Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 142v
Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.84.
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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.
The machine reads it as
- 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
Cite
Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 142v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0284?run=74