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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 3
# Folio 31r, page id 00068000:0061
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 32v); this page is its right half.
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 115 lines, status machine
# Lines: 115 recognised, mean confidence 0.80
# 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.

quaeritur an possit ex esse X + 3 = gu. ita et X sitractus fit a + Bs -. 1
fit a 5 + q = vY et X 2 a vV : 9q
4 5 6 7 8 9 10 1 1 n quolientes si quadrati dpudantur per 3, sunt B 9 10 10n
1b 27 36 49 64 81 100 1ut 1193 0 1 3 5 8 12 16 21 27 33 40 4856 65 25 804
2 0 1 2 o en
1b B1 256 625 1096
v - 4 = v
0 5 27 85208 64 - 16 4
8 -4, 814 3
X = 
sit v = 8. et 9 = 2, g0 v =   _ _ 4 :
12 + (a - 4 181 1
V. + gu = D ag - 3. 1 v = ag - 49
8- 2 =53 8+2 = 3. 4 8- 2. 3.  v- 9 = 5  8- 2 =
261 256
si un et st divedentur per a, debent residui esse eqales t isi vet quidi
si 4294 et B + dividan ter per a, iebent, vel residui este aequiles,  bll simul facere a
tantque q et  primi inter se
v+ q=  v est major quam que
2 2 3 4 4 3 C 6 y 8 8 910 10 1 12 12 B 14 1115 16 6 17 18 18, 19 20 20 21 21 19 14 24
 33 8 12 1b 21 27 33 4u 48 56 65 75. 85. 9)b. 108 120 13 H76] 175 192 28 125 243261280. 30 320341 36)  q)
si a primition fit
va - : a est intere Cio fgg = a fi v = act + 4q n ∞ + 49 = V:cofiet
ac, L 299 = 5: 9 1 4 299 = a8 Erg res d reodita est fucilior
H v. ex SEB, 8= 2 prSE fini aptis ou per et
vidend an possibiem sit 1 24q pos diviti per a
sunt pudemi cuter se, fiot s
f2 3 3. 2 = 2. 2 = 
quis
b2 B
Residui quadi
quoidoh dim bex tut 6, 2 3 3 0292
lon
1s07
oc 0 i
125
al
Nucmndiidus per 2 078g. 10
V, Residmi Numeroru 01 01 01, 0 1
quadralam 0 1 0 101010
dibplam Eonctula 0 V v 00b 00000
biquadiatorm 0 1 0 P 0 1 0 101 0
per 3) Numer, 0 1 2 3. 4 5 6
Rresidui numeram 0 1 2 0 1 2
quadulam 0 1
diflaistam 0 2 2 0 2 2 0
biqualtatam 0- 1. 1 0 - l--
Resieni apadior
quadralor
01 2 3 4 0 1
0 14 4 1 9 1 4
duplor contorum 02 3 3 20 2
biquabutom 0 1
pr TRlesidii Nlama 0 1. 2- 3. 4.
quadralom
ducam qu
tiquadratom
2
4 
0 2 2 4 4 2 7
E et 5 non possent esse a
si postuletur, ut X sit fractus
et sit X+ = = yy
9al2 822. 4 X = 4 sit 4 + 3. 19 - 1 -2. 3
Resisui quadratorum per Sdibisom 0. 1. 4 4. 1. 0. 1. 4. 41 0
sumira vel sisfeantiae
per.3dale
duplam quadrolam
3 1 11 1
023320
ee Bimii R s Nen possunt componi duo retisui
unn biquadrati per 5 divisi alter bini dupliquadrat per 5
divisi, ut summa vel differentia sit S. Ergo. Aunem 5 non qula rat
. 16
I
256
V, qu. primi inter se
, et q pui, iem β01 9 prmm intli se
9 10 I1. 12 13114. 15 16 17. 18 1920
89 + 14 = 100
0 1 2 0 1 quia residut et duplo quadrato eum
0
chesitro a  biquadrato componit 3, etsi
0 2   2 ipsi sunt primi inter 
0 1 1
0
exeluditur 3
11641
quia summa et differentia pesidui a biquadento et a diulo
quadiato, non componit 0 vel 5, quamo radices sunt
spiimi inter se, ideo non quadat 5
on
+
14  2 Hvisib. per 3 14 + 2 = 2
q= 2 v = BB ab - 299 - a
vn - 9, divisib per a
19-  divisib per 3
d
vt q. l  10g2n -8 i
H tus a
19-3 = 2
Bv - q divisib. per a v 449 - a β v + Hi
20 = aB + A+
+4 desta tab, aus pera, v+qq a bd v
108
29
2
B = 34. - n
resi ma a n biquadruli
et in duplo quadulo non facit D1, Q
quando non sunt primi inter se
0
Residui duplolu
73+16
3