Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 89r
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: 0.84.
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One image of two folio pages side by side, registered by the library under both labels (also fol. 88v); this page is its right half.
The machine reads it as
- si sint quatuor lterae les a. b. c et tres aequationes tunc valor unis literae
- Ita habebitur:
- beq 10 + 1 a + 12 b + BC
- et ooqu. 20 + 2 a + 22 b + 23C. 0aequ 30 + 31a +32b + BC
- tione 6 in qua
- nempe ex praecedenti, quo omissa c, invenimus aequationem in qua aberat tam
- a quam b. Nunc ergo ex aequ. 6 facierius aliquam in qua habebitur
- valor ipsius C, tantum pro 10 ponendo. 10+ 13C : pro 20 20 + 23C, pro 30, 30 + 33C
- +10 int2t. 32 420 in t3c. 12 + 30 in +1A. 22. aqu0
- et habebimus: 1e 1+13C
- eodem modo mutatis mutandis habetur valor a et b
- pro a, mutatur 73 (n 1 et contra, pro b, mulatur 3 in 2 et contta
- C+
- jam inquarta aequatione 40 + 41a +42b + 43C aequ. 0. substitu.
- untur inventi valores, quod fit multiplicaone per crucem, ut paulo aute
- opus vero erit collocale valorem, ipsius C in ordinem, et fier
- 1XC 110. 21. 32 = +13. 21.32 C. aq. 0. Unde apparet quanta facilitate
- Notabile in
- - 10.31. 22
- +20, 31. 12
- = 20. 11. 3
- + 30. II. 2
- 30. 21. 12
- - 13. 31. 22
- 423. 31. 12
- -23. 11. 32
- +33. 11. 21
- - 33. 21. 12
- ex aequ. 6. fiat aequ. 2 tantum enim
- aad formulam aequationis 7 adjiciatur
- alia formula, hoc uno ab ipsa differens
- 20. 30
- quod loco 10
- 13C 23C 33C ubi contingis ipsiu
- contra. Ergo si eadem dentur
- set +10. 21. 33 12. 21. 330. ag. 0. Et eoiem modo habebitur a. valor ipsius a, ex aequ. 7
- pemaente
- -10. 31. 33 + 12.31. 23
- + 26. 31. 13-
- -20. 11. 33
- bipsia i munco
- mutando 3 in 1. et contra. seu coefficientes
- ipsius A in crefficientes ipsius et contra.
- et poterit scribi aequ.9.
- generaliter acitem illud apparet praeclarum, in vulore ipsius C non ingredi
- + 30. HI. 23
- = 30. 21. 13 4 32. 71. 12
- in absolutum terminum nillqu ingrediatur coefficiem
- ipsius c. eodem modo in caeteris aequatione pro b. (nempe in aqu 8) vulorem
- quod in aequatione pro Csnequ)
- absolutum Terminum non ingreditur coefficiens ipsius b.
- iseud vero adhuc praeclarius, quod quain stis aequationibus 7. 8. 9.
- t quantitas multiplicans literas a vel b vel c; est ubique eadem
- quoque in contracium mulata sint,
- possunt potius signa mutari in absoluti termino. Itaque distinctius sic scitemus
- solis te sign et ne signa
- Le +1.
- si gua petenda ex sinistris
- characteribus jn miniorbus sine inerioritus
- signa nominuloris omnia tantantur
- mutantur mutatis signis Numeras
- joris valoris C
- quod si ordinemque secundum
- charncteres den sinisttos ita stabit:
- a, 11. 22. 23C
- -11. 23, 32
- 27. 32
- 13. 23 31
- Si in ulla 1. 2.
- + 10.2, 32 aequ.0
- + 12.
- 2
- -11. 20.32
- 1z. 29. 31
- 5eq. 0
- = 1 2130.
- diperini o
- =0. 21.33 49.0
- + R10 23. 31
- 1. 3. 0
- 23 31 42
- 1o2 20 A)B reviter
- 103 (0 C +, aequ. 0. add
- 2020b+ aquo
- Catao 10 + 41a + 110+ +C 59. 0.
- hec 400 ( a0 a + n OB, 1B3G) ay o-
- + 41F) 410a
- 1308 0. 123.
- eter aequaliones tres autio suntat
- jum jungatur equatio
- lles eperauilo
- ibere.
- +11. 203
- r13 2. 30
- 10. 22. 33 aequ. 0
- + 10. 2322
- +2.1032
- 17. 2032
- + 435)
- ita in O supsletur 0, in D, 2. in Q, 2: in D 3 8
- Ex aeg.. 1I erventa fit aegi. 0. cutus oumia perse pallut autem in sigo
- ubique praeter 1.2.3
- +428
Cite
Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 89r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0177?run=74