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Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 103v

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: 0.86.

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. 104r); this page is its left half.

The machine reads it as

  1. estat ut similiter oculari demonstratione exdibeanus
  2. aequalitatem. quadrati ACFd, et rectanguli CKTL quod est prion
  3. aequalitate paulo demonstratu difficilius sine extrinseci assunta
  4. segmradem tamen qua ante via, incedendum erit per onvest
  5. gationem segmentorum. Primumigitur ut KFd transferatur in HdA, epod
  6. tet ab ACFd resecari CFdM, restabitque cAM. Rursus HTK, cum transferrit
  7. deleat in ALC resecari debet ab HDA. Cum etiam Denique etiam Kdm ause
  8. in debet ut rest qua translatione babebitur ex AC M DI, fiet
  9. A K T LCM D unde aufer refecari debet KdM ut fial Ck TL. sectiones
  10. dem la port figurae transferendae faectas in faciendas in cino loc
  11. amus et in alio um ergo k FC secta sit pe deo per MD, ideo
  12. imiliter HdA secetur per vio ductam congruenter. Et cum Hd A secta sit
  13. TK ideo similiter KFC fecetur per FX et per KM ideo similiter
  14. XFC secetur per =Y congruenter positam ipsi TK, et Y congruenter posita
  15. ipsi KM. et ut KM seravit Var secat alicubi tm, nempe in X; ita
  16. ix secabit alicub. Md ut nempe in T. quia Et quiq YF in KFC respon
  17. et insi Kdm in HdA id unumque ex alio fit transpositione ipsius kFC in
  18. Na dei sectiones ipsius XdM repraesentando in YF ip, repraesentabitur
  19. W per Bd. Et = Y repraesentabitur per 42, et Y per ZC0. Postremo quia
  20. vel HTK transfertur in ALC idso sectuis sctio ipsius X Z Y per X W
  21. repadtentetur in ALCper No. ita d tandem assecnti sumus desideratum
  22. n
  23. mnes partes quadrati ACFd transpositae constituant rectangulus
  24. Nam CAn manet utrique omnune, 2 L Z+ co transferetur
  25. in A0HG Zd in NLCB, +BNC H in XAM XVAM, et denique 2G qued intrur
  26. XTL
  27. Unde talis pro CKTL, Unde talis prodit transformatio: quadratum ACF
  28. secetur in duo tria Trapezia BMC , DDGZ, ZPCo, et duo tri
  29. angula CAM, ZFC n et manente CAM, transferatur _ ZFCd in AON,
  30. et 398 in ON LC, et D M C( in XVAM, et denique ZGY Co in KTVX, atque
  31. ex iisdem tribus trapeziis durnus triangulis AX AM, et AN AON tribus
  32. traperiis ONLC, XVAM, K TV. X fiet rectangulum CKTL. Schema
  33. tale erit
  34. ACAM = CAM
  35. FC = AON
  36. ACFd = DBGZ = ONLC = CKTL
  37. DNCI = XVAM
  38. (2YCO = KTIX
  39. postquam ergo quae situm assecuti sumus remoto jam pegmate
  40. omnibusque machiramentis ratiolinationis, rem ipsam velut de integro
  41. aliis sic exhibere licet, hactenus dictis omnibus refecti dissimulatis:
  42. Theorema: Quadrata crurum trianguli rectam
  43. guli simul sumta, aequantur quadrabo Hypotenusae
  44. demonstratio ocularis
  45. sit Triangulum rectangulum BAC uius angulus rectus A, dico quadrata
  46. super AB, et quadratum super AC simul sumta aequari quadrato super BC
  47. constituantur quadrata ABGE super AB, etCACFd super AC; et easdem partes BCKI super
  48. t
  49. Nam ang 1BG = ung CBA, et BI = BC, et BG= BA, erqu. B
  50. unt 1391 et BAC, et ang. 1GB = ang. CAB ergo angulus 1GB rec
  51. BC adet i in GE
  52. ad angulus BGE rees ex constructione ergo recta 1C, et EG cadunt in
  53. gicum act eotur
  54. 1GB, a
  55. G ipsi, erunt id et E in directum, et Gt h eu Ac minor q
  56. g. 1BG = aug.
  57. minor GE(= AC
  58. cadent G+, E
  59. 1B = BC et A = BA congruero
  60. et ob ang. BGE reZ
  61. ectam
  62. alem
  63. GerC
  64. ex constructione, et 1GB etiam rectum (quia
  65. aleo
  66. irectum, et 1 in B ectum, majoremque kF (id est AB) ipsa D F, id est A C) cadere,
  67. in ret FK et eK secabit Ad, sitque punctum intersectionis M
  68. ectum et c
  69. ob angalum rilectum, e
  70. F, D, X, i
  71. ostendemus pusto Anm
  72. in
  73. d ttu
  74. oqi di
  75. 15 et per sputatur par allela ipsi AC socans AB, BC, in 5 et A
  76. dan
  77. in A + se Sectonergo foi est quadratum ABGC in
  78. per
  79. le
  80. iangula
  81. in ABtK, 1G2P, et
  82. otidem traperia et triangula prio
  83. scilicet duo ABIR ASAL (congruum ipsi 1GQp) et duo triangula
  84. imiliter rectangulam BITL,
  85. AFR (congrnum ipsi Beg) et BS A (congruum ipsi 1EK) ATR, BSA, quia Cergo
  86. ute et
  87. =ASAL, et BPZ= ATR, et 1EA= BSA, aequalia erunt
  88. 13p9 BGt E
  89. Fnspectire prroribus congrua, trape
  90. BIR, et +G2
  91. (Trapez 1G2 = Traper. ASAL -p1IL rectang
  92. ABGEquadrat Triang. BPZ =
  93. triang. IER = Triang. BSAS
  94. Ergo AB GE = B1 7 L.
  95. Unde schema tale segmentorum congruentium n AGEstaBI
  96. (Trapez. ABIR = Trape Z. ABIR
  97. Triang. ATR
  98. et AE lecabu
  99. A
  100. ABR
  101. ABG2 et BITL

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 103v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068195:0206?run=74