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# Piece: https://leibnizlegible.com/api/records/342/text
# Catalogue record: 342 — Ex regulis Dn. de Lagney confer additum ad Algebr. Newton. p. 339
# Incipit: √(αα+β) = α + 2αβ/[4αα+β]
# Date: 1707
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=342&katnr=57918
# Work: https://leibnizlegible.com/work/00068199
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folios: Bl. 64 (from the shelfmark LH 35, 13, 2c Bl. 64): 2 pages, canvases 127–128, page ids 00068199:0127 to 00068199:0128
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068199&page=127
# Lines: 125 recognised on 2 of 2 pages, mean confidence 0.69
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# 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, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 64r — 00068199:0127
# Source image: https://digitale-sammlungen.gwlb.de/content/00068199/jpgs/default/00000127.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 50 lines, status machine
Ex regulis Du, denagne
dx Y(X + abXX + aC)
+abxx+aC)
X + (abX +aCXX
47
As
L
 aqase
(a+B)
conter addica ad elrebsi essedton. P. 23d
(
+ab Xx +ac
XX, abxXtaC =
4X+ + Mabxxtaec
appropinquamt
jam
Zacte
b et C fere lb. a, adeeque fere
c mma inaa nn um+le
e
lest usas) le amntn et
29
E
sumatur
2a+ 2altec = aa +(b sit
lest unit
mmtln= mmtrem tee sit e
fit In = 2em + ee un et e fere ln: 2m
pl. In = (fere) 2Cm + ln C. Ergo fet
2H1
Emm  4= qcmm + lne adeoque
2Imni amm +l)
siet ln
2
fntiamus
C= _+F
em d eta 4 ep et radix 2n
ma umn fere: 15 valo
et Mmae + ln)
aet
m
amntn
iet Smmtla(en(n) + ((n) unde rursus
S.
e
e
ne immalu= m (M) + 2((n) In
t
4(m) (in J+ I(n
iclitp

## Folio 64v — 00068199:0128
# Source image: https://digitale-sammlungen.gwlb.de/content/00068199/jpgs/default/00000128.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 75 lines, status machine
propesila Ergo
lut
s
l +a
lantum
fere = XX y-SCimalus
XX4 aC)A
u abxuta
= XK
e en etfiet fere y= in + ulmn: Amm+u)
seu confere = am+lmn, i amm + ln = (M) ejus
quadratum mm, 16m2+ 24mmln + gulnn, ilbm + 8lmmnella
auseratur ab mm+ln, et fiet: Hm
fIm + 8lmn+ mmllun
 + gunnum +bn
+16IMM
(m- 24B In=gunamm
   vnnan. apundem
ita
er
1bH
errer primys
= I(n)
16m +Ebin
+8mm+lr firt y seu = (m)
2∞
am +2mu
e
ammaln
am LZlin
ommeln
it error secunda ert
V
 3l
a
Qu
24 4M3+ 3mn 2i
se
() Al()
1b nct 8ntum llis.
6ma2m n+ glnnum L L 1
a
ibm4olmmtllun
lmn +OL mn
ammuln, ibm, 24lmmn
+llnn
un 
(M) (2) (n
t
amntin
a
e
t(n (m) (1) ta)
videnum explicando aut  (ab(M) +_ ()
1
s
Hoc etiam proderit ad quadraturas, ut ex irrationalitus
ablatur sertgressus
e
tiantrationali in si sit (X++ abXX + C
potert esse
e 4abxa +aabb=um et c Laabb = Cn,
el potest
at
ee x mn et abxa+c n, vel potrites
aum et abex + ∞
 Emmela= p. licc erros primu
C
ap
quam arcumem sit
ln E
 
47
2  Jho R
s