Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 192v
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: 0.71.
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The machine reads it as
- 1. X
- Y =X a. X
- X
- ax logx et dy= dy: y -d x chc. Y + c elque ax : x + alogX
- et d X = ux a. X, Y , 1 + logx
- logym aX lyx dy: y -b xs elogX Eb (E + hogx)
- C)
- d(xax) = ade Xa XbiB, 1 loga + bt ) L+ bX (log X F bg L log X)
- c.X
- y _ x. X et dy. y - lX a, X
- A 14bZC X
- 1, Z4b s -ax A es a tat X logx + P. X X. bogelogs t abe X X. u X
- y= X .X dy d (X2 L) = dx, X ,. X, a + elg a. X. l0gx
- a y=
- pa.XBa
- (aq
- CglB - pdy: y = a. X LX dH. X +logX (x X b 4 7 , + 1 log X)
- b. XC. L
- t)
- = dx p axb C b.X a + abtilog X + ab. 1. K X L logX loge
- dg: 9 = dx, Xb. X, a + ab X + a bc X. X. logxlogx + abc. 1 X X. X. log,
- axlx
- e
- x
- ax
- X
- a
- c
- = Xbrba
- Hic autam a sunt constantes.
- Ex X
- d
- id videamus jam si variantos per omnia et indefiniti sunt exponentes
- y- ZV log y= lL n lgx et dy: y , m. X +
- ex ex
- y = q ly = lm. n dy. y =pdm: m + duum, sit d m = m, n drlim) i dn lm
- y= M ly = n Im dy. y = amE: m) n + lm R n (dm du (:. 1) p + dp Ln)
- et d (m. ) = m. n () dn. + m. n. fa lm du + n n p lmln de
- Ee a () Cp, n oo + n pi lacm + pe ptutaq laba de 7 p plai i itup i qua p P olapui 4
- Et ita 2tiam in magis productis
- Haec secies comparetur datae dy = b dx + CXdx + C XX x +5X AX + q2 dx erc.
- e
- sit X.M seu seu X logm ge
- Et sit ry: loqm dua n = bdx ( sit dn X, tict N, = l = b
- M
- Et bx p lx dn = ex Ex et p tu = ex dxo: bx l d
- ret
- sed npq i = p In = log 1b + lX, et fiet 1b + IX : 12) dn :n = cxdx: bx lx bX (x
- M
- uge
- seu fiet dn(: nln) seu Un = (, c∞dx: bX +b H (X, beb 1b+ IX
- Sed si fecissemus X = log m, seu m - h siriet n = b sed hoc un licet quin sic ofieet y= log H b
- e.
- imo iideo nec hoc convenire i ut p
- 8
- 1a + abX log.x + abe X. X. loga tabidX. XD. X. Co)p tcC
- m
- satim habeatur velut per bx, ita enim slatim
- et y habobitur, nec opus ert progressu iar
- upt pulnde teu
- =11 F 6 praestut ergo sic conferce dy = m, n du + n pl Alm n + n p
- peu u
- et
- Et et sit m n dm = bdx et dm: m = dx et m n = ab et hs logn + t pr hogn - log b
- seu n X + logn) = log b, ubi ZX + bogZ = dato constanti, quaeritur Z, sed ita
- quare non liceent facere
- etiam statum finitur inquisitio, nec opus est prigredi in serre m d = bdque semp en = b dx: dim
- arbitraviam suppositionem sed manebit. ne a
- et nod pn p
- eta
- Imda = cxdx sen Vdx: dm) m. pd lm an = CX dx
- Mek
- tc
- sen. b(dx: dim) pI Im _ dln = cX dx Ergo p =, (Cc: b) (X: 1M) (d X : d ln) dlm: da
- sin pa = (c: b) (X: Im) (dlm: dln). Sed ita misus finitur progressio nec opus
- est ultra conferre. Sed ita in universum patet tales serres cum
- ad Comparationes non inservire
- a finitas, ex guili ZX + logZ = log b
- sed res utiliter serviet ad
- sit y = M = bX + cx fi et
- log 7 lm = lb + ta ly = n Zam(m) -+ dz lm) = b. x + 2CXdx. hanc aequavem
- dibidamus in duas ut sit Zadm = b dx et i idZ ln fiet ZEdm: dyln = - b. 2CX
- et m = bX + CXX
- seu 2CX: b = seu dlogus: d loglogm = ECX: b
- E quae duae aequationes defindunt m et Z quo posteriore Z logm = _ log, + log (b + CX)
- E Et
- dineruliter, sint duo termini summandi _V Vdx t dx sit quantitas summanda
- X dx Vaa = XX) sit dx = Zdm: m +. dZIm et fiet X - Zlnh et M = saa - XX), su hoc
- eno sit
- idio ja non licere t a X) et
- Aeni 2) = m d loi i asp. n f 1 rd
- (37
- 5iA.
- 7+e02
- st
- diu
- M
Cite
Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 192v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0384?run=74