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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 33r

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: 0.79.

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One image of two folio pages side by side, registered by the library under both labels (also fol. 34v); this page is its right half.

The machine reads it as

  1. Quaeritur p dx LCxx - bbD, Xx- cc pro dradratura conica Rationali
  2. sit x = f stv + aco = Ast compendio fiet XX, obb = a a N) - bbme, et Xx -cc = aa A,2- ee mei
  3. Be
  4. Ver+ V
  5. rabb, in ( -ec a A aa MA ep + Hbccpp, e
  6. aaCC
  7. ee
  8. Efficiendum est ut Numorator silere hujus valoris efi quem poductum habet sit extrasibilis
  9. Et primum fie videamus in possimus reddere ex rationalem deinde an extrahibilem
  10. (4frvaco +40fc3G (++V)
  11. +abbcc tv + 2p3) V
  12. Numerator explicatus ent B B a co +b aa sft vedco)
  13. +2fc Atv: n compendio ast + 3tv: eu
  14. bba ttob6bbcc
  15. +fFF∞ Faacoco
  16. Et explicando XX - bb = - lib t v - bb V
  17. = 2bb1 s+V
  18. +2afio stn,: n
  19. concendio a a + Hv: r
  20. quadvatice
  21. XX - cc = +ff + v +aacoco
  22. Efficiendum est ut productum ex ipsis ex - bb et AX- cc, habeat Numeratorem eus extra-
  23. - 2cc stv
  24. -cc tv = cc 24
  25. hibilem, uti denominator est extrahibilis. Et quo facilius obtineamus extrahibilitatem, tentemus
  26. an obtineri possit si faciamus hunc umeratorem rationalem, seu ut in producto evanescat
  27. irrationalitas. Qued ptaestabimus, si toefficientes partiun irrationaliu sit sibi
  28. ippositer ser silite. Pasu x atIp seu ase C (
  29. Exclerquea teductum ade b productum autem est, aa XB ac 5o3 tZ)tp + a 7 A1V. itaque
  30. Unde prodeunt
  31. +a 7
  32. uit tollatur irrationalis fidt fiat aa 3 + a Av ~ ag_ gH
  33. duae aegrationes aa a 3 = gs et 2a = -297, et produtum enit , aa- 4 3 ) t V
  34. ob a 3 = gse fiet (5f tv + aagi co) (8- a) = g (9b8 - ac) + v + 1p y)
  35. Eob a 1 = -92 fiit - afgeo + bbgs p = aa fco - ac P. per hanc aequatiorem fit 2p = afio (at): ste c
  36. Undo rx priore aequ. fiet fet ((9bs ace) + (a -g 5 tB = (g. aua
  37. (acC - gbb + (9 - a) ff) t V = ((a-9) au + aa f qusat 4) coco
  38. qu (9bb+ acc 4
  39. Sed non potest tv esse in ratione constante ad coco, quia n posito esse simplices,
  40. ut hic supponitur, forent etiam in ratione constante inter se, et Atv mutaretur
  41. in rationalem, quoad Variantes, quod non licet non succedere aliunde constat. imox fi constans
  42. Ergo si velimus tollere ration irrationale consi in producto altius assurgendum est,
  43. et Et cum productum sit ex a s +2d Atx in a3 +2 AV sit aa 5 H 477 = hG
  44. aa N1 + 4 2Y +v + Za N 7 A Fn, oportebit esse 7Z = - 5 Y
  45. et auiso ++
  46. compendio f f tV + aacoco vocetur aeg et L v - ip = aY, fiet ( tago - aaque lbY
  47. a S = aaqu bbr et a B = aaq = cer et fiet (aaq - cer) (afco - bb1) = -(aaq bbr) (afco - ce
  48. + 2a43
  49. seu fiet afBay = aabb. 1P9 - acc fcY + bbcc r Y - - a 7 co9 + aac clsq + abbfcor - bt cc 21
  50. fit anfbon uad t at r:
  51. n
  52. seu 2 a fcog f 2bbcer ip = aa (bb + C) 19 + a C bb + Cc) F cor et explicando
  53. 22ftva +2afco tbbC et vip - 2aabb cep = a bbtCC, afftvi + a cocoast- pu
  54. seu _ bb + cc (bb + CC) H 2bbCd) D WN + 2bbCC 13 + aa cocor =0
  55. (1bb + cc) af - 2 a 5) Co +B - 2 a25 c03 = af(lbt ce) c 1 1p
  56. aco - se si esset bbcc ad f ut f ad _ et (bb + CC) a5 - 2 bbCC ad (bb + CC) a f. - 2a, ut fad
  57. posset dividi haec squatio per fV - aco. Et foret. Ebbec = aaf seu +bc = af, sed rursus
  58. asbe
  59. ebb + ec a 2bC
  60. Daa (bbt ec) bc = 2635
  61. + (bb +cC) abc - 2bbcC a = (bb +CC) Abbcc: a = 2 VC: a
  62. et porendo b + esse et fieret a = bb ce er posito + ~ + sit a qu( ba C) = a bc, a a (bb+CC) - 2bb cc
  63. Cui aequationi satisfit porendo aa = be, fieret enim aa qu (b -c) = BC qu (b = c) seu an = bc- Unde
  64. ta. Et divide Ent erguus 2bbcc = 2af = df = ga seu 9 - 2bb, 2a35, : f- a = 2a -2a, a (1.)
  65. 2 aa far s) ( F C0) F (bb +c - 2bc) ap ) txer dividerdo totum per co, fut
  66. = 2a Et Ablu CC - 2bcb a a = h(a - si) fit h = 2 qu b -c,: a- 5
  67. vioeo re non bene sucredere, sive enm ponas f= a, sive = - a non potest in omnibus tribus
  68. 2 (bb. + cc - 2bc)
  69. termlnis quaesitum obtineri, ut sinunt sit divisio ubique fieri possit per +co, aliculi eum fet
  70. sit f- - a fete
  71. (bl + cc) Wo
  72. _ a purci) a teset
  73. quoo si non succedit haec depressio, dificls s vix est ut spetari
  74. per e+ lo, aliti per _- co
  75. possitus rem praestari posse. Habemus prostandam unem aequationem 3ti gradus
  76. et irrationalem tollendam, et unam oti ob iationales habenq antem
  77. junde sunt aequationes destractititiae +g = C, h sunt anteque assumtae
  78. emnt E, isco, B. E
  79. C v L, B, e, c0, et ob ti tundi grades, rurtus, es hn 10. bue 1
  80. explican per B, p lossuntem
  81. uo
  82. aa 52+ 4 7 Av
  83. Aatai 7C
  84. a 2B
  85. a 2b +a
  86. aa utac rad + 2ab
  87. F + bd + cd
  88. 19 - co 1 _coro
  89. Aat C)Co
  90. cop +

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 33r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0065?run=74