Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 116r
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: 0.82.
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One image of two folio pages side by side, registered by the library under both labels (also fol. 117v); this page is its right half.
The machine reads it as
- Calculus differentialis
- ratiobalis, in literis rationalibus integris
- sit aequabio generalis ad differentialemad curvam
- quaesitam data: X. + y. + X. y
- X + y + X. y8.
- aqu. dx assumatur alia
- dy
- etiam generalis differentialis, quaesita, ad eandem curvam, quae sit
- X. + y + X. y
- u
- EX
- aequ. a
- XP. + y) + N: y
- aequatio inter X et y. sine differentialibus, aequ. 3. inter duas scilicet.
- Factiones unam aequationis 1. alteram aequationis 2, trarum duarum
- factionum terminos multiplicanto per crucem, fiet.
- NXbxp + yCxp + X. y Axp + ye Xbyq + yC yq + X. yRy4
- + Xb X. yY + yC X. yr + F. yhX. yY
- aequ. XIXe + ym XC+ X. yn XC, +
- + X lxyg + ym X.yg + X. y MXy9
- aequ.
- Xlyf + ymy f + X. yn yf
- Hujus aequationis quaeratur iterum differentialis, quae erit:
- B X b ap dx + xp db dx + gc dp da f x p d x p de dus 1 Xoy h dpdx + Xp t dr ts
- .Xb dxi XP abaxa + yc ap dx + Xp dedy, t X. yh dpdx + Xp dh dx u
- h) dy
- Xb dgdy + y qabdx, + yc dqs dy + yq de dy, + X. yhdgdy + yg dhdx r) y
- .. (d4) dys
- Xb drdx F Xyrdbax, + yc drdx + X yr dedy, + X: yh drax F xyr de dx
- Caridy ti dy
- .. dr) dy
- .. dr) dy
- de qual.
- Xldedx + xedidx, + iym de dx tix edudus, +. V.: yn dedx +xe. andx
- (dn) dy
- Xldf dys + yf dldx, + ym dfdy + yf dmdys, + x. yn dfdy + yf dn dx
- an dy
- Xl dy dx + Xyg dl dx d ym dgdx + Xygdutys, + K yn dy dx + Xtg du dx
- 1. (d9) dy
- daidus
- unde fiet:
- (a9) dy du) dy
- Unde fil. Xb dp expab -Xlde -xec 3 + xbdr +xpdh = xldg -Xean
- FoC ae rygab= gride- yt al Hyc ar +ygdh -ym dg - yf du
- ge
- sectuecone
- xyhdp +xgr ab =xynde- Xygd +Xghor +x yrdh - xg ndgs - xyg du (7) XD F GC + K. yti
- aequ.
- abdqu rc AC ea +C) Expt Xtdg) Xeplu)
- gedus tygde yndf.yfdm) + yedr) +yq(t)-ymdu ) Neryf xyu
- txbagtxpdc - xldf -xedm +xbAr) ex (dh) = X ((c g) - xeldu)
- + Nyhaca y de xynds xsam YX y ( o) + Xg rAhi) X dg) -X. y g a)
- Est autem aequatio 7. identica. Et quia fieri potest, ut fractio in aequ. b.
- deprimi possit ideo non licet comparare numeratores numerator, t nominatorem
- nominatori. sed multiplicandas st a termini per crucem, ut inde
- fieret aequatiod.
- aequ.
- dx (6
Cite
Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 116r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0233?run=74