Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 5v
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: 0.85.
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The machine reads it as
- primo
- ax
- do
- Co = Sydx. y = s(xrb. X+C, X +d) Otiol ax- 2f sry+ 2ytoz + h Nyi taK
- sit X (ao) CaxL a sit (460), ax + ab = P) C12 Svy + 113 SvZ + 133 YyZ + 100 p)
- (5to), ax + ac = 12) (212 (vy + 213 12Z+ 223 yZ+ 2004)
- (6to), ax + ad = set (32 Nvy +313 10Z +323 (y2+ 300Y)
- Fiet ob aequ. 4, 4 sgroze 2hlyZue tate = f2. 1. hop Avy 42. 13. 1ptrt . 13. 100
- 25 Vvy +2910Z + 2h FyZF ak
- aqu
- 2. VI. 100p 1py, tr. 113 100p Y) B2BypryZ + 12. 1VV
- 2. I3. 113 2 (vy 12. 12. 125912) 12 13 113 B Ny) F 113. 11317
- L + 123. (239
- Eodem modo procedetur ob aequationes 5 et 6. +1.190p
- ab
- Hini comparando terminum Termino, nempe
- coefficientes ejusdem irrationalis item rationales,
- habebitur tet valor ipsius f, ipsius g, ipsius h, ipsius ak. Hoc modo
- f = 112. 100p
- 113. 123Z
- 9= 113. 100B, h = 123. 100B aK = + 112. 112Vy
- 112. 123y
- Et pro nota initialit B too substituendo 2.-
- et pro prP, 9; pro b, c, fiet
- f = 2. 209
- f=
- 112. 113V
- 6213, 2232
- 9= 213. 2009 h = 223, 2009
- 212. 2239
- 212. 213V
- Et pro nota initiali 2.. substituendo 3..
- et pro 4,r; pro c, d fiet
- 312. 30OY g = 313. 300Y h = 323, 300Y
- 313. 3232
- 312. 323y
- 312.313P
- +123. 123y
- + 100. 100 p
- -000,000 ab
- af = + 212. 212vy
- L +213, 213VZ
- +223. 21397
- +20040094
- =0001000 ac
- aK = +312. 312 vy
- incipiamus a comparandis valoribus ipsarum f,gh;
- ductis ab irrationatium coefficientibus; et ope aequa-
- tionum inde ductarum inveniamus, Zue, y, v.
- +113. I13VZ
- +313, 313V3
- + 323.32397
- =300.3007
- =000,000ad
- Ex ipsius f valore primo fit Z = 112. 100p - 212. 2009 - 312. 300Y -212. 2009-7 Exipsius fvalore
- pr et aecundo
- 213.223=113, 123
- y = 113. 100p = 213. 204
- 212, 223- 112. 123
- d
- tio
- secunde
- X3. 223 - 313.323 2
- 313. 300Y -213.2092 .... g....
- 212. 213 = 312.323S
- V = 123. 100 p - 223, 2009 = 323. 300Y - 223,. 200) - B ..... h . . .
- 212.213 - 112. 113
- 212. 213 -312.313
- +112. 213. 223 100p (212. 213. 22738009 = +312. 213. 223. 300Y (=212. 213235009
- - 312 113. 123
- +212. 113. 123
- Ex binis valoribus ipsius Z fiet
- Et ordinando +va o 32 idemque faciendo in binis valoribus
- (1) + 113. 123(212, 2009
- =112. 313.323
- 4212, 313.323
- ipsarum y et v, fiet
- .=213. 2232312, 300Y = -313. 323)
- Etbrdictanda +213. 2231 112. 100p
- et permutando
- 12 et 13
- 313.323.
- 4 212. 2232113. 100p
- - 312.323)
- + 113. 123.
- - 212. 2231313.300Y = + 112. 12312137.209
- + 112.123)
- = 312.323)
- = 212. 2131323. 300Y 4 112. 1132223. 2009
- +112. 113.
- = 212.313dam
- unde permutando + 212. 2137 123,100p
- Ope harum trium aequationum, licet quidem invenire rationem duarumm ex in
- = 312. 313
- determinatis inter se, per determinatas, sed non omnum binarum quamvis indeterminatam,
- 0(3 et 023
- alioqui V, y Z habeent rationem determinatam, ad unam eandemque indeterminatam
- Piq sit e et r:9 sit co, et pro aequationibus tribus inventis scribemus has tres com-
- pendio expressas 11 P + 12C0 - 10420 211 + 2200-20920 31V + 32c0- 304 =0
- 11. 21 1 = 10.21g = 12. 210 = 11. 209 - 11. 22W. seu F11. 22 - 12. 21)c = (11. 20- 10. 21) a
- et pari jure (31. 22 - 32. 21) co = (31. 20 - 30. 21) a. unde per se consequitur (11. 3L = 12. 31 Xa (. v. 103
- Non licet autem Et pari jure habebitur , non licet autem simul habere valores ipsarum P et Co, ergo
- malterutra ut postremo evanesceret, efficiendum foret, ad eoque opus duabus hypothosibus. Sed quia malim pet
- Et ex 1et 2 fit, 10. 269 = 11.201+ 12 20C0 = 10. 211 + 18. 22W, unde
- 2. 20 - 10. 22) = (30. 21 - 31. 20) 1p: (32. 20-30. 22): et aequande
- has valores 10. 21.20. 32 10. 21. 22.30f 11.20. 20. 32 + 11. 29. 21. 30 = 12, 2021. 30 (10. 21. 22. 30)
- 11. 29. 32 + 12.20.31 =0 Hinc in aequ. 1. pro 20 ponem
- 1
- +
- tractari eodem modo, tollamus
- et co = (10. 21 - 11. 20) 1
- seu F10.2131
- 12. 20. 20.31 + 10.202 et 10. 11. 22 10. 17. 2
- arioria
- u2. 2
- 1c. 22 - 1. 2134 = 10. 22- 12. 20, 4 et fit 11.22 -+2. 21 =0
- inventum
- et 10,22- 12. 20=0
- = 21: 11 = 20: 10. Et pari jure 22: 32 = 21: 31 = 20. 30 unde 72. 1 = 31 : 11 = 30 : 10
- rod t 2E,inut ergo aroportinales 1b, el, 12, ipsis 20, 21 22, et ipsis 30, 3132
- (VI =100P
- C c0 = 30Or
Cite
Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 5v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0010?run=74