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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 188r

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.

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. 189v); this page is its right half.

The machine reads it as

  1. Aequatio X ac. habet 4 radiies. Ae quatio
  2. Aequalia data X = = 13aX + 142 =() =0 habet 4 Radues. Assumatur
  3. alia X + 2I X +22aX + 2aa = (2) = quae habet tres radices, sed ex quibus una est
  4. communis priori, quaeritur 23 summa productum trium radicum, sed tate, ut, trilem modrum vadicum
  5. seu midorum quilins aequationi X salisfieri pt, ita, ut radix sit l 6q2 sit
  6. etiam radix aequationis 1. quod fieri pt quinque modis quaeritur jam quomodo
  7. E quot valores habeant 21, 2 2 21, et 22, summae et summae rectangulorum,
  8. positos inrectanguli seu producti vabrum summam, e et brrectansulorum et trirectam
  9. en lorum summam nihilo aequati seu in posito 23y 24 73 - E
  10. pro 23 substivebindo 23 y 13-y
  11. an
  12. Vic VVroendum quantum um
  13. ratione consequi liceat, aute calculum. Nume calcal pra quod puto
  14. quia et vs est generalis, eadem manente postertore aequa non videtur ze ferpo
  15. quanta sit aequ. 1. sed calculo Ut in aequa ostendit ostensum est si
  16. cqu. aequ. 1 sit primi vel idi gradus. vid. Act. Cips. ann. rdum
  17. in cta Erudit. Majo 1633.
  18. Sed nunc calculum, tentemus pro
  19. hollendis tibus aequ terminis, qui sunt omnes inter medii in aeq. eti
  20. gravy1.
  21. Acqu. 1 mult dicetur per for (3) mulam X+3IX+a et
  22. aequ. 2 maltiplicetur per for (4) mulam X + 41X + 42 aX + 430a et fiet
  23. X = X 13a X + 14aX
  24. 3I
  25. 3ea
  26. + 1331a.. +14. 31 a X
  27. aequ. (5) at
  28. X,uXaxtaaX
  29. +1. 32a.. +14. 32a
  30. +4 +271. . +2. Ma. +23. H aa XX
  31. 42a 1. 32. q aa .. + 23. 4243X
  32. E 43 4a.. + 21 43aa.. +22. 13a3.. + 23, 43a
  33. ita hos sex terminos compa-
  34. rando tollentur literae quinque
  35. nempe 31, 32; 41, 42, 43.
  36. et habebitur aequatio
  37. in qua solum erunt ontae
  38. quaesitae 21, 22, 23, cum
  39. as datis 13, 14
  40. 3(= 21+ 41 32 32a =, na + 21. 41, 1442 = 23, 43a) = 13 23 a - 17. 17 - n. 7. 1] - 123. 42
  41. 14 a (+ 13. 2i ead + 13. 41 a = 23. 41 a + 22. 42a _ 13, 21a, - 21. 23 a - 21. 22. 41 - 21. 21. 42
  42. imo cnorle
  43. 14. 21 a f 14. 41a + (13, 22 a,+ 13. 21. 41 + 13. 42 a = 23. 47a (F13. 22a7 22. 23. a - 22. 42. 41
  44. sed haec melius praestabuntur regula aliqui assignata Tollamus interm
  45. utcunque saltem ut aestimemus quadum
  46. 42 = 13 a + 21. 22 = 23 a g ( 41
  47. 42= Ex ida harum Rium fit
  48. + 14 ac + 21. 23a: 22a + 21. 21
