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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 7
# Folio 19r, page id 00068220:0037
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 11v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068220&page=37
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 132 lines, status machine
# Lines: 132 recognised, mean confidence 0.74
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# After the first blank line: the recognised lines in reading order, one per line.

Xego l+m An+p seu xaequ sl.
Zagusium co aequilump XGx agosi 
X Xcos NcEX
X aequ sI + 3 2y seu sU aequ X- 2y
X 1
s
XHaego S1 + sem + 2yX. sm aego st S ImX= S3Z Eigo Sl’ago X - 3y x + 3Z
Al(. X - 3yX ∞t ZX aequ s. 13 X aego l + Sem Agist + y X ryy lmusen). Py atae
sOu fiet H12 aqu xy axZ X- aX+ 4XZ + 2yy - c0
Nys E
X - + Xsy + 4xx Z+ Exyy xconqus l X equ (+ SLm aego Sl 4 yX 3yyX + 3y ( lmu
=la ZXX + 293 + 4tam CoXcoseu ((’ago X, (RY +5X2 Spyyr5xco- 1yZ
Egquordine ila scribemus
Si aequ x
SH, aequ X? - 2y
SI aequ X - 3Xy + 3Z
Lx. Exy ipp. 7py GXyE
2y. 93
ubicunque divensio parcum (. 10) imper ibi estsi sun
cydoisibilis per aliquem divisore ago ex 1- 1 - 1. erit 3 aequ. 2 et Zoqu ∞ erco vy 1
oner
X. y. Z per sestante, (quacunque potentia faciumt 1. )ota ut sunt + 3XG + 4Z - 3Xco et
eis ducta sistent quadmlice faciunt respondentim ipsis  Axt Exerc
dulm sin numeri, si cubice triptum Excepto casu
Ml aqu g. sim aego fh Simn aequ h C Immp aeqo. h s12 rego X - 4Xy 14XZ + 19y o
tro duo aeque in seimice, ita sunt 29G- 5y2+9yco etc respor
ducto, quocus nemut duplu dentua ipsis 2yy. 5 XyX 9 X y
posito laego abc n aequ abd n aequ acd paequ bcd et n 714 ∞ 50 sl aequ X - 5X y + 5K Z + sXyy.5 Aco = 5 yZ quadratne quo casu faciunt duplus lalsar. (ut oxrgus qui. hypt
(16 aequ X -6Xy +bX ZY9X9 -6Xc0 -6xyZ- 29 4322 +6yc0
362Sl aequX - 7Xyt7X Z 114X9 = 7X C0 - 7 X9Z - 7Xy +7X Z + 7XyCORY E. 10
si cubice sriplum dereliqua
quum tabu numerorum vidi exqua plura pysteria
pum havulam cenima dixerimae
ere orseries observantu
ciuntuilla
4X, quia
et
+ dup
 sac +
u
quos duos valores ipsius (Imins conferendo habebitur fIma sed per aequationem s aequx. 9X y +9X +27 Xy- 9X co- ga -36Xyr18X(19Y710∞Y1 (. 7acotg   hxy9X )
hox 25 Xtqe
1
Nota omnes quae afficiuntur numero sui gradus crescunt authmetice, ut
differentiae ipsam
12 5 X7 210
6yco. ergo procedit 7 Xyco. 8x yco et.
ryy Nyy Xes ea ipsae Y. Xy Xy Xy et. similiter in aliis 24
 aliae secus ubique progossiones recte et fransolisie
 _ quadr 51 aequ sl +2sl m. Ergo 25 (2M ego (X -BX + 8X
(4Xyf 8XcL 1bXy 67X7
16X 4Xg0. + q (1 Z  yZ 67X70. + a-1bj 1 468 
ut
 
Ego fiet ((m aequ. - 1aX yZ + 12 Xylo + 4 X2 + 4X5Z 12 ∞co + y- 47c0 +6c0 omittipt
sit aequatu pax + bX + CX + d aequia et X + x pX + qX +r aequ. 0
hy Ex antentur (ax bx + exX + dx  (ax X - aqx - ar aequ.0
ine
8xE
2+2traoqus 1 (=8X Z 20Xy (t 8X2 ( + 3X, 2 16Xyf 12XZ gxy cdf 9Xy 2+ 8 c 2y87 co) Bs qo
(abX + bb X + cbx +db (= abx acxx - adx + ar aequ.
+ ap +aqX
162
libx + b X+ bd  bbX B cbX- d alx + BX clxudl Pab B acbe albxr ad
(+ a bb X + aba + ad bx (= abb X ) PBVBX ∞∞ ~C bBX =d bb 
= ap
= ad X + aer X
+aeq X
+ ac
4b ac
+ ap = b aep.
+C ac
C ap
+d ac
- c ap
sit A3 aequ. X - 3xy 42Z. jam Es( m aeq q I3 = (1 et fiet
2l’m aqu. B-6~d (+6 ∞Z (9
X6 D 26X Z- gXy 46 XyZ  2G - 33
t  ck 3b 18ky 9
seu ((3nB aequ y - 6xyZ + 322
729
1457
891
V. (1)
agig
aequitio data X -  pX +q aequio etfiat
Paequ hy. seu y aego  p. 3 et ge quaequ 3Z- S seu 654
seu (l aequ 37- 4 aqu N fiet: 12 gaqu ∞ pu et  m aequ p. 17 - 2pZX + 3GZ unde (+54
tollendo X ope duarum aequationum etH1 et 2. utique (13m ascerderet ad cubum
verum  quia S( aequ 3Z- 9 et quadr. (l aequ. s10 - E(Vm3. ideo fiet:
(977 - 629 + 99 aequ x - Z X P + 6 x Z a X p = -. 2 pZX - 2 p. 27 (324) = 3 12M
videamus ergo an ope aequatinum 1. 2. 3., habet tolli possit sublata X
haberi possit ralis valor ipsius (BmZ qui non assurgat ultra qua
grationalis, vel saltem daon assurren ultra pecidentia Golidentunus quadratum
licet e ex duabus aequ. so et 2. sequatur aeque 3. unde (Bm non
quoritur ansaltem possit deprimi ex aquia est X aequi
aequatio autem 3 per
1ne per compendium vocetur v. s erit Xaequ,  P: 27+ 322 - v , . 2pZ
pt omnimm tolli
X+KX +IX L x + n ay. 0
pendiam semtatur X6 +  +  X + L X + MX + n Bl unde ex aequ. 1 et 3. fiet 
ruusus ex et fiet: _ +K X = CxX + mX +n Eeq. o Uade ex 1 et 5.fiet + lxx + mX +n aqu v
ph.
+ ph
=quX -ot
qui
+pp
unde ec 6 et 1. fier: 3 i XX L ux )
E
=cohx
ix
dub indeca Bet 2. fet
+pkx 774
ntt ah tP. Cg  pp X e H dE+ quti + qup. Cpte pp
guia tam in quaud xG
quiae tam in quam xytinent v ascenec ad gladu veratum
y aequslm.
rac + -1.
1-
 ++ 
-
7
openon
ean
3.9270
243
(9
c.
=7. T2g
r
= 102
qu. 91H