Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 3 B 19, fol. 10v

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: 0.75.

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. 9r); this page is its left half.

The machine reads it as

  1. X. y. Z
  2. X
  3. Y 5.8 a suno
  4. Ixtiy 17a. ix dy B b. Ergo iXB a - 1y p b 4 1y. er 9p 177 - b. 4, 1X, a L
  5. a - b +Zip c. et a - b - Z1p, d. Ergo 1Zp) c + + 4 - b - 42
  6. et et fuer e+ d p a - V. Rursus novissime a + tiZ p g. et a +b - iZ h2
  7. enitque 1Z H ae + B -Hi g - 4 4b. et fiet a + b 1 9 + ti Supersunt ergo nobis
  8. solvendae aequationes duae: b d d 5a. et a + b A 9 + si seu a- h e 9 - b
  9. seu a+h a - h, 9+ bg- b. sit ia +it p l 9+b) fier l a -t B 1 g- b
  10. ex unde ia_ (1g (+ H f ih p e ig - db, + et .hp 19 + 1b - ia, a rusus h altibajus
  11. quos duos vulores aequando: Pg + l l(=ila ial + Pb - Pg. et 9 2ial + i1b - f.b
  12. quem valorem inserendo in invento valore h, fiet hp al - al i2 + ibl 2 - (3b - 19l + 1- 21a
  13. restat aequatio a B B +C + d, quae illud ingens habet commodum
  14. aut h, in ipsam intrent. Ergo ponendo ap C+ malsiei rem + ne p B. f, d
  15. er Cr. 6 + - m. et a V +
  16. ut per se subsistat neque
  17. sed unn adhuc restat aequuatio inter. iz valorem ex duplici toppositione conditione, penultima
  18. et ullima nempe e (aes+ b
  19. 2 12 t ) - h. seu C + ho r a vel 3 +d p ae
  20. 2
  21. sit dei vel d F h2 - b
  22. a
  23. + m
  24. 3 supro p 2 ial - b
  25. Resumendo a +Bi s + h. et b+ C+ d a
  26. A. 1. Apera bpi 3. e Cx ae. His hibus aequationibus satisfaciendum est.
  27. a= h 9 - B. seu ath auh 9+b9- b. et C7 a - t. ergo Ep art a. h
  28. sit . 4 R 1 2ach. ergo ex P arhp a- h et ap pK = 1
  29. 2
  30. i
  31. Ph et et a - c = Ph destant resolvendo aequationes. 2. et 4.
  32. aequatio 2 b + d2 p a - C p7 a - c a +C - Ph, at c b d
  33. a VetB StCta V9 +te B ergo (et tep BCCd. ergo hp
  34. a p C xhi. eit Cs a M. piei (a (a arma m + li et ar + M. et 1 -
  35. et c H - R + . ess + 13 n. +N. + d, 9 H( b)
  36. 4m
  37. em
  38. (E+ hi p V(D +S sit bp h - n. fei ( hn + + 8 ex h e dn + et bp
  39. sperest aequatio ad huc una, ut CDe, dCti sit bp hun trei h +n. et bs -
  40. superest e (1o,
  41. Iso
  42. +19
  43. et
  44. 2
  45. +
  46. = q
  47. g2(4h7 - bv. seu h+
  48. 4;4
  49. Que + p g - d + 3 - = sit E79n. sei
  50. 4n2
  51. 414 E +1 A F. et + rt - pr
  52. 2i2
  53. 17 4. ergo M h i 2 ∞ +1
  54. sive mp S. n
  55. 41 Ep + 1 BY ergo F2 si X ⊓9 - vn
  56. a + b n9 ( H) Ergo Ct tp 9.
  57. Habemus ergo tes aequationes vilde singliaes: c bi p a. d 49 a b4 e . 9
  58. ubi explicab quaeliber aequatio literam habet, sibi soli prosuram sn hp Tanc. devaue
  59. b17 V92-e
  60. et e sn a+b fC. et a-bf
  61. cur h H 3et c ay 5C- c. p5(+ C. a CH sec - f c aet fC+ f
  62. Codem modo proh. a. c. f. C. 1. ponento d. a. g. M. n. p. fiet de map. et ap M n + mp. er gu mn. mpo
  63. et aequando a duos vulores frei fC + f12 Omn 4 mpr. seu nt
  64. T. dem modo pro s a: C. f. e. l. substitendo b. g. c. 9. 7. 5. fet hp qus. G1 qu + 9S ex Cp qu2 qsu. aequandoque duos valores ipsius
  65. fo. et aequando duos valors ipsius C, fiet fp s Multiplicandi aq. D et t m se inicem siet:
  66. p p. so
  67. foi q
  68. 7+ fu e e 10
  69. 21
  70. at edem jam f ru+ F fiet ergo aequatio novissua p n - pB Y gr n po
  71. + p
  72. et reducendo: (n re nVY + se p pt C
  73. p2 5= 10)
  74. p
  75. en) re Se( seB ( r C
  76. e
  77. u
  78. d)
  79. et fiet: Mr ps rC + S e N. qua aequatione divisa in duas s e. seu nlr ex.
  80. altera p sit suen. seu ple en eit: lr en H ex. adeoque 111P. seu n p P. Ergo eps L.
  81. sed hoc admitti non potest, feret enim erio. ergo nec haec divussio
  82. pone nerija rprp fsp sre no- suso pr. sit nrl+ rep p + sen+sip fietu;
  83. nrl - rep p) = sen - sEp ertque Z (F) ~ en -le (A ena
  84. unde miso
  85. Anbruinuus ner pesa
  86. 1
  87. sui. Hola enx, - l en le (en t pn (psed en
  88. ilo ex H D ultex
  89. CBi fori non deberlt, quia nondum a generalitate discesim
  90. nisus tit pAB. fer V465 B 4S tundem sit i
  91. reprrs en. sit le eN. fier: Xry + py, r sK
  92. fer V B Bs + ( V H B2 (3 + 1
  93. fer vi B +divide in duu Ov + B v P 2DBV 1 et 2BRV DB
  94. fiet; OD - βBH + L et 2V7 dB
  95. eutque Dp +L.P B 2 V. et fiet + P+ BB B aB hi vr B. Pai 41+ Y, .y3B Uux Cs eni fi, quod qunder poesito )
  96. litem sabi opus it 1Y . Y opetu quadinto Y. g1. fei ay. 1 FiYG. Lpsi cs a. Sa s. fer. rosi po i cot i t ogra H E b
  97. C N 1b ri a
  98. res cgeaec
  99. a + b p 9 + t
  100. exte pa oraeri
  101. b2 4f t et b 92
  102. Sed tribus harum aequationum
  103. quibus libet satis fieri sufficit
  104. ex quibus tribus utcunque assuntis,
  105. semper una erit litera cuilibet
  106. propria ut poterit inveniti
  107. h
  108. Notetur haec inserendi
  109. mettrodus.
  110. a
  111. C + h B a
  112. aex 9 +hi. Crg. C abi gr c Xh)
  113. b +C + d p a. g0 9 4+ d 7 a
  114. n 11

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 B 19, fol. 10v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068268:0020?run=74