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Leibniz-Handschriften zur Mathematik LH 35, 4, 19, fol. 4v

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.

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. 5r); this page is its left half.

The machine reads it as

  1. Ergi qu acantaa
  2. Ergo xaequq Z- a. Habemus ergo:
  3. Z aqu bz aa + aa +cC. seu
  4. ZZ aequ bZ+ cc- aa
  5. siu Z aequ bsua ecc nb
  6. Unde facilis constructio est, ut
  7. rea
  8. si triangulum
  9. ea dimichia
  10. rectangulum fiat cujus latera sint
  11. AH. et alia recta quae possit dimidium differentiae
  12. quadratorum a excessus quadrati ab AL super
  13. quadratum ab AF, ejus trianguli hypotenusa,
  14. assumens dimidiam AH erit latus AB
  15. Quaesitum Trianguli quaesiti ABC. unde caetera
  16. habentur.
  17. fitit Z orgo aa
  18. seu ZZ aequ Lax + aa +. Est autem
  19. X, Zaqu. a XFa. seu QX +4a
  20. Ergo 22 equ. 2b6x + bb. quos duos valores
  21. aequando fit. bb xx + 2lb x t bb aego 2ax + aa fac
  22. er ortia fit aequando et ordinando fiet:
  23. xx + 2a X Equ. abb+ cbl -ra
  24. saulxe
  25. et unde erit.
  26. a). aa bb + b (abb) a bb
  27. am l No uare a cuins facilis ins
  28. cas dtat, un
  29. et X + a sive AD aqu. sbb - aa cc + bb
  30. XC F: c jam Z. X+a: a. b. Ergo
  31. erit fbb. a an +b. ciunus facilis satis per
  32. rectam et circulum constructio est unde constructio
  33. AB seu Z aqu
  34. haec ducetur. super data LM se b describatur
  35. semicirculus, cui inscribatur Me media proportionatis
  36. inter datas a et summam dutarum a et C et
  37. in producta ML ZP asqual. LN. erit Mp
  38. latus AD seu Z. quaesitum
  39. Hini sequentem duremus constructione:
  40. sit datus ang.
  41. rectilinens GAF. et AF
  42. vel AG dit data sdiffe entia segmentorum AD. DC.
  43. eeperpendisitars ad AB latus ad verticem et
  44. angulum datum ad Ad segmentum ad angulum datum
  45. ut data Ai vel a ad AH posito GH esse normalem a
  46. is sit FL opta duta quae possit aggregatum quadratorum
  47. AB et BC. jungatur AL centro A radio AG
  48. descriphus formicirculis occurrat in M, jungatur ML.
  49. inque garduntur sumatur MN aequal. AH. eritque
  50. LN equalis ipsi AB quaesitae
  51. ∞3 - yy aequ 2 ax + aa
  52. y aeqo
  53. q
  54. Zuqu Xa
  55. xogo l =a
  56. qq 99 2xy aequ. 2aX +a a - 2bb - 222
  57. X aegu LZ- a
  58. yaegu bb.
  59. Ergo fei 2Z = b aego 26Z+ 3ta H (aa)
  60. seu 7+ - 262 + a aZZ aequ
  61. 4- ut Z sit
  62. lZ= 2bZ2, laa ZZ asqu bb
  63. nm Z2 17
  64. Bt e +2 3
  65. mmzZ - 2bZ+ laa
  66. + Alu 7Z y 3m EE h
  67. +2bn taegu paego smm+ Il
  68. pp ZZ +2p9Z + 94
  69. quequ. IIla a +26ml
  70. Ergo llaa +ebml. jum + (I aequ. bb
  71. sit maego nl. fier llaa + 2b ul nu I FU
  72. superqua
  73. qu describatur semicirculus cui
  74. inZZ + n Z
  75. ergo habebimus: v +bV X aq + 2baB = a aqu. 0.
  76. sit a aequ. Y. fier vE- vb + 2b
  77. sit 2 aequs.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 19, fol. 4v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068016:0008?run=73