Leibniz-Handschriften zur Mathematik LH 35, 5, 3, fol. 3r
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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One image of two folio pages side by side, registered by the library under both labels (also fol. 4v); this page is its right half.
The machine reads it as
- lno G
- 2b2. 1674.
- on
- net hodu catesqua invenis
- se ratio nihili est, quia evenit in qualibet aequatione uti
- methodo tangentium ommuni reducta ad unam incognitam
- capitatem. Mroclaro admodum consilio cartesius adhibuit
- liferam .V nam cum opus habeat litera B, P manifestum est
- ipsam esse duplicem, nam n figura superiore
- rabetur BP, et (∞) P. quod si ergo ei dedisset nomen
- v.g. P. tunc habuisset tres literas duplicis valoris
- p. GX. Y, at um ut litera D, seu AP, est
- semper eadem, ergo BP e x. patet non nisi duas
- esse literas duorum vatorum. Nam V. et s. non nisi
- unum habent vatorem,Quando datur aequatio: v - 2∞x + X + - s,o quae est
- genenalis. et adhuc alia, v - X 1 a. fit X B v - a. ex et a
- et = 2 YX B - 2v + 2aD. et X V= 2a D + a
- quad
- Unde ( - 2V + 2a0 + v - 2a v) F + et - s 1 0.
- unari non posse, tare
- enim non nisiun
- si e incogluta aeparet
- quod si elidere velis v. fiet K a + X - v. p o. recto
- Si puss BP, 8y H v X.
- At haec si BP sit linea consans cum
- Quodsi ponamus B2, 87 y.
- scilicet ei. At est parabola.
- Hnc AL est linea recta; et fiet: y. B v - X. Ergo X, vP - xy
- 8230 = 2VBY) F225
- Unde _ = 2V X F
- = 203 + 207y et X
- Uene (B ∞) (= 28 v) (+ 2re VD) B. V F eY VD + rV C
- + BrV2
- mntus qua nisi duarm incognitarum nem
- Hinc ergo salis ee rideo hoc quidem casu elidendo X redir in eadem, quae
- proverustent non adhibendo V = X.
- i sit TEa Lar 1 v - X. fet S 2aX V - 20∞ +X.
- et X p quae aequatio jungatur prioreg generali: v 20x +X +s - sv
- 1 - y et X 52-25 y +y
- fiet: rax + y - j adeoque
- as
- qa
- X 1s
- detadeoque hunc valorem utrae aequationem generalem inserendo, fi quia
- =L VX 1
- v
- -Zv
- 4 aV das V ax V
- + ZVY
- ta
- 1..
- et ordinando : ( V 4 + 4 av y + 4a v
- + 4a.
- = +asex
- +
- fiet.
- V= X 1x +y-s
- 10. multipliando, per 4. 2. 0. methodo
- - 4a252
- + 8av H.
- = 4
- Huddemana, sequetur
- sive dividentus per 4 fiet: X + 2 a V H 0.
- 52
- a
- +8a ubi in locum ipsius V substituendo Sra + x fiet:
- +trax + X -s +2a20. Multiplicetur aequalio setermina adhuc
- aliter per - L (X - ) o(X + 1) 2. et fiet : 2y+ - 8 a v
- y4
- - +a p2
- F 4as2 v
- + gapv
- 1 ubris pro na
- ubi pro + 4as B ponatur 4as Yax + tasX
- = 254
- + Sarsve
- 70 et fier
- + 4ars et pro 4aY, quia v2 2ax + 2X trax + X, erit 4 a v
- 4
- 8a3X + 8aX Prax + 4a X, et substitutione facta, erit
- aequatio: y porro ex aeg. D, multiplicando per s, fier: a s+p s V + raBs 2+2450
- et pus
- 2a H. sive y4 pa y + rans
- 4 2a2)
- inseratur is valor in aeg. 8 fiet: y 4 - py - 2a0s
- fierex aeq 2 sequens: Y - 4a 5 -ay. 70 + 4a05 v, (yt + 2ab3) +4 a vc 4a v4
- (a + b
- a = b
- et pro s2 substituendo, y +EaV +2a ex aeque D
- +rav 2aV
- =gar
- + 4 a2s sive -yt +2a . +4a30N~
- Quae aequatio est absunda, sequitur um
- -2aV .4 4aV
- V, vel pne - 20.) + 4 at et et b0
- +20 24
- ul sue portie las egudte se elitiratua quantatiti car ul qud q aespr
Cite
Leibniz-Handschriften zur Mathematik LH 35, 5, 3, fol. 3r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068021:0005?run=73