# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00067993:0566
# Permalink to this reading: https://leibnizlegible.com/page/00067993:0566?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 282v, page id 00067993:0566
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 283r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00067993&page=566
# Source image: https://digitale-sammlungen.gwlb.de/content/00067993/jpgs/default/00000566.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 57 lines, status machine
# Lines: 57 recognised, mean confidence 0.87
# 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.

sesse
l
Quod si ergo proposita figura Analytica imenori potest
alia etiam Analyticas cmjus crementa sint ordinatis datae proportionalia
quadratura omnium partionum figurae propostae generali constructione
Jam alibi a me demonstrutum est rectas crementis proportonales
haberi potest.
esse ad quales sunt ipsae BE, CF figmae ladiuita
quandam constantem quam vocabimus  ut ipsa DT pro ductam
adi por quada ipsius HL, seu portio inter  ordinatum
DL, et tangentem L7, in exe DT intercepta
in qua ratio DL ad DF, sit  perpetuo ut
Orposita ergo qualibet
alia figura
dinat
ommunens
Hoc problema per Analysin (so vere mndum satis esst in nostra potestati
DG ad + a.
advocanda est ergo synthesis, et datis figuris seu DL, inquirendae
sunt DT. quod ordine faciendo et de gradibus ad gradus figurarum
procedendo, condi poterit velut Tabula  quam  constantem
quandam propessionem mox  detentum in pm certo habendum
est, quam facile sit antnuare in infinitum, etiam sine culculo
singulis repetito; quo facto facile detegi poterit an ablata
figura qualibet an sit ex numero quadrabilum per Quadratiaem
Calculus autem investigandarum DS, ex datis DL. non est difficilis
Analyticam.
post publicatam a Slusio methodum tangentium
Ut ergi ordine procedamus, s per omnes aequatiole duat incignitus
aequa d incognitorum contnent, gradus assurgemus ac primum:
X + b Y + c B 0. unde  H b ponendo AD+ X, CD, V,
vel contra; DF  +. unde opo regulae stusianae, fiet:
si ANX fer t H  V D sin CDB e fier: t g a x
jam  pust aequatio multiplicetur per X ponendo AD X, CD y, vel
E1) X
10X
contra ADH V, CDHX. DT +.
ex aequationibus sequentibus ita habebitur infor
ipsis +, et huju ope valor ipsis =a , 2DG
2) a + Cy + BX B0. Ergo poncudo CDrS,  D 2
p =dx. et po X subsitendo= CG abcit te  ly t ab
Ergo Z H
-cv- ab a5a∞ + Cy + ab pu - ac
emendo vero CD X. Dt p y.  fier: t) - cY, et pro y substituendo
ajus valorem, - d X - ba fier: t p, 102 fba, ad eaq 25 e et
erit Z  - dx = ab a,  dx + ba  d F
21) ab 4 acy + at X + e y + fyX + gX , o.
ad
ponendo CDB V, DL B X. fier:  ac +  + 2cyt + f xt  - ad X. fyX. 1g1.
adeoque + = ad X - fV X - 29 X pro 2g X ponatur ejus valor,
ac + 2Cy + fX + 2 ab + rac y +2 adX p Cy + 2f VX.
unde + + adX + fY X + a a cV + 2CY, sie aed F~
+20y-
sive act arert +rac V + reV = s+. X N0. sue gX  ract rey ra rerst
-ft + ad +fy
adeoque a b + ac ) + adX + e) + S. VX n actqe Xx + rcoto X -racvg X 2e)  p
At + ad + f