# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068198:0397
# Permalink to this reading: https://leibnizlegible.com/page/00068198:0397?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 199r, page id 00068198:0397
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068198&page=397
# Source image: https://digitale-sammlungen.gwlb.de/content/00068198/jpgs/default/00000397.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 152 lines, status machine
# Lines: 152 recognised, mean confidence 0.75
# 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.

vertep
lenitatum an saltem ope
cummasumanarum licere
curvam conicam reddere smmabile
mensurare
quadea
naato
sit sectio Konica _ centro praedita AY. ejus
Axis directus AX aedata. Veilex A, fangens verticis 
centrum C. ircus carvae AY, abscissa AN Xordinata XY
sector ACA ACYA, asculatus tranversum AC+) et
jugatum CE, a semilatus rectum Y
qu laa
Ex ircus
Exarcu a verlice A incipientis AY altero extremo Y, ducatur
tangens YT, occurrens ipsi AT tangenti verticis, in T. et A7 sit F. His
3
3
potest
ubi posito in Hyperbola + significat +, in Ellipsi -.
etiam theorema sic epuntiari: sectorem ACY A esse ad 9b mo
regtrum ex b tantum ascriptum LAFY, (id est circum scriptum
est LAVB aAri
trapetium seu monogonum
in illipsi inscripitum in Hyperbola) ut 1 F , H + = B - = t ete
a
est ad unitatem
aa L. It
2a 4X = -
et aa H
irgo Ce 
aa sdt
2a
a +4
a 1
aa +. 4
jaa
5a
ag
DaHt
seu aa +
aas d
a
+ 1 3a + + = 2a
aa 7 
a sat
aa + f a + a + Jaa + it a
(dt. jam
Hinc ACYA: 9 = ac
aa + 1t
a+ +Y+
1
a- t14 = 
aa + Ht a- tr+ acH att+
1+  et aaa (t - q2 a (dt + a (at
aa + 1t a. trf a+ tsY S aa H a 2da tr4 2art
Ergo 2a
a.: 141, log (a - Fr +1) + lag. (a XY + 1) = a: 141, log. a H
aa+Y+1
porro X: g. 2tt i, naq H seu aa x pHX = 1t q se   a  a liL
Porro sector AC YA in Ellips. = triunus. CXY + trilin. AXYA
porro sector ACY
In Hyp. = trinnus CXY = trilm. AXYA
et aaque sat = 9+X]9 7 sydx. jam y = srX + Y XX) X- 91t
Ergo fiat sect. ACYA = tianue CXY + trilin. AXY A
v
H
aa H
aat
seu gy =
194+
a paat +t
4Y gH +.
aa + H
2 199 aatl + 2Yqu + 1
14
Bt
A at 4 2aat+ t
a
taattaa fhaat H . + oaa t)
a + 2aaH+ F
29rt Hinc X: y = t: V, ut esse debet
2aat =
S aaX + HL = 2gH f= a NX:, 9+
log (a - + 41) = log (C Aaxe HLoa + (a Sag FX = a AX) - log sarq +rX
aa L H
seu y =
aa L H
a Tirg + rX +a YX) - log SErg. + rX
logu (a4 tY +) d + gy + xy  loq (a +) - log (  (a. frt1) =
0
at ( =  a logsa + t) nta log (a +)
de + 20d a f6
4a + t id a +t
2
aa +
aa  tt
H = a4X : , 29+X, et _ _ 2td1 = (29 +X) aa dx + aaxd log (a Ferg FrX + a L Fra) -logsa vhrgeu altr
Cy dx = + aaq aa +H
4+4qX + X, 29+X:  (1g + X aa + H = aa 2q t aax f aay
1
et at gapax 
seu 2Fdi - 2q aadxp: (2 )29+ X
do - d (a r2rq. F rX) = fardx. 2Y9 + 1X et dcorco =, flar x. 2rg+ X 1 (+ a rdx. 2 sirg gr (4) + ar tr. 21412
9+X(+ Y +rX
eX
Ergo et: saa = H) = quodx C dxt H dx : 2a 2gX + XX
d a sArX = fardx: 2Y + 1X
2p
sqa
Hinc 10g (avirus fnt)a SArX
LX
r 
Fx
(
((+
sit se co
lEyq - 1)
02cq- )ab 2r9 (+ rX L rX = 2aa
sit C = dab + Cx deo = Cdx: 2Yab +e  ubi pro xponendo valorem 29Et: aa L +t, fiet
ummata
Ergo )Ca ydx = Co sydx _ (duo sydx
dco = ox  Cux sqa L tE,: acab L abtt +29H) sit q. b: c =  29: a, et evanest
 in hominatore Wy-H2rX + 
sed hoc est pro parte extrahibele
T~I
a: (a -X) = t: (1 .t,
e
ax.
a: (a -X) = tF: (ax- H
H - 
CXYV
a: y =
y = AX:
a (a-X) =
x= 2 a t:
1 =l-6+0b-6
1+b 1Fb
in cu
au 2d H. 3 ad + H
F1 - b + bb- b etc
+b - bb + b et
log atv)
a
ato
sit aoq-  abstus ex  abirus
sit deo cox: fab
et C0 = Ylab L ab X)
seuco=ab, 
et yerat = (X, 2  2X
eut 0g se y dx =
d ax  (Auxab, 4 2 d XX)