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Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 69r

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.

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. 68v); this page is its right half.

The machine reads it as

  1. Ex aequ. pro aeq. 5. articuli 19 inveniendas
  2. oay aqu rur c pl siis mno Crnginid uis onsce
  3. -23712, : 9, 127234 237126312 923)
  4. esCgala A 712 2. 152 2723 f 2 p2. 22SI2. 2342, : 2513. 2372 F 1712. 23 512. 12723 - 13723- 14712, ., 1 723 + 23712
  5. (2. i se quigrlut
  6. eo bd q ur es-l uinderiu
  7. pro aequ. 6. articuli 19 invemiendam
  8. it isi
  9. r
  10. + 1729. 23512. 12723 4 1712. 12525. 23712,:,7 7125. 23512. 23712 4 7112. 12513, 12723 = 12723 - 23712,:, 12723+23712
  11. Ergo tandem mundando
  12. al + bm me cemeat Ct a b. ad
  13. Ad artic. 21. aequ. 1.
  14. F seu in t a = mt 1
  15. aat b + bbr Bla + Hmb = fnu F Ib fit a = B5l-Bgm, et
  16. ast= atm = 6fl - bgm
  17. tam aglebum = afm+ us
  18. fmx + fly- - glX. + gmy
  19. siu colas fma = f1b gmb seu 4 E
  20. Aid artic. (23. pro aeq. 2 vel 3 arlic. 22. scibatur
  21. =Cx + my erpo seu X, =
  22. et 292 = les 3,2 4+ 5e2 = 3in - (= 15, 125: 122a) seu
  23. 212 (6) 3 12123, 312 a = 15. 235, : 123 a et 22318 112. 323a - 15. 125,: ma. seu se quia
  24. 1232 (323, et 112=8,12, et 15. 235 = 37. 235 et 15. 125 = 37, 127 hinc ut omnia enuntientur
  25. et 123 + 313 = 3131723 ex artic. 3 articuli 29
  26. isp secundum justitiam fieb: 212= (123. 312 + 112. 323) a - (15. 23524 37. 2372), : (123+ 323) a, id st _ 212 - 12 123 a - 15. 255,: 123 a
  27. et 3232(112. 323 + 1230312) a = ((5. 125 4 37. 127),:, (112 + 317) a dest 223-712 323a - 37. 175:, 312a
  28. ope ergo aequationum 6. nempe duplici aeg. 2 hic, et duplici aeq. 3 ha, et ope ag9. 2, et harticuli praecedentis,
  29. id est 14 et 15 huius habnimus, 2, et quae sunt 6, habuopus ae99. 8, et 18 et 16, et r7 859, E0, 18
  30. 8, 18, 16, 17 et 11, et 13, quibus invenimus nondum habitos valores, ipsarum 312, 323, 212, 223
  31. 37.15, et 237: 127 vide post 1 aequ post aeg. 13. ubi feliciter evenid, ut valor ipsius 2377. 123, sit idem
  32. superest um ut praestemus
  33. qui jamante fuit repertus, evitaturque contradistio, in quam alias incidi potuisset. 2p
  34. 513 f313 = - 13 + 113. suastituamus valores
  35. s -2t 12. 123. 313Ar d = 37. A7 11579 431 323 19 7
  36. quo aqu qui valor aequandus
  37. equ. l. articuli hujus pro 213, 513, 313, 713, 13 In aequ. + segtago
  38. ipsarum 513, 713, fet 1seteS as per aequ. 20 ut usqe articuli 29)
  39. valori aequationis 18 articuli praecedentis 29, in qua evanescit 312 et 12 quia aequales et sir explicando
  40. seu 313 :13 = b9no) 15, 125 - 235 + 312. 323 Trr, :, 37. (27-237 4 112. 1231YY,
  41. secundum aequ. 12 articuli 28, prudit nova aequatio ex his duobus ruboribus, per quam non video quid impediat