  49. Exprinasil 42 = 14. 21 + 22. 23 41 + 1422 a + 13. 23a - 23. 23a, :, - 14 a - 21. 23
  50. (
  51. (127
  52. opendo 14. 21. 41 + 14 a 42 + 14. 22a = 0
  53. (30)
  54. 22. 41. 42
  55. 23. 23
  56. +13.a 41
  57. =23a
  58. +21. 22
  59. dua 4
  60. 1318 13.4
  61. 21. 2
  62. 1
  63. B. 2
  64. +21 2142 +itaa -
  65. - 22a
  66. (31
  67. 13a. 42
  68. 23a.
  69. S. si4. 1 7 14. 21 7 14aa7 12a
  70. 121. 233 22. 23) 21.235 21. 23a
  71. 23. 23 a
  72. (22
  73. 7 21. 23522. 23)
  74. =21. 23a
  75. (33
  76. q. 2ba = 0
  77. tereva
  78. 2. 2ha
  79. +,1 4. a 1 1422 a VB 1taa 212) +iua V E.na a qa Jia 36+18
  80. 121. 23.
  81. 13, 23 +4.3
  82. a aG)
  83. S-22af 21. 13.
  84. =(1q. a para atta 2 14aa 22
  85. 221. 23513. 23a(- 13a 23a (13. 2)
  86. 23. 23a) +21. 22, + 2. 2L
  87. 1514 21714. 217 21, 21 1 144a 114 4244 32
  88. 222. 13522235 22a521. 23a51321
  89. . . 22a ju. 2IIna 1a
  90. 2za sutra
  91. et 23532. 18c
  92. 1+. aX4, 2172t
  93. X2. 23) 2223 5. 22a f2t. 13a522C
  94. 17, 4a7 at. 2227 21. 21I 2t. 21) 13a
  95. 221. 2391
  96. vaS. nas23C
  97. +(4. a 1a 1
  98. La.130
  99. 1+ +7
  100. nat 52a
  101. 11. 41 + 10, 42 + 140
  102. copendio L
  103. ta) +. )2I.LIBa 14. 211
  104. 30. H. 42 + 323 3a
  105. 2141 + 20 42 + 22=0 314 12 =
  106. 41 = = 10. 42 - 12a, : 11
  107. 41 = - 20, 42 = 22a 3: 21
  108. +10. 21. 92 + 12. 21 a = 11. 20. 42 + 11. 22a
  109. 42 = _ 11. 22a = 12. 21a, :, 10. 21 - 11. 20
  110. 41 = 10. 22a - 1220a, :, 11. 20 - 10. 21
  111. Ergo
  112. 36,10. 2aB11. 1a F 10. Na 1. Na + 3ea 10. a 10. 21 - 0ma 11 20
  113. F1. 20a. 11. 22a = 12. 204. 12. 2a = 12. 20a. 1021 F 12. 30cL. 10. 20
  114. 33a, 18. 1 - 2.10. 11. 20.1+11.20
  115. 10. 12 3eu
  116. 31a, 11. 224. 10. 2] f 11. 2a . 11. 26
  117. +12.24. 10. 21 - 12. 2 a 112
  118. =0 3f 10. 11. 22. 22. 30aa treterrzona
  119. a n. Jira 13a 7
  120. a
  121. 2)17.L
  122. =10. 11. 21. 22 31aa - 10, 41. 20, 2232aa
  123. +10. 12, 21. 2),3, aa + 10, 12. 20. 203ca
  124. 411. 11. 20. 22 31 a4 + 10, 10. 21. 21. 32 a
  125. =11. 12. 20. 2131aa =10. 12. 20. E.375
  126. -10. 11. 2. 29. 33aa - 10. 11. 20. 21. 33 ac
  127. +10. 10. 21. 21 33aa + H1. 1. 30. 20. 33aa
  128. prss aaquo
  129. aqu. ex ag. D explicata
  130. sed si aeg. C explicete scribe
  131. vellemus plagula esset
  132. complenda, quod tans
  133. ncenti
  134. iprodeunt
  135. +10. 12, 21 22.30aa
  136. +11. 12, 20, 52. 30 ac
  137. = 12. 19. 21. 22. 8a0
  138. 2a
  139. f1. ta (1.19c2
  140. (22. 1343 33. 2301)+21.
  141. +2
  142. siea 212.
  143. l
  144. 2
  145. cnipiie
  146. es ues soastara ) iss ne dras
  147. n

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 188r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0375?run=74