Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 95r
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: 0.76.
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. 96v); this page is its right half.
The machine reads it as
- Haec videntur succedere
- 0
- sit aequatio data f+gyt hdus = o siat m+ny =o et differentiandus dm ++ ndg seu
- seu logn- seg: et n = b . den
- am: n Hdn: n) y + dy = 0 ~ f: h fg. h) y + dy sint dn: n = g. h (et m = s(n f: h), seu m = (( 3 , f. ti)
- et sit y = se - s (bsd: , sih): 119.h posito F+ gy + h du = 0 si 5=0 tit dy. y = - 9. s et hgy - : ( q. brs
- data
- seu y - 1:, B et y.
- dacitur, us observes orine s tiare co
- e
- atem euto licet sulmitadun omenu a
- 1p. B. 4 cg. 1
- Sit f + gy +hdys + Kyy + lydy =0 Aessumatur m+ ny + pyus =0, difeaentiando dn tans anas p y+ jusdus = 0
- inttoplocatae, per 9
- cui addatur assumta multoplicata perr, et quod prodit coincidentietur datae, (biet
- am + duy F ndy + dpyy + 2phy dy ∞ fgt gis + heluys + Kguys + l4 dus
- mr +mu +pruus
- per ydy fit p = 19. 2 dytr = hq per gus fit r = dp k9: p - dpip = kq yl qu2) - ap. p
- seu r = 2k: l = dp: p iper y fit r = gq: n - dn: n seu 9G: h(9) - dn : n
- Ergo 2K : l = dp . p = g: h = dn: n. Ergo s (ck: 1 - g.h.) = log p = logn = = loglq - loghq
- = L logl = L logq = logh = logq seu -25 (2t. 1 - g. h) + logl - logh = l0g g.
- seu
- q = l: hih num (52K. 1 - 9. h) seu q= l :hitr B e . t. ) p = l: , 2 ht . 1 3 i = 1.: M B ..
- r= g: h - a hq) . hq
- ontandem am +rm = fq, fietque tandem
- O= dm + (g: h = et h q. h9) m = fl. tih bd adeoque per priora
- P(( sim -= dcndtibus, fB ) posito q = l: ht b S. 19 - g t.
- Unde tandem B - = lq Vi + hq Y + S(b s Bh) aetq) ica B, 54) (Se d. e existen tes= l:, hh 6 Srt. 1) - get
- posse abesse l, quin simul absit H; nec potest abesse M
- in hoc calculo non
- sin s aostt. facilem Terminus suppleri potest faciendo y v v = yt e
- possum
- quia simul absit g.
- potuisset etiam assumi in + + sp du+ gapt d = ofiet ram + rany + rndy + pdn gy + pnydus = 0 si n constans, abest qu
- Si ab sint 9 vel K sit nocet
- amus
- qui si sic n A + seagigenelo er =0 fiat du E + Peyng eptar = edl yr rAt - t gex d. Apius B. 1 dr
- de +dp y + pdu
- tit am pregus + ampry + rram F ppydus + Prydp + py ar + rpdy trpy + rdr = patys + rdt- topy.-t pay - + d
- pytri
- qu (pytV
- sed si velimus evaniscere ydus, faciemus im + tr -o fil da + (tyg o) depyuo) - pg r) A(I3t 10) = 0
- ubi evanes cet gy ponendo dm = - dp: p
- ou am +2ot dmy
- War
- -rduo
- tytio
- Ltlamyys
- +W ap y +Wpdus + + ap yy (+ tpydus =G
- + drty
- - Y at y - r Fdy - pat gy (- pty dy)
- = duopus
- sed sic calculus paulo per plexior
- Interim miror haec proverure ex im + PytY -0
- unde int tale derivari videtur
- Fytiv
- dm x = , su = kg, - d (4)
- au
- ob y et y7 fit Fu lio) = K 9 - d(B)
- N
- ituque dm =
- qu (+9 + 10)
- ~ fit gp + hisus etequs
- Capui
- onx- rtK
- cq= Wd rF,ih = H dm + dp - pdt,: K fit dm - spbr .
