Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 18v
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. 19r); this page is its left half.
The machine reads it as
- vr Co de +A dco + (n: a) co dZ + Z dZ = 0 sic transformare liceat
- in ipsam edo + β dv + (V: a) v dx + B dx = =0 ut fial D = β7: a
- fiat7 = x + h et co= v. fietque
- V dv + A dv + (M: a) v dx + E dx = 0 et fieri dabet s p. at MM: a) dh _ = 3 (
- + (n: a) D dhdx + ex d h dx
- seu RM: a (1+ dh) = E (1+ d E)
- Sed ita rursus evanesinit assumtitia h, unde difficile videtur obtinere
- Quaesitum
- hyy + my +n =0 inde rhydy + mdy + yydh + ydm + dn
- sit aequalio iuta ejusdemformae b)du + cdy + eyydx + yfdx + _gdx,
- fiet: h= Eb M = C n = sgdx et fit b = sedx et c = sfdx
- fe h yB i m - o fiet hydu h dy + ydh + am = 0, et
- 5yyy 3K yydy +7dn M 2m ydy + ndy +. yy dntydn + d
- BKy + Myy + ny + p =0
- Sit equatio data ydy + β dys +), dx + B dx =0 quae multiplicetur per 3k7 + h.
- et fiet 3k gy dy + 3K Bydy + 3HYgydx t 3KBYdx +h βdy + 3K Jyy ax 13kBd dx + h8t
- BC
- k est constans
- D=
- + h julus.
- fiet 2m = 3RB + h et n = hβ et p = shBdx
- +hVy ax
- dm = 3kV dx Ergo 2K dβ + = dh = 3K) dx adeoque h = 3 3K (β3 - 3K s)dx
- dn = 3H x 3k D dx + h) dx = βdh + h d β. sed ita prodit ipsius d d
- hin aliquid generale ducere
- quid si sie gy + my +- fiet rydy + ndy + ydm + dn = 0 Haec
- Clhty dys +my
- valor ad huc semel Non ergo
- yamyu +nytp -o fiet
- equatio multiplieltur per k et fiet 2Ky dus Hm du + Kyam + Han = 0
- rurus sit aequatio vata yndys + Bdy+Vgdxdx=o haec muttiplicetur per 2ky + h
- Ex differe sit y+ myyt ang +aap =0 di hoc differentiata dabit:
- 3yydy +2 mydy + andy + yydm + aydn + aa dp=o haec multiplicetur per K
- i
- tiet 3kyy dys + 2Kmyay + aKn dy + kyydm + aKy du + aa Kd p = 0. it data
- solvenda ydy + β dy + (3: a) y dx + d dx = haec multiplicetur per 3Ky + ah, et
- fiet (56) 0 = 3Kyy dy + ah ydy + a (h dy + 3V: a) K yydx + Vhydx + a hddx -0
- + 38K 7 dx
- Hinc compatando exydy fit ah aequationes 3 et S. setrat
- +3BKydy
- ic
- ex ydy, ah = 2Km 4 3BK et ex dy fit (7 nod βh = kn. seu ex essit 2( -3 (BK a n
- et ex yydx sit Kam = 3V: a) K dX seu dm = (9no) 3(V: a) K dx seu m = (3: a) S) x
- et ex ydx fit, fit a si dn = (10mo) Vh dx + 3DKdx et po h ponendo valorem ex aeg. 7.
- fiet a edu = V (N: B) K dx + 3bR dx. sed ex aqu. 8 est 2βB: a) sax - 3 33 an. sed ita
- et ex 12 et
- cum _ evanescat, natet B haberi bis, adeoque non haberi arbitrarias sufficiea
- 1 fit dn fy) 2. 3)) sp ax 2aY βd∞ + 3 aa Bdx = 2.3
- Redeamus ad simplicia ibi mi Miscendo lagarithinum aby, sit
- m at fdy: y) + my +an =o et differltiando fit al dy: y + m dus + yam + adm =0
- seu at myd ygem mydu + al dus + yydm + y du et posito m esse constantum
- fiet mydyus + al dy +y dn =0 Hinc sipody et du multiplicata per eandem varia.
- vilem, potest solvi aequatio hujus formae, sed sed haec aliunde solvi potest, seu t
- ponamd, l esse variabulem riet aleus: y) + a sag: y dl + mdus + adu = 0 et pro sdy: Y subtitu
- endo valorem ex aequ. pro po sita siet all dus : y) = m al - an dl +lmdus + aldu et fiet
- Ry dy tiaß dy + Xyy dx + aBy dx = quan multiplicando per : m: aa. fiet
- Im ydy + In Bdy ut ImV: aa) yyax + Lnif. ) dy dx Im(B: a) y dx = 0 fiet al = m (3
- senique n AV. a nV: a) ax + asdn = lmB: a) dx
- indx + aa Ban = (BCm Ax =) ABI dx
- Ydx 13 x d β3+ 2. 3 aa B3 d B
- anal y = 0 sit aequatio hujus formae
- aH dy me jus dF.= lmydys + allius= myy dl + al da
- eu
- 3
Cite
Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 18v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0036?run=74