# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068194:0041
# Permalink to this reading: https://leibnizlegible.com/page/00068194:0041?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 21r, page id 00068194:0041
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 22v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068194&page=41
# Source image: https://digitale-sammlungen.gwlb.de/content/00068194/jpgs/default/00000041.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 59 lines, status machine
# Lines: 59 recognised, mean confidence 0.82
# 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.

Oclobi 1e8
Curva Conica per Rationalem. Tandem
sub sime in pagina dequentis.
Constat ex caltulis alibi initis si inveniri possit summa
aa + E XX
vel Hyperbolici. loco ex
haberi dimensionem arcus Elliptici
Loco dx s taanae
p  fractionis numeratorem et nominatorem per saa EXX
habebitur: dx  aa + XX, ac + EXX
aa +C xx
seu dx Y at + XX + bc X
seu
a
aa + C XX
aa + B XX
aa + = XX
+aCXX be X
a ta aa
Quod si ergo formula C possit aequari uadrato, et ex ea radio
quadratica extrahi, poterit dimensio arcuum Ellipticorum
et Hyperbolico rum revocari. ad Quadraturam Figurae Ration
per compendium
sit ergo a+XX + dK aequ a yy; faciendo Sa aqubtC
()
 et a aequ bc
a + afXK+gX ayy aequ. 0.
ponatur X  Z oqui C X = l aequ. 0
ca
aa
et y- m aqu 0
Multiplicetur X per fomuent X. 1 per formutam arbitia
seu fiat. X seu fiat x- l  AI+ Zx + 3y + 4 Xy + 5XX +6yy
+ 7y XX + 8 X + 9yX aequ0.
og +nyg
1+ 2X + 3y + 4 Xy + 5Xx + byy +7 yXK + 8 X + 9 y X
X
oape ree
pagus
31 132 X + 31713A 3 ex + Hax +30X y 3X  149X
et similiter
daequil m - y
rodtantur jum vidine Termini Instituatur jam comparatio
El+. 31 m aequ. a  1+ 2l + B 32 m aequ. d. 3l+ )1 + 33 m aequ. 0
Xy 12)
s
XKy.
8 aqu 49. 33 aqu a . - 7  -38  qu 0.  + 81 + 38m F - 5 u f. 0. - q 114B 15 qua
l
Cx.
uo y
+st =2 +3em aqu. 2f  - 3 + 4l - 32 aquo )+ et = i +32) +l - 31 +35 + il +ma a
XX
ut decem literae (praeter 1. 31. l. m) et decem comparatitiae.
in aequ. 4 substicuatur = g in locum 8 per aequ. 1. Et  in aequ. 9. substituatur a pro 33 peress
et in aequ. 5 substituatur 38 pro 2 per aequ. 3 et in aequ. 6 suostituatur = gl 118M pro 5 per ae qu. 4
et in aequ. 7. subst. - 38l- 35. sd aia video non nihil laciari et neri habei
ipsas let in tandem ascendere ad potentias, ita ut invenori non sit
in polestate