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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 142v, page id 00068198:0284
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 143r); this page is its left half.
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 71 lines, status machine
# Lines: 71 recognised, mean confidence 0.84
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

sit curva GC, referenda et duae rectae EB, Ep, ad quas referenda
curva per ordinatas CB vel CP, sit EB, X. BC, y. EP, Z. CB, D
ductaque  LM determinabit ut sit teangulum ELM isosceles
ut moguli Et M, e V Em sint aequales, definietur angulus BEp per ratione
EL ad LM vel EM ad L_
XX Fyy = Z7 + vV
datur EB: BF  seu X: BF = R: F fit BF = rX: a = y +CF.
jam CF:  Cp = EF: EB seu CF: V = EF: X sed EFi X = 1BF +EB) :X
seu EF: X = BF : X + EB: X = rr: aa C + aa: da = rrtaa,: aa
ergo CF: vv = rrtaa, : da seu CF = v sertaa): a. Ergo
fit ek YX: a = y + v Serrraa): a
Datur EP: BG = seu Z: PG = a : Y fit PG= YZ: a = v + CG
CG: CB = EG: EP = seu CG: y = EG:Z seu CG : y = EG: Z2 = Ep + PG3: E  Z
= YX aa +rY,: aa ergo CG = y Y (aa +rr): a et YZ: a = v + y serrea): a
y = rRea YX = Y sertaa) :a = YZ = va: trtaa)
fit X = a7Z = vaa + vvaa 2  (ortaa) 
y = YZ = aV,: VeY + a4)
XX= aaZZ + rrVV, C . + 2arVZ: irtaa
gy = rrZZ + aavo - 2 arVZ,: rrtaa
ax + ry,: Y (rrtaa)
Corntad
st AE, C et A AB, W fint u = X - e et fui  = C + (aZ+ rvB, :, virtaa)
y- r2- av, in frrraa
tandem sit CR llique ordinata ad ipsam EF, e
et detur CP: PR:  seu v: PR = a : 9 seu pR = qu: a erit va
sit EK _ _ 8, et CR, c i = vB + (9 uv: aa) seu v = cua: rantiq
et EP seu Z = EBsiu G, + _ PR seu Z =  + qr: a = B. 8 + qco: dac + 49
ergo tandem W0 seu AB = -e + (acG +  la quoesaa + 4) + (raco: suatqq)): (srraa
seu W= e trrraa Tggraa +9aa + arco,:, sqataa trrran
et y = Y∞ Y sqqaa G + Yqco = aaco: sggtaa srriaa
Hinc  ut ergo omnia explicemus ab integro, sit  sit curvae _ CC Axis
EB, quem in E secet alia recta EF sint a C puncto curvae duplices ordinatae
nempe CB normales ad axem et c R obliquae ad alteram rectam divectricem H
an sit EB, (3 (quod scribere malo loco X) et BC, y et ER, 8, et CR, CD
CP. PA s.
ED BF: EBsent sit _ r: a et sertaa sit 5
CP: PR seu  a + P PR: CP s sit  4 q: a erit CR seu o
erit CA seu Co: Cp = sqgraa: a etiqqu taa sit p et pR: CP seu co = q: p (eu PR. 
et firt Y = ap 8 + arc, : p5 et y = Y58 + (r9 - a4) cd,: ps
si AB sit x, et EA sit e firt 3 = X + e = apes + arco; ps seu X =  apcs + arco = eps, ips
sit jam aequatio ad curtam rax + 2 XX = gy fiet
-rupseps + Eaps ape + rapsarco as + 4 aapp g a aarrcoco +2  aapr GC
=,YrSSG - (r9- aa) cocd - 2Y5 (29u a a) C
jam proter secticuem conicam ACC sit circulus (A) CC secans priorem in purctis ec, 4 aut duobus
cuue Viameter (E) A) occurat ipsa ER in (E). sit radius h et sit aequatio 2hZ - ZZ. = vn
posito (1 esse Z (A(B) esse Z et (B) (C) esse  jam B (3) constans sit  quel )Gsitg
vel (A) G sit g et AG sit K et fiet Z = X -K et v = y - g; adeoq
bi jam pro xatus substitueudu
2hX - 2hR - XX + 2KX = KK A = yis + 2gy-99 =, inventos supra vatores fit
0
Ppss
Apcap es Ansprarco
+ rapeps  +2 areps C
+29ps r5P + 2905 (r4. aa) Wd
 aa pp ∞- aarr Coc 2a par W
=YY SS8 -(Y9 - a4). 1C - 21ssrqu aa) c0
aotrninaequa
Honilad
Ergo XX +gy = (a a + rY) (vv + ZZ), : (rY+ aa) = vo + 2Z, ut ante
pari modo v = a YX = ay, : Y (ertaa)
et Z=
+ 4 eepp ss - 24 ap epse- 2gareps C0
Fmul autem
EBF sit rectus
 ducatur
normalis ab EF
O=
sectio.
ircu
lum
eeppos