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Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 66v

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.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

One image of two folio pages side by side, registered by the library under both labels (also fol. 71r); this page is its left half.

The machine reads it as

  1. (14) Ex articuli 13, a99. 3 et 4, quaeramas 513: 113, et 713: 313. Et quideme
  2. aequ. 1 3 fit 513 + 4.112. 123. S12. 523. 513
  3. 11223. 112, 123 113
  4. 4. 112. 1232. 512 +23 = 112233112. 123,512. 523
  5. seu 5B + 4112. 123. 512. s2Z 51
  6. 115 11223. 112. 123 113
  7. seu D12. 123. 512. 523Dhh-S) ()Uh = (3+ 0) 11223 sh et ex 1 et 2 fiR extractioni fecta fi
  8. defunctis = 112, 123, 512. 523 f 112.523hh + 123. 51 hh = 2, 112. 123. 512. 523hh seu 51223h= f~- 112 123. 51. 5C3
  9. sed ut in eg. s succedat extractio sit Hinc sequitur 112. 123. 512. 523 (7 mo) esse quantitatem negativam
  10. utjam amm a qu S succedat extractio, fiat
  11. ex aeg. 5 firts b(f. ath) 11. si h. Ex 9 est 123. 512 = bb (2h- H): M. 523 et
  12. ex 10 est 123. 512 = (f - 4hh) (b: h) = 112. 523 quos deos valores aequando fit 12. 523 - (, 4hh) (b: h) 112. 52
  13. (11m0) = + bb (H- 4h4) seu 112. 52A - (f- +h hi bh) 1 2. 523 + A stlbe bbf - 8bb ffth + 6bbh (: ahhil
  14. =at bbf obbsthh (+1bbh) - 4bbhh ( 16bbh s: atk bbff (5 - 12 hsC): ath
  15. seu (12m0) 112. 523= 65 Fs5- irtih qbs- att): = bb bs hc 166h aF f - 166d: +tih
  16. textratendo f 112. 523 = (12mo) bf ss-ath + _b (f5 - 4hsi): 2h. Tantum ergo superest, ut fatiamus
  17. H- 4his aequalem quadralo f- 2f8 + 85 seu f = (13tio) 4 sh + 88,: 28 et fiat sf- +hh=
  18. V 16ht + 8hh 48 + 84-88hh,: 484)- (.26.) 4hh - 94,: 28. Adeoq ex 12 et 14, fiet
  19. 112. 523 -fista) by 16h ( 1bt2 - 8titis P : 8995 seu 12. 515 = ah- h8,: q
  20. Ergo per g fit substituendo valonem in 10 fit 123. 512=) (( og, f1) 16 + 4tt9 f. 4h 8
  21. seu 132 123. 513 (b ) Clot) ) (b:h) , 88 - 4 hp. unde 112. 123. 512.5, 16= bb 4titi: 8
  22. unde vera reperitur ag. 9 per 14 set ex 15 16, fit 11223 7 (1800) (b; ahg): 16h otha, quod itidem
  23. consentit cum aeq. 10 seu fit 1122 (b: h) (T (+th - _8 : 28). Et ex 6 per 17 fit 51223 b. + 1bt : 484
  24. am M 23= S1223 =, Z. M. suq = Lt (b: h), as 2- g + 16 H + (9 l 1 5h2,: 44q
  25. + ∞ + prodit valor ipsius i 112. 523; sin sit + ∞ X, prodit valor ipsius 23. 512. Unde patet n
  26. in 3r esse 51223= fb, h), 16h- 8: 4g non mutati signo. posito ss aha esse
  27. 4kh - 8: 2; spe inen emne non contraria signa ut in aeq. 14. non vero contrario signo.
  28. lldeta Ex his jam s. )B = ubi possumus sponete in aegq. 15 et 16 repertas esse 512
  29. et 525 5EG. per 12, et (12. Et ex aq seu ita in valore ipsius 51Z: (iC3 ex aeq. 4
  30. seu 513: 113 = 112. 173. 512. 523(f - 2h). 1122. 112. 123h ficc
  31. erguees 2t. 8
  32. etr 1 = 8 bb, glih - 4
