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Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 232r

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: 0.88.

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One image of two folio pages side by side, registered by the library under both labels (also fol. 231v); this page is its right half.

The machine reads it as

  1. ex basi quadiantis
  2. HF EN = ACCAE) AE seu AE _. sive momenta tangentium et langentium complementi simul, aequantum quadratis
  3. Jam Momunta tung Coroll.d.Hinc sequitur summam ex tangente et tangente
  4. Comb. t.ito bregiu demonstres. in Ho radii. Ergo sunt quadrabilia.
  5. AHF altiludo AE= altitudui FZ. diimidio complementi, aequari secanti, seu HF = AH. quia AH = AED et HF= AEH. Coroll. 2.
  6. 3.35. Ina
  7. Conl 3 Et
  8. item
  9. Hinc differentia inter conchoeidem et Hyperbolam, quadrari potest aquatur Tangentibus semicomplementi
  10. Coroll. 3. item tangens arcus dimidii auctus tangente complementi aequalis secanti complementi.
  11. ull. q opomentae tangentia sermiusptti ex basi, quadbtia . Torelles Ergo, um. 7. prop. 25. dud. Hyprb
  12. C propib
  13. Dla similia: AEF et ESF HG. = HE. Eitang. sunitompl. quadrabil. Error
  14. ADCEF= DF= FK(FK = AE) ob Dla ADF. ergo secans (complementi) in tangentem arcus dimidus (complementi)
  15. aequalis radio in differentiam Tangento, et Tangsentis auus dimidis Ccomp) Coroll. Hinc haberi possunt et tan
  16. gentes auu dimidii in Tangiarcus dimid. compl. Si a Tang. arc. dimid. in sec. anferatur Tanus. arc.
  17. dimid. in tangs. quia sec = tanus + tanus. compl. arc. dimid.
  18. DED = DF DG. seu quadratum differentiae secantis et radi, est aequale differentiae inter tangentem
  19. et tangentem arcus dimidii, ductae in disserentiam inter tangentem et Anum. Esto secans d. radius a.
  20. langens c. tangens arcs dimidi . 1. sinus b. fiet: d + a syda = b- 1, 6- b. = + bi -ei- He bc
  21. iam d= 7 c + a. prop. 11.
  22. pone
  23. sceoitimus ad Ia simuilia intermissa, de quibus ante prop. ab.
  24. HC = xe = xH habulims HE EG= KECIF,
  25. restant:
  26. op. 13.
  27. da = bc + af adde prop. 20.
  28. ubi idem aliter demonstratum, (insignicalculi
  29. confirmaine
  30. HEGt = XHEF. tangens in differentiam Tangentis dd semiusplementi et sius aequatur diffeentiae secantis et sunus
  31. Ergo ce. seu tangentes seincomplementi in tangentes vel tangentes complementi in
  32. complementi in tangentem semicomplement.1.
  33. c. ce = de- fe
  34. tt
  35. qu rconta)
  36. quadrabi
  37. A. 4. corill. 3.
  38. tangentes arcus dimidii pendent ext da seu alindra Aperbolic, velquadia.
  39. tura hyperbo circuli, con rocidectus
  40. (orll. 2. cumque A sit d+ e ete = d. sit d = c + e+ . 2cC.
  41. ideoque e seu summa Qvadratorum Tangentium
  42. semicomplementi, vel summa quadrata Tangentium
  43. a per crp 11.
  44. arcus dimidii ad basin pendent ex quadratura bo. Circuli, cunharda tysp
  45. He GF = KH EG seu sinus in diffcrentiam sinus e completmenti, et tangentio semicomplementi aequantur dise
  46. rentrae intersecantem et sinum complementi in tangentem semicomplementi, differentiam sinus et radii
  47. bof. be. = d - f5 a - h. = da + fb - db - sa :, b.
  48. = ZF (21) EN. ob Plum ENF in quo posita basi EN. altitudo est ZF posita basi EF altelydo est NI
  49. Ni
  50. AE rad
  51. ead. circerttyp.
  52. quadrat
