# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068016:0008
# Permalink to this reading: https://leibnizlegible.com/page/00068016:0008?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 19
# Folio 4v, page id 00068016:0008
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 5r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068016&page=8
# Source image: https://digitale-sammlungen.gwlb.de/content/00068016/jpgs/default/00000008.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 77 lines, status machine
# Lines: 77 recognised, mean confidence 0.85
# 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.

Ergi qu acantaa
Ergo xaequq Z- a. Habemus ergo:
Z aqu bz aa + aa +cC. seu
ZZ aequ bZ+ cc- aa
siu Z aequ bsua ecc nb
Unde facilis constructio est, ut
rea
si triangulum
ea dimichia
rectangulum fiat cujus latera sint
AH. et alia recta quae possit dimidium differentiae
quadratorum a excessus quadrati ab AL super
quadratum ab AF, ejus trianguli hypotenusa,
assumens dimidiam AH erit latus AB
Quaesitum Trianguli quaesiti ABC. unde caetera
habentur.
fitit Z orgo aa
seu ZZ aequ Lax + aa +. Est autem 
X, Zaqu. a XFa.  seu QX +4a
Ergo 22 equ.  2b6x + bb. quos duos valores
aequando fit. bb xx + 2lb x t bb aego 2ax + aa fac
er ortia fit aequando et ordinando fiet:
xx + 2a X Equ. abb+ cbl -ra
saulxe
et unde erit.
a). aa bb + b (abb) a bb 
am l No uare a cuins facilis ins
cas dtat, un
et X + a sive AD aqu.  sbb - aa cc + bb
XC F: c jam Z. X+a: a. b. Ergo
erit  fbb. a an +b. ciunus facilis satis per
rectam et circulum constructio est unde constructio
AB seu Z aqu
haec ducetur. super data LM se b describatur
semicirculus, cui inscribatur Me media proportionatis
inter datas a et summam dutarum a et C et
in producta ML ZP asqual. LN. erit Mp
latus AD seu Z. quaesitum
Hini sequentem duremus constructione:
sit datus ang.
rectilinens GAF. et AF
vel AG dit data sdiffe entia segmentorum AD. DC.
eeperpendisitars ad AB latus ad verticem et
angulum datum ad Ad segmentum ad angulum datum
ut data Ai vel a ad AH posito GH esse normalem a 
is sit FL opta duta quae possit aggregatum quadratorum
AB et BC.  jungatur AL centro A radio AG
descriphus formicirculis occurrat in M, jungatur ML.
inque garduntur sumatur MN aequal. AH. eritque
LN equalis ipsi AB quaesitae
∞3 - yy aequ 2 ax + aa
y aeqo
q
Zuqu Xa
xogo l =a
qq 99 2xy aequ. 2aX +a a - 2bb - 222
X aegu LZ- a
yaegu bb.
Ergo fei 2Z = b aego 26Z+ 3ta H (aa)
seu 7+ - 262 + a aZZ aequ 
4- ut Z sit
lZ= 2bZ2, laa ZZ asqu bb
nm Z2 17
Bt e +2 3
mmzZ - 2bZ+ laa
+ Alu 7Z y 3m EE h
+2bn taegu paego smm+ Il
pp ZZ +2p9Z + 94
quequ. IIla a +26ml
Ergo llaa +ebml. jum + (I aequ. bb
sit  maego nl. fier llaa + 2b ul nu I FU
superqua
 qu describatur semicirculus cui
inZZ + n Z
ergo habebimus: v  +bV X aq + 2baB = a aqu. 0.
sit a aequ. Y. fier vE-   vb + 2b
sit 2 aequs.