Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 55r
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. 56v); this page is its right half.
The machine reads it as
- ic modus reducendii curva conicam per duplicem viam, generalis ratio omnem
- commam irvibionalem quadraticam reducendi ad rationatem
- a X + bX + cC. = a X + 2 ab X3 + 2aC N2
- conferatur datae
- (8)
- + bb XX + 2b ccX + C)
- ext + f X3 + gg X X + h X + K4
- et a2 se V t ceR cc= YK
- et S9g - seK+ =b
- 2 l9ge - e set = f
- bofrete
- Epp Yi 4
- prietirqx
- supersunt ergo duae aequationes
- et 2 YK 9g - K4 s eK + = h, adeoque ex 6 et7
- adeoque sla B3: f = s K: e
- sit jam aequatio ad curvam conicam
- Iaus Semm. = nyy = co. fiat.
- mm= yy
- Co p X + 49
- D= X + Y
- ft e cm nyg mm-nyu. mm yy m mongus + psmrramextbX+
- mrgu
- = mmnyy
- Videans anliat Hujus fractionis Numerator
- ponatur designari per formulam 2. et fiet:
- p6
- 137
- irq he = K f.
- Ergo
- ut
- Ex 8.
- 4mr3- m tnen 2r9+ 2pgr +aupq
- chtr marXm +24X IYX
- +H9 F214X Apark
- 8G2pq rX L pprrXX
- n+onpaX+qXtanqX +n BX
- D) X 4Y
- 14
- m - pp vi in + np =
- = mr-rm ion + nq (( amr-mmprp. a +pY + 4 np g
- Et una ad huc aequatio (15) ex aea. 6 explicata.
- Quod si calculum retigere in compendium placeat, nova suppositione facta.
- +
- faciamus b =0 fiet f= 0 et h = 0, et ob b-0 fit g = ek sed ita pro
- tribus equationibus non sufficiuant tres literae, quando inter se servant legem homogenecru
- quoad incoprita nam gque tgmo pro pualitera quasi essetat; ita enim in effectu
- nae sotum sunt imognitae _ K P: Y et 99. ar seu p: r et L: Y
- et puto rem
- succedere, quia in cognitae non solae servant in ter se legem homogeneorum
- ita ob d ob 17 fit r= q pqt m 4 mn - 2 npp: 2m - m pp- minpo
- imil ter ob 18
- sisitum reperit.
- y habebuntur aequationes.
- Sed calculus en protixior.
- ita res utiue
- Eu ergo aliam
- viam simpliciorem, torlamus in forianta 12. duos maximos vel
- duos nnimo Qumeruloris terminos, et hrabemrus depressionem
- nfingos
- ab X ad X. Ut si tollamus duos infimos
- potius q. rr
- l f21)
- fiet mr +ng= manen Yg
- ita habetur vel rr per aequationem planam. et 4M anpu=m
- et 4m + anpq = 2r4 + 2peet r m + nin et habetur p; perrationalem.
- et ad huc in arbituo nostro, manet aliquid, quantum velimus esse vel er vel qu
- modi havem earum proscriplam servenius
- imo quod est maiqus sublatis hoc modo duobus terminis et xt depressa ad
- XX, licel potro XX deprimere ad X, et ita rdeere omnem indetermi
- galam ex radice eximere.
- Et generaliter hac methodo pergere licet
- lam in radicilu universalibu reducendo eas ad singulare. et deinde
- ex singularibus red eximendo indeterminatam certe hoc loco
- Ex oq. 2 fiet a L n n q 4 m itn = m in = m rt = mr it intnn - An = mY ,n
- +nn
- aun
- ann
- ann
- 4(29)
- fit q- mt x Fa = +m p n seu g3) mr c vel q = nir vel 99 de
- Su qu meti
- ex aeg. 22 fit in 69. 22. substituendo hmr in locum Bubi h = H1 vel. sn)
- et 4m + anptom = e 2hhm + 2thnm + phG 2phm F Eptnm
- P = 2m = hh m - hhnm,: h + Dhn = 2n H, ubi posito esse A Cx h= +1 fiet
- si facimus et sit
- X P = +M i-n: 1 = n seu p = + n sin sit n- sn
- y = +m X4 + MY,: X+ Y quod est absurdum sit enim y= t Ergo 6 dentemus ad hibendo n
- fiet qu
- rgo h= in fiet Am + n sn P = Lnm + L num + Xp In XB + Zph i
- _ 2- n. nn: C. n+ rna et y BY m 1 n na X + mr In: X+Y
- M. nor2an
- seu y - p inmumn X x mrantiam quod jucedit
- PPxX + EP
- x tirxim
- + qt Xx + EpuX
- sid
- XY+2YX + X
- 9. +293f21117
Cite
Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 55r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068049:0109?run=73