Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 19r
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: 0.80.
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The machine reads it as
- vita
- sed hinc patet ihil nos luga lucrari nam hic res Ardem cedit ad
- quadratum.
- In quiramus in, talia problemata lungentim
- inversa, nubi datae sunt lineae concurrentes verb. gi
- Circuli ut si ex datis AP, detur (C, linvenire lineam
- Ein ciculi secantes sunt positione dati
- dyox y: BB. BP- Ap. A sit AP, p. e
- su
- BP px Ergo dus epx dus. dx = y. p X Ergo fit dypodyx = ydx
- y. po x3 gosit 4qugu = pp + XX - 2pX. Ergo ex 1 et 2. fier
- dy: dx - g. 199- gy p a +
- sit AB, X; BCy AP( p. PC, q. fiet
- (2).
- dy: dx = y: 149- yy et yy + pp -2pX + XX = 99
- diferentinle determina derique q) Nem exemplo tentemus sit et fiet
- sit p= 4 + _h fiet yy (+ 44)+ 2gh +hh - 2g4 - 2hX + XX = 99)
- et h= x X et qua xx ht au et q = yy + hh + Xx - 2hx, :, 2X. 2h
- dy: dx = yg:, p - x = y: , 4th- x = y 29 gy +hh + XX - 2hX + 2hik 4 2XX - a hX: 27 . 1
- seu dy: dx = 2Xy - 2hy, :, yy + 3hh + 39y -6hX
- dy : dx = y: pu X
- yy + pp- 2px + XX = 99
- siiie
- p qun siet ujus (+ 4 + 2gh a hih = 2 X - 2h X +X X (99)
- non a
- Ergo 9= y9+xx + fh - 2hX,:, 2X - 2h
- 1a
- et p. X = yy (+∞ X +hh) - 2hX + r2 Xh - (2 ih LM-x + 2Xh:, exo
- Ergo dy: dx = ek 2g. x -h: yy x sit X- h = Z
- fiet dy: dq = 29Z:, yy - 2Z quae solvi po. proinde.
- rata indinavia si esset qq a, 49 = pp + pa. Ex 2 fieret.
- aun
- yf (p pX + X x = (x p) + (p b seu p. = XX ∞ : b - 2
- ne
- et p - x = gu (XX) - le X + DXX,: b - 2X Ergo
- to per 1 fit dy: dx = b = 2X y,:, qu + 3XX _ - bX
- lem ex aeq.7 vel calculi prioris, vel ex aeg. b. hujus
- cognosci posse quod queat solvi, seu et quod non nisi unica
- A, = y + e β HB: X = dy: dx seu HB = xdu: ax
- Satis faciat Ap, An
- se
- (1
- yg + A_ = Egy + 29Xdyily + Xxdtu .dx = t
- elatio inter het p
- e
- (6)
- a
- Ap. p. PH PN
- rgo
- F3.
- Cys
- p. X4:y = X:, H - y
- AN = y + Xdx: dy = N seu dy A F du: dy Z n - y, : X seu pa - py Xy =y
- Sindetur quaecunque relatio inter x + ydyi dx et inter ytdx. du
- Salui potest problema pir extensionem cumalum
- a via Z a = tr do:du Hiac ex 5 et 7 addilis
- seu ytx p. pr
- fiet X + y + ydy: dx + x dX: dy = p + e seu cydy: dx + Xdx: dy = p Arc + PB: p + X
- Hinc si aequatio differentialis proposita reduceretur ad homoceptotam
- et i in ipsa homoeoptota a omnia reduci possent ad X+y = co
- et ad ytus: x +Xdx: du = W haberetur ejus constructio a per curvarm
- exsensionem in rectam a= XFy = X + y + 2Xy. W = X ax. di + y dus: x + xy
- 102- Co = - + ∞g + X ex idu + y di dx
- Zu untrrcus
- min man nuloratus
- siormre, dtt dus problemm
- tutu. Zn osnns in
- evemalus
- X = y dx dus
- P pay -pdys =ydx
- P= yax+ xdy, idy
- =9= y ay+ x: dus
- Ergo si aluo relatio
- inter p et q solvi
- p problem peradinano
- et est determinatur
- non latis
- ista videntur
- cohaerere.
- qu
- Ex quo non l t oumin
- alicubi habeat
- ationem quae
- equitur u
- id
- ibet curva
- tum
- noum au unu
- cumae
- unctum poss
- po arbitrio. Assamto punc
- d .
- alu gia tipu tij d imegbet pionus . B
- curre
- acis
- B3P. G ay. dx
- si X+y et ydyi dy + xde: dys
- dentur ex se invicem solvi A. procera
- per rectificates.
Cite
Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 19r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0037?run=74