  42. determinari aliquam ex is Inveniri aliquam ex lis quae supersunt quantitatibus 15, 37, 112, 123, 125, a
  43. 235, 127, 237 de quibus nihil ad huc habetur quam 37: 15, et 237: 127 si in aequ. 19 7)
  44. Hic jam tentemus periclitemur novalo H pothesie, et faciamus (20mo) 6 125. 235 =
  45. 39) Hic jam periclitemur nova Hypothesi, et faciarmus 15. 125 - 295 = 37. 127-23,, ita enim
  46. ob. 312, 323, = 112. 123 freiet per c9. 19 artic. 30. fieret 313 = 113. unde (3ho) ex aequ. 18 artc. 20
  47. faeret (125 - 235) 115 1300 nn -200 um = (45o) 12 (127 - 237) 537 11ool-2oomm. sed hoc non
  48. licet nam ex 4 et ) hujus, fieret 14390 nn -200 min = S100 l - 200 mm quod est contro hypothesdi
  49. prestat ergo redire ad aequ. 19. et explicando, et faciagnas
  50. n :a et ex ev. 18 artic. 29, fiet
  51. ampendio 125 - 235 vocemus 25 et 127-237= 27 erit
  52. a+ vere vt + uvoreu
  53. 17
  54. l’ex aequ.
  55. Yise Y300 nn -206 mm, 8 15 :, 100 ll- 200 rum, 37)
  56. quod est contra intentum
  57. per et 125+ 235 21 et 127 -237= 23 erit per 12 ee arstic. 29
  58. 125- 235, 4,:, 127-2770
  59. 19 artic. 30 fiel 15. 25 + 112. 123, 21. 25 ) B, :, 37 C 37. 127. 237. 27 4 312. 323. 23. 27 a 313: 113, C
  60. introbique dividi potest per 25 et 27, fiebus
  61. 27 + . 923. 23. as
  62. 37. 127. 13
  63. 15, 125. 235, 25 + 112. 113 2. a
  64. i2 (idest ur. 123 vel 3123d9
  65. unde tandem habebitur n2. 123
  66. Ere. 125. 235 - 37. 27. 17. 237 ita taudem
  67. . 23 ab - _2 2) a
  68. es in quibus nondum implicantur et reliquae i
  69. seu 312. 313. eu fiet 112. 123 4 312. 3
  70. 25, 225, 17, 237
  71. (ex quibus pendent 25, 27, 23, 21, B, V) sumi possunt pro arbitrio, quantum patiuntur jam habitae deter
  72. 112, 123 vel 3(2323, habemus per Pitera
  73. nn = 2od um et similiter
  74. minationes, et scopus. licebit etiam ponere 15Brest DDag:, 3de et
  75. atu
  76. inventas quantum
  77. quat conditiones postu laut, determinatas 112, 2n, 31E, 18, 213, 313, 123, 213, 323; jam absolvamus
  78. substituendique erunt hi valores ubique pro 37 et 15. opieri pretins upere
  79. u
  80. utile erit i exprimi tam vec v quam et
  81. 171et 3 artic et init. artic. 8((pro 4e, esp
  82. (19to), , 3
  83. explimere ipsas v, Z, y inde terminatas ubi fors
  84. et dendo aeq. 1. et 2 artic. 16 pro ut tandem obtineamus irrationales Suy, Y0Z tyZ cum ipsis pqdere
  85. Mer y, adeoque et reliquas vide antur aequ4. artic.
  86. en
  87. artic. 30. et nitio
  88. deinde an sabis fiat initio articuli 10, b. tum pro valore
  89. possumus intir dissimulare quae instituimus
  90. riationabs in aquiutio sata Hi pu n
  91. idalonis pratio dantur irrationab, in aequintio dati His podib, um q cemratius
  92. parte ulie eiupari
  93. aibenta salisfacunt eq altuonali
  94. 12723- 23712.23
  95. 12723 + 237125312. 313)

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 69r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068255:0137?run=74