum per
quadratum producerequadratum. Quare quanqua
vel 2a +
3
3a  ar 1.
ia
tisic
e id
Aa +4a +5X2
A + aet 2a Ht
1 45
15
6-35
1
4 + b. eH.
na aa + bh +rab
ab ta bb:
ate