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Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 194r

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: 0.83.

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The machine reads it as

  1. In crculo aCf ducta chorda ec. et ab extremis dianetu f. g. junctis rectis gc. fe
  2. et ex centro a. recta ab. ducta, perpendiculari ad gc. ajo Triangula rectansula:
  3. Di = =D GF - C1.
  4. abc. et sdc vel dgc) esse similia. Nam ang. efc = ang. gac. ergo
  5. et unu fec angu vel fce angulo agc vel acgaequalis Tuangula ergo efc.
  6. gac similia, ergo c. 4ofe et barfdc, abc. Z. E. d.
  7. rrgo D abc. simile Triansulo Characteristico Cyclocidis. Sed hocperse
  8. A febet hfC et ifc. sinilia sunt seu hf -Cf =
  9. patet
  10. Di- FD1G5 2
  11. H
  12. f 1c = cfc3C
  13. porre quodr. fit = Aq 7L -LH, a et LH = +q LA + Rad . - LA
  14. Ergo FH = Ra, FL. - LA Rad + L A sed FL = PA Rad + L A - 2 F ALB.
  15. Ergo FH. Bq 2L A = 2TA L
  16. G2+LF GL
  17. GF 2 Gt.
  18. in circulo L 1 sinu ess A4, a- 4. β3, B a 4 (3, 19 a
  19. idem LH sinus = EgF, GL L F, R4, = . β ha - β3. -
  20. Mulliplicetur, per a - β. fiet vel R9 a + (3 = 2a β.
  21. fiit: + a + B - 2 a (3
  22. + 2a B
  23. 4a B
  24. +2a (3 + 2aβ
  25. =B a + 2425
  26. FH- R9 GF = GFGL.
  27. R9 GF- GFGL
  28. FH.
  29. GF + GF GV - a G1GD - (F 1. GF + G1 91 - - GF G1
  30. GFD = GFGL _
  31. Ergo FI GF + GV - 2GF, GD,
  32. GF
  33. GF -GL.
  34. GF - GL.
  35. Fi
  36. p sG0
  37. GF - GD
  38. YGF- GL.
  39. vel FI GF+ GD = 2GF, G). Ego FI, GF- GD = rD
  40. tq 2a (3 - , = Rq 4 aβ - 4( = Ag, 6a (3 - 9 (
  41. Ag +a B- 4 p = R4. 2a(. ( summum pener a Z. C.
  42. FC = R9 GF = GF GD.
  43. Ego GF - GFGd FI
  44. V, = e + +a β3 + 24- 3a et hocum quidem
  45. Si jam diffientiae sinuum sumantuer:
  46. Sit a 1( 2aβ,
  47. erit d diamenter in
  48. f a X = b. Ergo b = X.
  49. GL. LF
  50. ob Plum rectangulum AL H. a. +3 - 2a (3) = Aq, 2 a B - (
  51. R9, 2 a β - (..
  52. 1
  53. GH = GL + LH, gergo GFI = GF GL.. Ego FH = GF = GFGA = GF- GLGF.
  54. FH2
  55. CI = CFHC. Ergo FDGF4E CF. HC L DC.
  56. FH
  57. e
  58. lono ex his colligi posse puto fi, quod quaerimus. Eto fh - (a) fc = (b) fi fX).
  59. es ic = ifehC.
  60. erit
  61. DEi - GF 4B L FD FI = FDGF
  62. ZH
  63. c
  64. crgo hf If = CfB. Ergo si f sha sit diametca fg. et hc sit gc. et 12 sit de.
  65. GLGL +GL LF. =GL LF GL
  66. ad + ab = a +b, a
  67. AI= EC
  68. HF
  69. FH
  70. GF - GLGF
  71. GF AgGF - GFGL, = FH
  72. cylinder Ergo parattolicus = sum cylindio omnium FI, demto
  73. demtae ducta omnium gd. in f1
  74. FI
  75. 5G0
  76. GF- GP
  77. Ergo FI =
  78. rGF- GL
  79. FI FH = GF = GD, GF= ACHCF
  80. Ergo summa quadratorum, CF pendet a summa quadralox diametri
  81. et summa omnium Gd. ductam B diametrum
  82. FD. FI, seu FD = FDeGF. Ergo FL = FH
  83. FL
  84. FH
  85. FL
  86. FH
  87. FH
  88. Iuspiciatur figura 2d deductibus in ea demittatur ex H. puncto exhemo rectae Ak. sinus compiti perpendi culari in
  89. AE rad E
  90. Ergo XV AEB. (gradrab.) = sin. compl. E Tanus.
  91. pro K). ejus aequationem: erit:
  92. Sncypl.
  93. AE H. rad.
  94. sinesii. Sim. Singpl. rad e
  95. AE d +0
  96. Bosins A A0 sin ypL. Ergo XJ. AEB AOBD
  97. radium AE. cam appellem esto XY. ne literas multiplicemus nami testum XY
  98. datur autem quadratura summae omnium AD. quia K), quia H cylinder
  99. XV. aequalis momento sinuum et ided quadrabilia
  100. HElan AH sc.
  101. ra
  102. sF
  103. ino Fd = Bd GF - F1. Ego F8 EF - F1
  104. 4
  105. AO. AE
  106. RY a rad= momentum sinus. Ergo cylinder omnum
  107. rad.
  108. Ergo XVAED = mom. Tangs.
  109. ey
  110. Ara Bosin C Aad E mom. Tangs. seu Radi cubus in vinum momitanus
  111. mdto compl.
  112. = mon. Tanus su compl.
  113. rad
  114. sin compl. 1.
  115. bupaditus cubus in Tangenlem, aequatur sinus complement cubo in
  116. sinum.
  117. siri
  118. 294
  119. Aade rad. suni rad suum
  120. horum idee differntiarum inter sec. B Tanus summa quadcabilis seu boum rad. D - sinrad. Erosi quadiari possent sut rad fricopla
  121. in copl.
  122. Sin. opl
  123. suuicgpl. C
  124. sin compl.
  125. sii. copl.
  126. summa quadrar
  127. potest, puto ertiam
  128. radicem extrahi poe
  129. Imio dubito de radice
  130. G) -GD
  131. 18GF - GL
  132. Y 9

Cite

Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 194r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 44). https://leibnizlegible.com/page/00067993:0389?run=44