# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068196:0546
# Permalink to this reading: https://leibnizlegible.com/page/00068196:0546?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 275v, page id 00068196:0546
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 269r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=546
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000546.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 104 lines, status machine
# Lines: 104 recognised, mean confidence 0.79
# 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.

idem salia ratione tentemus, efficiendum est
Et VV+ mV+n et vV+ pV+
habeant  divisorem comminem  is sit v+ F ducendus in Y+5 dabit vv +rV+ r5
ut praevitere possum
unde si  comparindo tret r + mv+ n = 0 (sed rursus rr + pr + 4 =0, ergo fit
pr+q = mrtn. seu r= n - 4: pm, quo valore substituto in aeq. rr+ mr 4n =0
fiel nn-2ngrqu. + (mp ( =mmiu - mpus +mmq + utop -Cnpm +  mu = 
seu +nn. + mnus  t mp 9
inque + 2nq
porsus ut pagina praecedente
jam  ob formulas 25. et 27 item 26 et 28, coincidena,
fiet: m 2e p, et n = eetg et q = ee + h. (per compendim scili et posito 9= - C: t. 
Ctaque Een
et h  - L cC) fiet ex aeq. 29. per 30, 31, 32 33 talis Ketrgeet)  4e  4hect (4e + 4hee
etheernus +4e eagee) +e + 49 ee
rneeregi
sed ita evanescentibus terminis fit 99+ hh = 2gh, hoc est g = h, contra propositur
seu t res non procedit, nisi sit
8: 2 - f = = cc seu C = c = f seu f =0 quod
est absurdeme countra hypothesim. Ergo altera opus est via quia illa com
prendiosa non procedit, nempe saltem faciamus terminum nominatorem extrahibile
(ZCC) XN  quad rato nempe (ECe  Xx. v. fit xen- 2trC X, quod fieri
non potest mutando radices pi, ergo oportet iustimere traus formatione
nempe  c 1. F + x W et CF C 1. t - X ua quanda quadrulis  fiet
CC XX = WWcocd Ergo X = Nepe 1 CC -XZ oco quadrato. seu fiet
1c  coco + Xx sit  X a bec fiet (+ ib a = XX+ 2XC + eoco, seu
laseri auo quaduti fiet c  +eb  x  co ret xon ny jam at jam duo Quediat
qui faciunt quadratum hane formum habent C ram _mn + nn et 2mn
et fet ni D2m n Ct ommun um na et 2 mn, et fiet
m2mmnts+ n + (Dmmnn- ( munt un, erit
(x+ b(+ C =0 reducnda
ad 2 radices aequales seu
n debent esse C5 = nm -nin,  et X = 2 mn:b ergo n = v X: 2M
ergo eo un Xx: amm, et ponendo a = 2Vm, fiet eo nm.
quodsi omnea velinus tuncta e inci et tk cC Xx = mm - XX: 4nm
se fiet   = et mm +nn, c = bc Atr. 2
sit LCC = XX = qe quadrato nempe  ce  ZsI. F C XeB L Xx e adevque fiet
x VV. = LcC E Hto C VX + XX CV et fit x- 2 Fr:r CV + XVV
seu X - (2S1: F CV: v et r L CC - XX = XV - Y1. 2C =  LCVV
ser d q
= 2VFI: 2C: vv =+ Si:LC prodst: 2C scrilamus 9.
x = : vo1 et YECC -xx = B9: vv -1, - q. (uam si. B 24 -Aq = vey9
dicibus non mulatuo
Y=CC = XX + f:c Xx fiet
 sit Z CC = - pp = e (p  - XX = (pp - 2pX V + XXWV
hacmithrdo seu X = 2pY: vvFI: debet esx Ergo pP - xx ( seu pp - 2 eC vi
sebt est tad quadratum a Y. 
Hinc nume intor
et tota fractio eti
YE CC = XX + f: C XX =
da d 2 padiusae qualessit sic XX yati sid
oraqa enouaq ve
=vegu 9 v 97- 200gg(9919
n noq ai
490 29que + qq qqu
seu vet ixrap- + ppor
vpp- Epp vv + pp + EF: C ppBV
et ipsa plixa
 ad hnc per eti pote nttea
tu oipus erat hoc ambitum
inffecerat sine mutatione ipsius X, multiplicare nam eratorem per
nominatorem, et fiet Arc. GEL =
V hcc 1  X -2F xx +
CC - X X
 qui mumerator B aequetuo quadrato ab LC = xXV, et fiet E C - 2  x + = s x = ( C9 - CKX VV + X vo
seu sit XX = CnD - 2C E: vv- et sid hanc formulam pursus aequare quadrato prior est difficultas
reduci pe haec quadratura denique ad urg X Scc - nc xX + cp vel
ad has duas
et  ejqsradix jam in est in numeratore. Si faciam
CF: 2 = X
 C.: . FX
c 122 +x = quad to vB, si f X = vv = _ C s: 2 et dx = 2 vd v, et substumendo utrobique X assin
nuneulto assurgeret ad b, sed v in 2D dr evanesceret quis foret et in nominatore. Res erg
hocuodo reducta est ad simplicem fraction quantitata ratinale sine  fractione
scil Et haec Methosus semper strocedit multiplicems i cc - Xx per CS:2 - X, pdub
et Gpecaduo 2 ec sit 44 prodila  ad e quata 4 - gqx - gxX 4 cF X.
 et 9- x De rebei esse = cr  mC s1. 2 = mX YC. G: C mScs: Cm
3yf-fy + et 20
Fat X = y H, (icF
gy + kgy 160  
an lat
N ut
fit e = -n -=
ergo Bh = h6) + 2 bb =
h F bn, + c. Ergo
problemi sua natura non
habeat Duas radices equales
eas uon cccipiet; nempad  sed ex
hoc  loci constagente se
tacgunt, quo
muttalise
mose ee
possunt deprimi
trrativantitatis.
ad inserores
y aiey ee
sit h= pC - = b
MC- 10b +Cc 
e + eb +  bb
unia eoanlscunt
demhite =  b - Cc: b
res ilidem non succedit
n sumpe res
aiti