Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 88r
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: 0.80.
Original at the GWLB · Page image · Annotations (IIIF) · Download text
One image of two folio pages side by side, registered by the library under both labels (also fol. 89v); this page is its right half.
The machine reads it as
- sbX + CC
- sext s
- Ergo
- ex+A bxta
- A2begh.
- a
- O
- yy= bxtcegu + exiss ih + 2
- exts
- bx +c
- bbxx + ybCCX + C + CCXX + 2efX + 4 + 2ghb CX + 2gh cc ex + 2gh sCff
- + bb9
- sen icekt. ) XX
- =
- Abccqeue
- +2et
- reccan
- e
- 120t
- + e
- c2 si
- AbX
- C5=0 et RCg9+ Fhh L Cgh+ fgh =0-
- ergo s
- 99EE= -c. Et fit cgg. cht
- 199-
- (jametin quil seniens ad dimensionem
- Unea onice esst ejusdemformae
- +h ceffghi sequt per qy. hit
- bexX + bff2X + cc ff (sed ita
- XX +, lEccgG: XX - cc
- 7 2c89
- terninus al ter
- eccs.
- Ham comparemus, cum formanqnerati ejusdem jormae, nempet
- comalam
- eXX + mX + n,: px + qxr
- Et quia video g et A_ esse arbitrarias iuntiles
- Sed
- x sed video admistis g et h, ipsas o et e esse arbitrarias imitiles, itaque
- reu sic de integro ordiamur y = seCX+C + hS
- seu re XX +2CGGX + cC gq
- 1)+29h1.
- seu yy =
- + 2fth.
- + 2C gh
- 23
- +ffHh
- +2cf gh
- XX + PX + cf
- ∞+ F
- X+C
- X+f
- vy = ) +Cg) lilx+ suh , 29t
- (4) Px am x tan
- XX + pX +a9
- X + f
- (4)
- A+C
- (Vx + am Xtan
- ex + px + aq
- Comparando jam ipsam formulam 3 cum formula generali 4 habebimus:
- 9+h = l et cg+ fh = an
- et C+ f = p et 1f = ag. reservatan
- ultimm oquatione comparatoria ipsius aem cum respondente, fit A= l-g f = p -c
- et et ex aeg. 6. fit cg + lp - el = gp + c9 an et ex 8. fit Cp - cc = ag. et
- et Lspp. 9 - aq + lp: 2 + an,:, 2 spp: qu aisex -
- et sS 1 spp. 4 =aq - lp. 2 - an, : 2 spp. 4 - aq et f = - App. 4- ag + p. 2
- Restat, 2C99 + 2fhs + 2Cgh + 2fgh = aM jam g9+ gh = 9l per 5
- (20
- et fil 2c99 +2Cgh = 2cgl et ex aeq. 11 et 2cg = an -lp + c1. exgo ex 7 et 20
- 17
- fit 2c99+2Cgh =, aln = IIp + Cll. Et eodem modo hht gh = hl. Ergo
- (24)
- fit 2 fhh + 2fgh = 2fhl, jam ex 6, et 20 est 2th = danf an + lp + cl. ergo
- ex 27 et 24 fit 2fhh + 2fgh = a ln + IIp + cll. Ergo ex 17 per 21 et 25. fit
- 6)
- 2aln = aM seu 2In = am. Quod est perpulchrum et simplex
- nisi qubtres
- incam ensionem x
- am seritum in
- Ellipseos et Hyperbolae, ac superficiem Com scaleni, si quidem hacmethode licet
- 7
- pro curva Ellipseos aut Hyperbulae, summandae ordinatae y, quarum aequatibes
- y b: 4 +Bv0
- posito b esse axem majorem seu latus primarum transversum, et e
- (29
- fiat v = X+Y fiet vV XX + eA 21X + rr, ,t 1 37. per 29 fiet y= + exx +r ee rX + eerr
- (20, bt: 4 = vr
- vel y = (+ eem XX + Neera X + cerr
- (30)
- B: 4
- = XX - 2 IBYX =, . 4
- a quam aequationem comparando cum sg. 14)
- (32 AXX + 2YX + rr
- (22) = bb: 4
- et p
- fit H- + ec: bb aa faciamus =e
- (34)
- (37
- fiet I1 = + p
- X ubi pateb ob 49+ hh + 19h = l et ob ccgg + ffhh + 2Cgh =hn. t necessario
- imadinarius evitare volumus
- adebere esse += =, adeoque l= saa et, et n = Yaarr = b: 4 adeoque oportet
- aar esse majorem quam bb. Igitur hic quidem calculus restringitur hactenus
- ad cllipsia; etsi ad Hyperbolam quoque i transferri possit interventu imaginariarum
- quae nostros calculos non impediunt. Sed sufficiet nunc remuin Hincobola tentari
- exaea 26 fieri debet.
- E ( (4) Placet tamen calculum generaliter
- prosequi. Ex aeq. 26. fieri debet ha atrr f Ba= L2ra et sit (4aa r + b (grraa)
- erto fit b =0 quod est absurdum, itaque comparatio non procedit Et opponit
- sese successui natura rerum. Utamur ergs quadam praetransformatione et
- idaatnrs ad . 27. danA c9. 27. cum equencibus
Cite
Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 88r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068049:0177?run=73