  53. u hoeid
  54. A AR ANsinus
  55. AR. Ad. sui opsecans qui
  56. investiganda jam quantitas ipsius NI. Satet X1. parallelam AE. Ergu
  57. licios ut ante substituamus. At = d=b. seu Ni = 8a ba. Alqui g. a. Ergo M = a - ba - a- ba ()a- b
  58. Ergo cylinder tangentium semicomplementi, additis demis Ractangulis ex Tangentibus senicomplementi 1 et Tangenti
  59. applicatis semmparabolae axi paralletis, aequatur momentis differentiarum inter sinum, et radium utiue quadrabitibus. Nam
  60. posito sinu b et fradio a erit b applicata parabolee Circularis axi paralleta Quia Anus est media proportionatis inte
  61. applicalai parabolae sircularis, det radium. Pr parabola autem circularis est, cijus altitudo, et basis aequa
  62. cadde iussign. 41. F Aeda EI. e his focile haberi potest est enim A4 Hq f- a- + + 2b adde
  63. Tanus
  64. ACDF= AD EF cylinder tangeantis, nto (complementi) demto cylindio semiauu (conchocu fu diund cat ae
  65. condioen
  66. Inaps. 4n. c3.
  67. (complementi) = secans (compl) in Tungs. semiarcus (compl) seu Tongens + Tangis semiarus, in Tang. semiareu
  68. seu longens in lunu simiareus + Quadu Janus semiauu. Coroll.1 Ergo quadrata Tangentum seniamus pendent ex G vadratura
  69. oroll. 2 Cylender tangentium cplementi (quadrabilis) dento cyludios tangenttum semius plenem
  70. aequatur Tangentibus complementi in otangentes semicomplementi (id est intindio secantum complementi demto cytindro radu
  71. vdditis Quadratis tangentum semicomplementi (qua vndent ex Z. Euc. prop au q (mo ex peric. ht dineus. Tamus cyl. turg. semigat.)
  72. Conchocidis et Hyperbolae.
  73. Ca = EN. quia in Dlo AEC.. AC EN = AE ( = AC)Ca.
  74. AaC AN. Na. V At Nrmile Vlo VENA simile Ylo Aa C. quia add ha-ACve
  75. aequalia sunt EN = Ca, et AC= AE ergo et tertia seu Aa= A N. Egi Ea = AC
  76. portionis circuloris
  77. AMEC = AC EN. Chorda arcue in sipum complementi arcus dimidiis, aequatur cylindio sinuum arcusdati. vel. Chorda
  78. arius complementi ad quadrantem (non ad semicirculum) in sinum arcus dati= cylindio simmum complementi (quadrabiti)
  79. AD Ca = AC CD. Momentum Secantium complementi = cylindio tangentium complementi quadrabili. aode prop. 18:
  80. EC MF = EFEa, vel FAFC EG. Chada arcus dims in differentian secantus acus dimidii a siuu complementi
  81. dangentium
  82. De) semiareus in sinum complementi, seu moneulum sermarus
  83. arcus dimidii Tansenle arcus damidii in cinum versum arcus dati.
  84. radio in differentiam sujus, et tang. pu ia semiareu. Coroll. Tangens amicomplementi in sinum cyli radio
  85. Tancens aus dimisti (
  86. in sinus complementi, dento cylindio Tanus semiuspl. At per prop. 46 junct. 20. Cylinder Conthoeid - Cyl. Hyp. + had. in sing gpl.
  87. AD HZ. EFEEK = XZAC
  88. AE. Momientum Juns compl = Ratio in diff. rad. X sinus adve p. 47. cort et. Ain. H tanus gpl. in
  89. lonus. compl. in sin. Ergo res eodem redit
  90. Quadrg torad. in arcu prop. 50
  91. 152.
  92. semi
  93. prop. 47
  94. prop. 48.
  95. prop. g. Repetitio prop. 14.
  96. prop. 49.
  97. Per PH. da af.
  98. inuig ant
  99. ui
  100. prop. 54
  101. prop. 55
  102. prop. 5b
  103. prop 3
  104. prop.bo.
  105. prop. b1.
  106. E EN = NC (d CG) A
  107. sin quadruli

Cite

Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 232r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 44). https://leibnizlegible.com/page/00067993:0465?run=44