LBr. 57, 1 · Bernoulli, Joh., fol. 9v
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: 0.79.
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One image of two folio pages side by side, registered by the library under both labels (also fol. 10r); this page is its left half.
The machine reads it as
- alm = 15. sumtisque per modum vulgarem differentialibus nalm + ln da = als;
- per ea autema qua supra diximus dem = adm, et ill= adi, ideoque andm
- londa = adi = (ob m = 5) a ds
- n
- : invenitur itaque ds ide diff. m = nm d
- L mdn -. 2. E. 1. Eito nunc quantas percurrens secundi genaris ml
- C
- cujus differentale invenitur sic: sit ut ante m =5, ergo N Im = l5, santis
- modo comun differenti alibus im+lndul = als, quoriam autem ut modo
- -1
- it
- C
- M, als = adi adi
- aa
- ul habebitur.
- inveniuntur differenti alia quantitatum percurrentium tertii, quarti exgenerit.
- Non majoei difficultate reperiuntur differentialia quantitatum quomodo-
- cunque compositarum ex percurrentibus ejurdem vel diversorum generum, nam
- m p = s du + m dp, et d- dm - m p
- (2
- 9
- x. in quibus si subitituatum
- valor iptarum dph, dm modo supra inventus, habebuntur differeatialia coecaesita.
- ut horum quae hueuque esplicuit unu videntur, unuta vel alterum problema
- resolvam circa curvas percurrentes. I. Ecaeritur F longiludo subtangentis eur
- vae percurrentis =y. o. Sumtii per methodum exhibitatu utrobique diffbus
- erit Xds + XId = des, vel subilitu lo y loco X) ydx + y ldt = dy = (ut dinea
- sionis numerus compleatur) boly, et ordinatà aequatione ayde + ylxde = abdly,
- ab
- ideoque ay +ylx. ab:: dy. dx:: y. subtanu. qua proinde erit = a+ x, et quia oblx
- geometrice deterhinari non potect, ope logarithicae facile sic conctruitur:
- sit etim curva proposita FGH, Ct = X, IH = y, determinunda
- eit tangeas in panito sl: Fiat logarithmica AB, cujus subtangens
- =a, et sumta in illa applicata CA = b = 1, producatur At do
- nec ocurrat logarithnica in B, erit DB = X, proinde Cd vel
- IB = lx; si itaque tiat ut 18+ subtanus. logarit. ad eandem sublans
- ita AC ad IL, erit IL subtangent quasita curva. Coroll. Ex
- Lac condintione patet subtangentem quae repondet punito G
- este iptam AC. Curva autem ipea FGH sic conducitur: -y
- et proinde Xlx = ly = bly, erit ly = XX = CIXCD. sumta ergo CM
- CA
- aequali ClX CD, erit CM = ly, et ideo MN = y = 1H. Exende sequitur AG = AC.
- CA
- Quadiatura spati CFH) peculiari artificio perserieta ita exhibetur: Quia
- Ht = X erit integr. X de = spatio quaesito, hoc autem integrale ita invenitur
- As = MX, CA = b. subtang. logarit. = a, C M (per constr.) = C1XCB
- XF, es
- datis autem CA, CM et sublangente per modum aliunde cognitum invenitur
- applicata MN seu HI Seu X = b +
- Xdx Leu elem. sp. C F H1 = bdx + Xlxdx
- X7
- a
- + XxlX
- xIx3
- X+(∞t
- 1. 2aab = 1. 2. 3 abb 1. 2. 3. 4a 63
- exle de
- 1. 2aab
- XlXde
- 1. 2. 3 a26b
- Xxl
- es ideoque
- 1 2346 ∞ Hujut
- serici terminorum singulorum integralia sumi poterunt, port quam orteaderiuo
- quo parto quilibet len nus in alios plures convertendus, Quorum integralia
- haberi postunt ut sequent caterculres ortendit qui supponit alx= aux
- axalx+ aa ppd
- dlx ds = X ap + 3 X( alx s- 2 ay2(X ds - 3 a p xdlx (4 aux xdx + 32 aax dlx
- H. H. 4
- l. 2
- 44 a f df
- filp dx = f. ap + 2 X p lX (- Z ax 1F ds - 8 a f als) + 4. aa p (X ds + 432 aas pallx (- 4. 3= a ds
- 4. 3.2
- 5 sie5
- a x allp s + 4. 3. 2 atpd
- 5. 5. 5.5
- 11
- 1
- ax= dx
- flxde = xlXdx + L X x allx )- L axds
- Xxld= XX dx + F XalX)- = applxdx-
Cite
LBr. 57, 1 · Bernoulli, Joh., fol. 9v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/DE-611-HS-958803:0018?run=74