# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068201:0479
# Permalink to this reading: https://leibnizlegible.com/page/00068201:0479?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 240r, page id 00068201:0479
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 239v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068201&page=479
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000479.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 98 lines, status machine
# Lines: 98 recognised, mean confidence 0.81
# 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.

(7) sunto duae ratices 56 + ac, et 1 ac, eud prior  b + ac
Notu quadrando aequalionem 27 fier 3. b + ac 
necesse est ergo
brsrae
posteror, b- 4c
D Utobrae
b +bitrac + ac v sed inde aequatio identica sinedubio
b + Sbtac
BFS6 ac  V, X ad. Eigo b +b- ac p - b - s6  ac. quod est atsendum
erorem  calculo latere. Videndum: Sb + ac p b + ac. Ergo (bfac,  ibac  a
deprehens est
sive 1 B 2b + , sive 3 - 2by + b  b 4 ac, suc tp  + ac 4) b, sive y p (4) (6. ac +b
Erit ergo b Fac rH rac 4b, et N ac 
+b () A ac
+b Et in posterore aequatione dubrum
f6 ac +b
restare potest, quomodo Explicari
debear, signem y signum _(+ Nisi velimus utrumque eigi
valorem utiobique ext adhiberi posse, unum exprimen quantitatem- sbnac, atterum + Sbrac.
ut veritas eorum clarius appareat simamus quadratum exate extrahibile, ut 4 + 5
4+5 r
+ 5.
2(+)ar5
Quare non licet facere 4 1 +5
Nam
sive  Unde patet debere fieri 2+
sansi
Sed
erit radix
2 + PA 
2+5t
nquaeramus radicem - S+te sed tunc fet, - 2 - 5
E- Sa+FI
- 5
2+3l3
2 = - s4+
sed hoc non procdit siot
potias
fier 19-5  3- Unde rursus patet debere
ccc
si sit radix extrahenda ex, 9- 5
unde patet ffien debere
mule
Jungendo aej. 27 et 28, fiet: 
(+197 + 2
F esse 1 sive
=E seu 3 = es solsum, daret eniu Y9 5  4. cum sit 2. nec procedit
+S9. 5 + 3
X e
(B 
unde fit 3 = 1 seu 2. Quotum rationem a prisi indagerre, aliter
+2 + 3
cur scilicet(4) non liceat explicare per cum tamen id calculus
fere videatur, altioris est indaginis et videorem a nemine pro merito tactam. luum tamen con-
quam per numeros rgcs
meralilet
fiderandum est, etiam sic extrahi psse radicem:
Sb f ac pi (1) b + ac Unde (b (4. 2bac e
 (V+ ac et C (+) 260 4 ac aq + , et F7 (+) 2by p ac et y +D iby +b, a
eb y +(F b, vel + +y +b si St +ac. Quam ambiguitatem ita eruntiabimus:
 ponamus +  aco, et (4)  β2, erit (+) p 2pB, et erit:
=(F) idem quod c β aco, B, aut + Jam aut aco, p B ponamus  A, fier.
 (3 +) y + (+, 2) b, seu radie ex 1+, N, + sive +, +2, F. Unde frec
(A, +) y + (+, 1) b  5b + ac. sivi _ y  (A, +) S6  ac - b
Unde gam:
Nb + ac Y ((+) b
S Casjuc  (C ) b
ut exploremus, fier: Nb (aco) ac 
- b (4, 1, ) V ac
-b (aco,  2,  () N6 (aco) ac,
sive ( sive
quorum veritatem mutriplicando
 (Yb (aco, e) b S (4c0) ac et toleendo fractionem:
ab (aco, v e  sir (au) ac
b. s V Caca)ac L(ao, 1(P ) 5 Cacosac, ) (aco, Yp ) 62 (Ye 2 1) ac  se li poi sipt n
et ordinando: b + ( (aco )b,  S. b. (4c0) C p, (aco,  β, ) 6 (y(2, -) ac (Y () 62
Et quadrando utrolique (coa, +)  () b ac
 1, 24t (ca, 1) , 1 (26) (ac) ac  (1 +. ( e04) 11,
1 -2 ( c04) + 1 B  b (ac0) ac  (x + 2 () + 1, 0 b+, + 2 (XC0) b ac + aC V
cum non vacet ita dligentius discutere
prcquis Zi
In quo vereor ne error calculi latea, quicquid sit
non dubitandum est e sucadere debere hoc examen remultiplicationis, interim, ut a
suprioa: b + (aa) ac  Y4 (( ) 6
fier: S4 +  H (B1)  +5
et Pp F
+ ac
= b (ac, Y(3, +) S6 + (ac0) ac
ad numeros applicemus ponendo ( C sive +
-225 
Jam ponendo BH F pier VB - unde 2
-2  (YC) 14 +5 et ponendo B Vp a fier Y (2 4, unde -2 +  p. 2 +5 p,+ 3.
- 2+3
Notabilehr
ut autea 73
n. 3+ 5 = +2. semper Moi
similier ponendo acop.  fier: Sg.  +3 +   3 - 1 p2 et puoundo PB.. fier: - 3 +
et sacedit, sintaotua puo saro subtiluas .d.-Sa re intantus anter midesre. 2 aluo este cun talu avicem coumarta