# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068196:0019
# Permalink to this reading: https://leibnizlegible.com/page/00068196:0019?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 10r, page id 00068196:0019
# 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=00068196&page=19
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000019.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 61 lines, status machine
# Lines: 61 recognised, mean confidence 0.78
# 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.

s
Gl, X 6m, X +N aequandum quadrato sit X = N. = N 7, fiet
5et 7 e ( 7 7 = hh. et 51Z = h+ Z s, h- 2 il. pe Chinentotales
Scilas ittg sicuplices estil se Z c Esto N = Ap h + IpI; 7 = Lh - 2 H, seet.
h = 51 - Ip Vl, ip = pY (p + YI) . fiet 5V: 2 = pCp+ H) + Pst. sed hoc non licet
si B sit isustans. Si vero sit p varians poterit fieri 5N = pt 2Yl,  et 2=4: p
se _ Fa ert X quadratus et Et similitor agendum esset adhuc bis, fieretque N = Y + 2sm, C et Z = 5: p
et deniue N = t + 2In V et 7 = v:t. qui valores ut concilientur, s. et
q: p =) s: Y et v: t = s: Y
quibus quatuor aequationibus praestitis, haberetur
desideratum
Dividatur aeq. 2 por aqu. 1 fiet pp + 2pel = rY + 2rIm fiat p = Z pV = r+ 2Fm, et p+ 2fl,: WY
(4
et p+ 2Hl, qe trum, s et f + ia, v = Ya2m, 5
fiet p = Y + 2sm, : N et (Y + 2Im : WV) + 2M s: W = Y seu Y + 2Ym + 2W H = WWY ac antsue
similiter devidatur equ. 4 per aeq. 3, fiet +++ 2F in = rYY m, fiat t ∞ = r + 2tm at+ 2:  = r
r - 2im = 2W M, :, WoW -1
fiet + = Y + Dm; 1 et + = r  - 7 I, et r + 2Im = rv ip = 2 In et r = 2. (m + 2W Ma,: Y -1
Ergo tandem (3Am + (2W0HL,:, wo - 1 = m H In = v V - 1. Maltipli
Multiplicando. per crucemfiet, 1+1 - 1, Im + 2oA. D +1, bo - 1, im + 24 In
fiat val gie sin +2 WV= Vm =2 WoHL Wontm t roC VM =+m) -2 In
2W Hl = seu  1 i 4- ut sM
=2
Y
et (up = WWo) An + 244 it
=2 p 1oW In + 2V In
sen ( +10, P W0) Im +eo (H et - Wo In) + in- W0 1G -0
si esset n = ofieret 44-, = coW -1, Im,:, im + 2Wo
seu
Wip = ow im im   IL: 2tm +2Wi
fieret
4: P
si esset  10 = _ p. g et 48 et um + 2H,:, 21m + 2Wos
fieret _sm l: ndm + cs = Y: ∞ et VGim 1GAt = 2Ysm + V 811
a quatio Dividi colest siC in uas ut sit cs  s 2 . Im et 29 sl = 24Y gL sint es  2 et 1 = + 1
fiet W0 = + F2 4 -1 - o p Wo =
sit WW -1 = pV- 1. fit Wio W _ g= WV, unde fac rerum
1 = - W et 2 m + 21 sl = 2m - 2W NR, sed ita fieret M = In quod non
licet s fiat 102 y 1P - 1 = ( W0W = e tiet  loco-H F + 8
DV L (Ptoto =  + 1) et
W YH (W00 -1) - 1oWo + = EH
12 4 17etim + 1o H) = roco  2, Am+ Y tn si eset n-o fieret
+211 1, im +w H ap V iin (Lm) + 2Y  2o H- cost = 2evotm () Im
W (Ymt. W Am +  pao MC Im) - 20 sl = 10ro Im + wwY su CmIn
quod si sit n = l fint i (toto tm: sen+ W sL) sint 1 sed totm +r W
im F WVIL
si esset cotm + Hl san twol, safieret Htam = W0, seu 20 = F et  1
et fieret fint coro n tw Hl= B= W0, Woim + st
Wwl tim
si Wm + M = W0 s + Im fiarat A(- Im = W, Hl - dm, et Ww = l et ( = su
Yb + W Il
et  ft sed ila fieret et V t= = - 1. sad ita in aeq. ), cun contra s invi
cemtolli debent f =1 et 10co - 1, ut fiat Im + Wil = sm, quo casu fie, et
W = contra prius invettum sad per o multiplia D, (id est a V = 1, et W1 - 1)
multiplandus est uterque numerator respective quivis per 
sede sa pa Ex his patit non habere exitur, nisi e et W0 sint constntes.
nihilo aequalem, ut ounia evanescant
Ergo etiam Y est constans. une et p et E sunt constantes Ergo ratio 5:  est constans
AC
contra intentum Ergo non licet sacere s = ph + 2 psl at
et similiter adhuc bis