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Leibniz-Handschriften zur Mathematik LH 35, 3 A 7, fol. 19r

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: 0.75.

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. 11v); this page is its right half.

The machine reads it as

  1. Xego l+m An+p seu xaequ sl.
  2. Zagusium co aequilump XGx agosi
  3. X Xcos NcEX
  4. X aequ sI + 3 2y seu sU aequ X- 2y
  5. X 1
  6. s
  7. XHaego S1 + sem + 2yX. sm aego st S ImX= S3Z Eigo Sl’ago X - 3y x + 3Z
  8. Al(. X - 3yX ∞t ZX aequ s. 13 X aego l + Sem Agist + y X ryy lmusen). Py atae
  9. sOu fiet H12 aqu xy axZ X- aX+ 4XZ + 2yy - c0
  10. Nys E
  11. X - + Xsy + 4xx Z+ Exyy xconqus l X equ (+ SLm aego Sl 4 yX 3yyX + 3y ( lmu
  12. =la ZXX + 293 + 4tam CoXcoseu ((’ago X, (RY +5X2 Spyyr5xco- 1yZ
  13. Egquordine ila scribemus
  14. Si aequ x
  15. SH, aequ X? - 2y
  16. SI aequ X - 3Xy + 3Z
  17. Lx. Exy ipp. 7py GXyE
  18. 2y. 93
  19. ubicunque divensio parcum (. 10) imper ibi estsi sun
  20. cydoisibilis per aliquem divisore ago ex 1- 1 - 1. erit 3 aequ. 2 et Zoqu ∞ erco vy 1
  21. oner
  22. X. y. Z per sestante, (quacunque potentia faciumt 1. )ota ut sunt + 3XG + 4Z - 3Xco et
  23. eis ducta sistent quadmlice faciunt respondentim ipsis Axt Exerc
  24. dulm sin numeri, si cubice triptum Excepto casu
  25. Ml aqu g. sim aego fh Simn aequ h C Immp aeqo. h s12 rego X - 4Xy 14XZ + 19y o
  26. tro duo aeque in seimice, ita sunt 29G- 5y2+9yco etc respor
  27. ducto, quocus nemut duplu dentua ipsis 2yy. 5 XyX 9 X y
  28. posito laego abc n aequ abd n aequ acd paequ bcd et n 714 ∞ 50 sl aequ X - 5X y + 5K Z + sXyy.5 Aco = 5 yZ quadratne quo casu faciunt duplus lalsar. (ut oxrgus qui. hypt
  29. (16 aequ X -6Xy +bX ZY9X9 -6Xc0 -6xyZ- 29 4322 +6yc0
  30. 362Sl aequX - 7Xyt7X Z 114X9 = 7X C0 - 7 X9Z - 7Xy +7X Z + 7XyCORY E. 10
  31. si cubice sriplum dereliqua
  32. quum tabu numerorum vidi exqua plura pysteria
  33. pum havulam cenima dixerimae
  34. ere orseries observantu
  35. ciuntuilla
  36. 4X, quia
  37. et
  38. + dup
  39. sac +
  40. u
  41. quos duos valores ipsius (Imins conferendo habebitur fIma sed per aequationem s aequx. 9X y +9X +27 Xy- 9X co- ga -36Xyr18X(19Y710∞Y1 (. 7acotg hxy9X )
  42. hox 25 Xtqe
  43. 1
  44. Nota omnes quae afficiuntur numero sui gradus crescunt authmetice, ut
  45. differentiae ipsam
  46. 12 5 X7 210
  47. 6yco. ergo procedit 7 Xyco. 8x yco et.
  48. ryy Nyy Xes ea ipsae Y. Xy Xy Xy et. similiter in aliis 24
  49. aliae secus ubique progossiones recte et fransolisie
  50. _ quadr 51 aequ sl +2sl m. Ergo 25 (2M ego (X -BX + 8X
  51. (4Xyf 8XcL 1bXy 67X7
  52. 16X 4Xg0. + q (1 Z yZ 67X70. + a-1bj 1 468
  53. ut
