Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 296r
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: 0.83.
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One image of two folio pages side by side, registered by the library under both labels (also fol. 297v); this page is its right half.
The machine reads it as
- 14. jul. 1691
- sangentes inversa, partem aequationis
- differenbialis summando, et reliquum hansformando,
- reducendo item ad ee homoeoptotas
- ydx: dys = 292bXX + CX 6yx -2bX +Cequatio differentialis solvenda, contenta
- in literis Bodenianis jun. 91. Multiplicando per crucem, fiet:
- 6xyydx = 2bXydx + cc ydx () 293 dy D- bxx dy + ccX dy. dividatur
- aequatio per yu fiet: 6Xdx b L b XX dyjgu cCx dy Fydx. grs
- pap
- b Xd
- seu 12XX bXX: y + CCx: y = 4 gy. se Bxx
- seu 4y2 - 12XXI + bXX = cCX Z0 non y7 - 3Xxy + bxx = CCX = 0 ut sreral
- habet Epistola Bodeniana.
- Sydx -xdy an etiam dabit X. a y
- Respondeo non dabit, nam d X auu adx ydx 1 e2C
- 2
- nam d, X a-y = a dx - ydx= xdys). Interim hinc patet sempeu
- seu homoeptotas esse X et y quoties formula diferentialis ess summa
- bilis, excepto quoe interdum, cure si quidem sit formmula in integris.
- si vero accedante erecti ad fractum quid ae accedat, tunc solis
- signis possunt differre im Si noluissemus adhibers in aequ. Z ad hibere divisionem
- per y, videtur res etiam debere procedere. Adoxjydx respundet
- (656XX ydy sed ita nihil luciamur. Itaque res semper ita instrituenda, ut
- plura praesentia si licet simul summemus. Quod dende resituum est, tactemus ut
- quod si rem semper reducamus ad homoeptota, faciendo
- X = _IB Z1 ∞V FIX,B y = 30Z +40V +3HI, ita ut coincidant 10, 20, Nem e
- licet transformando.
- et ex aeq. t fiet yi 30307 42. 30. 40 ZVC. 2.50. 34Z + 341. 341
- + 3 403Z
- 40.40
- sit ergo formula xgydx jam gy = 30 3027 t 2. 30 40ZV + E. 3031Z + 34134
- C
- N = 10Z + 10V + 11
- 2
- 40.4udv
- 1 = 20Z+ 20V + 21.
- fiet Xy = 10. 20ZZ 10. 20ZV + 10. 31)Z + 11. 21
- 11. 203
- 4 40 341Z
- sit formuta pro possita
- XX = 10. 10 +E + 2. 10,10Z P + 2. 10. 11Z + 1111
- yg = 20120 (7 + 2 20 20 ZV7 240217 +2121
- N’y = 15. 202 +3. 102022Y +210. 20HXBZZ + 2. 1020. 11 Z B +, 10. 21. 217
- ZoV, 10. 1021)D BV +210. 10, 21
- 2. 20, 2612
- X = 10 Z + 3. 1823V + 3. 10. 117Z + 3. 10. 11.11Z + 113
- vo
- Zev
- Prrro si detur X e X dy + y, ee
- Quaeramus differentialis fomularum homoeoptotarum
- b de du dv L Lvav d v + 7 = dy + dZ
- d vo + ZZ = 2vdv + 2Z43
- dv + Z3 = 3V do + 3Z 43
- dv + 9+ = 4v’ av + 4 Zd3
- dezue = vdZ + Zdv
- (D∞D
- + 11. 11. 21
- 20. 11. 11S V
- Et y, yx
- eodem modo scrabuntus
- mutatis rescondentibus
- dCdZZV + ZVV = Z2dv+ vvdZe + 2)B d3
- C, dx
- dv3Z+ eZ v = vAz+ Z + 3 Z vdZtsvrzar di
- uP
- 210
- id
- Et ita porro pergendo; hinc patet rebus redu reductis ad homve optota
- issima reduci qua difficultutem summandi tantum enim opus est
- nam in ommi formula rationali differentiali sculmandee hymocoptota
- sutumanda
- summanda qu’integra differantialem habente. non assurgentem ultra
- dimplices, et nam quotrescunque dx: du habetur rationaliter;
- tep et non assurgitur ultra gradum Z2 tantum opus esst, ut z vet vn
- ut coefficiens ipsius _ sit duplus coefficientis ipsius Z20 et vd
- et quotiescunque non assurgitur ultra gradum 73, tantum opus est
- coefficiens ipsius Z praeter conditionem praecedentem, ut coefficiens ipsius
- E ita porro.
- Et o stab Leo or Hs tipeitis cosiccales iptus 2 a.
Cite
Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 296r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0587?run=74