- Et Y = LCL Krop - Hkam = ht dp + hpdta: tK
- WWp - rt, k = cuwam + Wd dr- Yduo,: 5.
- et din = wops. xts = Warh +rdcoh,. WW
- apra dm = copsC rtk taph + path,. H
- (_ F -b9 -1
- rd + men
- coincientio e insitenis.
- unde
- superest rdm + uodp - paro + tar. rat = 34 si 2o = t fit 2dm + d (f) + d (F)- 3
- fq - tdr trat 3 Kg- t ap + p at et q ∞dt+ t ix B +t an A. a1) +d q ) t de- pat - tartrat:, K- f
- = h9 -1 seu 9) +p- tr, ih 2dm = 34 _ - t dx rpdt - tartrat, quem talorem o
- U; de
- superest ut conjungantur duo valores ipsius 4, nempe (3) et 7) Ex is fit Abdqt qth = t dp + pt - Fdr - rat
- 2
- fit Epger, Ks = Ep. pat =tartrat = Cr, k, 5. seu a (f v, 1) = K. f
- et prius per 4 se erat (R - f) 9 = + dp = pdt tar + rat
- et dabitur pax. t, adeoque habebitur quaesitum; seu log (p - r, : t) =
- r3: t
- (K- F
- seu p-Y-
- L S(X - f, ot)
- Resumanus certitudinis causa) iuta est aeqratio F+gy + hdy + Kyy = o assumatur in + Pytr = 0 sit dn = teu + eF glys 1byer
- gtuo
- eot qui neoi s ande
- Et ordinando idm Wulo + rducotu + Wopdus + dn E 4y f9. +913 + hq dus tKgyy = 0
- +W dr + t d
- = r du
- AW ap
- vol ram = B
- lu
- pmtor
- s
- - rtdus + tap yy -
- ex s fit am = t - d∞ = (ex 77) K4 - d 4)
- Hax-rat = 1 dp - vdlu ex dudbus rtes 2dm = 58 + K4 - d7 - d P
- - pat yu
- Exysis idm = d2
- ad
- ret tarerat- iopapduo prioubus su
- quod obtineri potest per aequationem
- porro si Wo= t, fit dm = 5 - d 7 = K a -) d F. Ergo q= p +t d (B: t) : K-5
- LaZd seu ram to modo sit in datis d = f+K
- Ergo si + = W, coinudent bini valores ipsius 2 dr
- superest jam ob du, aequatio, wop - rt = h9, seu tp - rt = hq seu e P= = ht et fit 9 = t+, (p. B: L): h, et duos
- ordinariam, faciendo v = y + e
- ipsius qualores aequando fit d (p - r, : t) : (P - Y, : +) = h: R-f ut ante.
- Rem tenteuus in exemplo sit XX dp + ∞0 = 0 faciamus v = eHy et firt t xx - dy + 7e y tiet f = XX det ee g = re h = 1 K = 1
- tam delet ess frK = 9 fiet xX - de + ee = 2e, sed ita hoc praestare st rebere ad eandem difficultatem ergo si adidaamus v = et cy
- et f+K 29 fiet XX de + 0C + cC = 28- dc. et fint = de =-de seu et e = c fint XX + 2CC = 2C( sey ee - 2C + 1 = 1 - = XX
- fiet c 14 L1 (2. 2XX)
- ed sne suppositione Wt fiet um = Es
- pursus me
- 34 - L 47 - 18 d F. = 97 tW - trot dr + trora t L lodp + t lopdu
- quro
- mescit C, ergo ala
- drodotensq u
- stitum siimantra te pos euo s tie toiti or ie o polorndo a simperuo
- loga-
- urH.
- 2H2 -aE
Cite
Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 95r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0189?run=74