  55. Ego fiet ((m aequ. - 1aX yZ + 12 Xylo + 4 X2 + 4X5Z 12 ∞co + y- 47c0 +6c0 omittipt
  56. sit aequatu pax + bX + CX + d aequia et X + x pX + qX +r aequ. 0
  57. hy Ex antentur (ax bx + exX + dx (ax X - aqx - ar aequ.0
  58. ine
  59. 8xE
  60. 2+2traoqus 1 (=8X Z 20Xy (t 8X2 ( + 3X, 2 16Xyf 12XZ gxy cdf 9Xy 2+ 8 c 2y87 co) Bs qo
  61. (abX + bb X + cbx +db (= abx acxx - adx + ar aequ.
  62. + ap +aqX
  63. 162
  64. libx + b X+ bd bbX B cbX- d alx + BX clxudl Pab B acbe albxr ad
  65. (+ a bb X + aba + ad bx (= abb X ) PBVBX ∞∞ ~C bBX =d bb
  66. = ap
  67. = ad X + aer X
  68. +aeq X
  69. + ac
  70. 4b ac
  71. + ap = b aep.
  72. +C ac
  73. C ap
  74. +d ac
  75. - c ap
  76. sit A3 aequ. X - 3xy 42Z. jam Es( m aeq q I3 = (1 et fiet
  77. 2l’m aqu. B-6~d (+6 ∞Z (9
  78. X6 D 26X Z- gXy 46 XyZ 2G - 33
  79. t ck 3b 18ky 9
  80. seu ((3nB aequ y - 6xyZ + 322
  81. 729
  82. 1457
  83. 891
  84. V. (1)
  85. agig
  86. aequitio data X - pX +q aequio etfiat
  87. Paequ hy. seu y aego p. 3 et ge quaequ 3Z- S seu 654
  88. seu (l aequ 37- 4 aqu N fiet: 12 gaqu ∞ pu et m aequ p. 17 - 2pZX + 3GZ unde (+54
  89. tollendo X ope duarum aequationum etH1 et 2. utique (13m ascerderet ad cubum
  90. verum quia S( aequ 3Z- 9 et quadr. (l aequ. s10 - E(Vm3. ideo fiet:
  91. (977 - 629 + 99 aequ x - Z X P + 6 x Z a X p = -. 2 pZX - 2 p. 27 (324) = 3 12M
  92. videamus ergo an ope aequatinum 1. 2. 3., habet tolli possit sublata X
  93. haberi possit ralis valor ipsius (BmZ qui non assurgat ultra qua
  94. grationalis, vel saltem daon assurren ultra pecidentia Golidentunus quadratum
  95. licet e ex duabus aequ. so et 2. sequatur aeque 3. unde (Bm non
  96. quoritur ansaltem possit deprimi ex aquia est X aequi
  97. aequatio autem 3 per
  98. 1ne per compendium vocetur v. s erit Xaequ, P: 27+ 322 - v , . 2pZ
  99. pt omnimm tolli
  100. X+KX +IX L x + n ay. 0
  101. pendiam semtatur X6 + + X + L X + MX + n Bl unde ex aequ. 1 et 3. fiet
  102. ruusus ex et fiet: _ +K X = CxX + mX +n Eeq. o Uade ex 1 et 5.fiet + lxx + mX +n aqu v
  103. ph.
  104. + ph
  105. =quX -ot
  106. qui
  107. +pp
  108. unde ec 6 et 1. fier: 3 i XX L ux )
  109. E
  110. =cohx
  111. ix
  112. dub indeca Bet 2. fet
  113. +pkx 774
  114. ntt ah tP. Cg pp X e H dE+ quti + qup. Cpte pp
  115. guia tam in quaud xG
  116. quiae tam in quam xytinent v ascenec ad gladu veratum
  117. y aequslm.
  118. rac + -1.
  119. 1-
  120. ++
  121. -
  122. 7
  123. openon
  124. ean
  125. 3.9270
  126. 243
  127. (9
  128. c.
  129. =7. T2g
  130. r
  131. = 102
  132. qu. 91H

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 7, fol. 19r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068220:0037?run=74