Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 321r
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: 0.74.
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One image of two folio pages side by side, registered by the library under both labels (also fol. 322v); this page is its right half.
The machine reads it as
- (1 (13) (1) est autem rB A
- Esto non Hyperbolica ABC. cujus, centrum A. Asyngtoti
- Ad. Scimehio dimmeter EAF. Semuilatus trans versum AB,
- en ommordinata
- 0 eique aequale semilatus rectum AG. applicata ad axem, diametim
- exdiametro ; et puncto curvae ordinata ad curvem BH. abscssa
- mptota HS. positaque HI= HE. erit 1B. tanens
- quae proluicatur, dum dccurrat Diumetio conjugatae in L.
- et opsi diumetro in M. erit resecda AL. intervallum Tan-
- tentis a centro in Asymptota 1E. intervallum ejusdem a
- jum ut ad calculum accedamus, constat IH esse = HC. ex
- daen natera Hpabitae GA- EA ex Hypothesi, Recrangulum
- BHE a AN +d
- ex na Hytolai uni
- H GA= A+ exhyporesi idcoc ava est
- dr 1By5 = AN= a
- (1)C I QA = FC
- n. Aer H X Ea Io n
- ()V MEB:. Ylo MAL.
- (6) Eopes Su Bebecta AL r B Nm = ErB D) sota, Lm - sot N
- t oprisM
- (7) Et quia D 3F- oA + AF. dOA = Z AE. L AE = At XN2AN- rea
- (1) ideo erit FD L et posito FA - X. et FB = y. et AO =b
- () ideo erit AD - b = 2 s2 a = 10 a
- (10) d +D = y = b+ X, CX = bx + X NSaX X. 1 y 1- xab .
- 1(1D posito item EA = W. HB - 7. erit per
- (1) erit per 3. Woq= a et H_Z
- et poa HG- M lnc F Y AEAFE - _ FE, sive Fs = X +
- (15.) et Am tx + 8 - X = bx + x- x -
- oc M b s (16) Et ded per 15 qualta 6. erit p Resectu AL = sX + X A
- sa bx 2b
- abX v
- ductui ib t, vet
- laq pive AF-
- centr
- deahus erit et t sspe icularis ex vertice in Asy mplita s
- tise canscur
- JH = HE
- Ergo Sy b = X)
- +b 15+E L = 2X.
- FE quia s A qur ea quae dabet Auzutus apud se hoem. al. 61. Cartes Geom. p. 245.
- AE. 1-
- Xex +6X
- ponalur
- 2b + 2X
- ismu at s.
- et AL = bX + bx
- ab + 4x 4 8bx.
- e+ AL -bx 4 X. Esposito b.. f.x
- b+ X+bx
- M fies, mbest nx + 2mbx = bx + X, fint f b+ x habebimus:
- barab n + m bx L fX et prot f+ X sunto g. habelimus et pro f+x sunto g. fiet
- a seu mb4 amb Mbs mxsatio XC X ponams f. b + X hubebem:
- mb + mx + m bx fx mb + mx + 2 mbx = bX + X b - spro X. ponatur m+. f. hateliuus
- mo + nx + xmbx = b im + fn, + XbC xmb + sxb
- alesest
- inb ans = bf - b pro bf - b ponitur Cf. scibed e. posita ostat
- nde sim un pralis potius b - f = 9. fiet - 8b
- fiet ande imb + his. = cf sive mb + nisX = Cf X, vel mb = ef x - mfX
- podendoque fx = g. pe mb cg mg. sive denique c. m
- potius gro X = f2 2b1d
- mx + 2mb= t Xh
- s.6 eeraudla s
- mpb
- s 6
- ne ou b b. eut
- ie ergo enor alculo
- sequitur alfdum
- hg, et hg = Yd y, ad nunc hiteris Cartesianis enuntiemus, fiet: Xa
- 9 Alit mehodo tentemus idem, ut fer apparecte veridas: mb A mx. + emb = b + Xb posito in b18
- ium mb posito rn. suit m - nb. fietque rike = Hb- nb
- .= b imb
- ertto l- i - 2m.
- bmt
- runque hatelimus nbi F mx = lbx. conamus b + x = n. fiet pr= lb X, fet mn = bX + bx.
- nx + 2mb. = H + xb. imb + mf. = ls - b
- .
- x = f- 26.
- fiet imb = nf = b vel b nsx - b
- m = q fiet qn = 2mox
- adxia
- bdlen l
- xxb bn = nr + 2nXb. = b = - b bn = 2 X ln = n7
- ed.1
- er X Xb pbo bt un L B, fe) b hbum nX
- teser 11 = r∞ 4
- Ex +b
- tn rex co- sbxt
- in l ibsp e cen
- alteri us sde
- Hs ad dium
- 2X A ordi
- desectae. Ergo
- ed uc
- x+ H b 1 Xb =
- 4b2X + 4b3
- 182 sbx + 2
- 3 posita 3, fiet:
- abjaecta 9
- dici. y + b-C
- si + - X
- sive su
- ot
- Cx + Xb - 2m bx = Mh = (+ 14 X
- nx+nb-2mbx= mu
- n. = 2 m bx = mn seu - mn= 2nlx
Cite
Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 321r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00067993:0643?run=73