  33. seu dema SB3 (21) 2ta - b, 2h-9
  34. jam in aequ. 3 articuli 13 pro 51 subssi hanus
  35. bb ima. ge, (49. s
  36. hunc numeratorem, pro 13 hunc denominatorem, et fiet
  37. + +th- 4g v 6 b Et. G
  38. quibs valoribus +58 h 21, 19, 17, substitut
  39. nes qu. 3. articul
  40. res 112. 113, it
  41. aeg9. 15, 16, 17 19, 20, 21, pro quibus continentur vasores rationales ipsorum
  42. b,- ric2. 10 b4 (i 1123
  43. 1 1 )m n m t ug sinae (1
  44. mucon
  45. pari jure ob 9, D- 0 t, ut praestetur rationaliter aequatio 4 articuli d, fie
  46. L =uo retinendo h, et pro f, b, 8, ponendo 9, C, V fiet 713 (1m0) = L. 31. 323)
  47. (c. t- hY, et 123. Sir AB to) (b. at) gg 32 1C do) (c. YY) asch- 1)
  48. et 2 et (200) 312. 723 = (Ch: YI), 4hh- et (3tio) 323. 112 = (C: 4h), +hh - Y)
  49. et Ato) 312. 323. 712. 723 = - (C: 477), 4hs - et 31223 = (5t0) (C: 4hs), Anh - V et denique
  50. (610) 12 23 = (6. 4671), 1 166 7 4
  51. Extractione igitur facta ex aequatione articuli 12, fes
  52. S1223( mm ). Etpum jare 32. 712 B F 33. 721 2 = dp2s f rrera un Amm)
  53. 12. 512 V + 123. 523Z = 5l223 + 2. p23. 12413
  54. seu compendio 112 12V + 123. 523Z 4 600100 a=0 et
  55. 312. 712V + 323. 7133+860. 800 a3 (4to) =0
  56. et sibtulis a tutis pro tollendis absolutis fit p. 71. G0 aV- 31. 714. 600 a2 2 600. 800 a
  57. quam reddendo identicam
  58. fiet 805 2600 = 3121712: , eL 800: 6052 33. 723 :, 127. 523 unde fit (800) 312. 712:, 12. 312 = 323. 123:, 123, 523
  59. seu (gno) 112. 512 313. 723 = 123. 523, 312. 712. sed aq. 9. sequitur ex ipsis 6 et 7. ideo, duae ex his
  60. t
  61. 112. 12351 + sir. 525 H3 F 1BE3 NB. SiZ quod multipl. spr 112. 13: , 113. fit 115. 12y. s1 P us. s2 siB vES. N2 rB ortcissed Iter
  62. bb 4- 8 16f +9
  63. 859mon acu p 17
  64. in aequ. C arsic. 16. potent explicari (. 1212. 1231) Aer 13, e et per VE. 123. Nam vir C 12 A 103
  65. = bb A . b atih. ps (112. 1 -b
  66. ahhrgaligh aeguets
  67. in Bs S gl g Ahsi +b. G(, 4 Ah 29 a haer tq b si (+ Pha q d citrh. 212
  68. unde U D seu (ir. 125 bb1
  69. adeoque 11213 a 23B =. = 113
  70. Seu (1m0) S1 = Au 2. 123. 512 125 = 11223 112. 123. 512. 527, - 2, ME. N3. 12 S3) Ergo Aa3 esB3. M. 13. 13 = bb. ih. q Eh. ist - 4thr 9- +h r chi q - n. pats. it il g. . q iB
  71. Ubi ut irrationalis reddatur extralibilis fiat 4.115. 123. S12. 523 - 11225. 112. 123. SA2. 523 = (2do) i. 123., 12. 513 f: hh,
  72. 513: 1132 (112. 123 512. 523 (f - 2h):, 11223(. 12. 129h Sed quia in 11225 latesit explicando 11223 ut
  73. in aeg. 3 fiet 112. 123. 512. 523 (4hh, 5f) = 11= 5() 112. 5237+ 115. 5125, + 2. 112. 123. 512. 523 hh seu
  74. ut imaginariae evitentur, et ptroinde in aequ. 3 debet esse smajs quam 4hs
  75. SM Si 11Z. 13512. 523 = bb (Ahh - ss et
  76. ahh - 98, pi2. 113.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 66v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068255:0132?run=74