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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 336r

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: 0.71.

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. 337v); this page is its right half.

The machine reads it as

  1. Desideratur ut productum ex tribus xed, x X +b _ XtC, Xid
  2. aequetur quadrato: ratione apta t ad quadraturas, seu ad efficiendum,
  3. (DV+O13,
  4. habendum Sontb, XtC, XEd dx. sit ax = 6R et 40 + 9. V + qL V + e t2
  5. et O C quo 1H V + _130 146. et 8= CoV + (v mitio (S hores
  6. et (B5= 112o 4, + 53201852
  7. 01v.
  8. 2v
  9. at
  10. s
  11. sa
  12. 013o v 7b
  13. 0131VS
  14. 1
  15. 82
  16. 2AdVHts
  17. 241.1
  18. 19
  19. 10V + uV 2 = 20v + 21V.
  20. 1 =44 00 = = 36, oc = 2. (6. = 2. 20.31
  21. in proq
  22. ponen
  23. q0
  24. ibus vntantis omnibus ase
  25. (
  26. 230HSIV
  27. Ergo sp. 10. 11Z 10H. 3. Ergo 3 Si. H ut 30
  28. 4
  29. su t 3010 s ita 2 1 si.
  30. ALeOL
  31. At ∞Y = 11. 11 - ab = 4 31.3, - seu 11 = ad
  32. ergo finiet ab = ad conte Hypothesin pat
  33. quare six
  34. rem redinchoemus. Maneat aeg d, 255, 6,78
  35. fiet vol 10. .10. H O2 ab o1302, 19 o131. 1
  36. excit a sit G - 0 t Ex aq oriuntur aegus. coparititiae co12 12. 1514
  37. 00 = 40. 40 + 4130.10. 30= 50. 60 + 613010. 30 Ex aeqi9. omutur 15, 6, 17, 18, 9
  38. lle
  39. O1 = 2. 40. 41 + 4(30, 10,31 + 11. 30 = 2. b0 1 + 6130. 10. 31+11. 30
  40. 02= 41. 41 + 415. 11. 31 ~ (et 61. 61 + 6130. 11. 31 = b ad0+
  41. 01307 2. 40- 260 01 = 6 Ergo 60 Z e ar
  42. ab
  43. O130 = 240 430= 2. 006180enr
  44. 61 307 6120 = q0 4130): 60 = 41 (4170): 61
  45. O131 = 2. 41:4130 = 2. 61. 6130
  46. sadt
  47. 1=6
  48. 0131= 14 2 = 2. 616130
  49. (au d Mb:40
  50. (2l
  51. Ex 15 et 20 fil 40 + 4139, 10. 30= 60 = 40. 4136266 Ex i Ex 1 et 20 et 22. fiet similiter
  52. a1. 91 + 4135. 11. 31 - ab = 6860. g: 40 + 40. 1930. 11. 35.60- ad
  53. Et ex 16,20,22. fiet
  54. Ex ∞q. 23 fil 4130 1607 -40, 60:) v. 30. 60216. 30. 40= 60 60. 2 At ab. 60, :, 11. 31. 60 - 11. 31. 40
  55. 2. 40. 4 + 4138. (0. 3+11. 30 = 2. 60. 91:40 + 40. 430. 10 ur 11. 32 , perq
  56. 2
  57. quae aeq. 27, deponm habet communem divisom noratorum, et fit 60. - 40. 66, v. 31 = 604 - (. a 41 + ab. 5. 10. 30
  58. te
  59. mosex Ex 2b etiam fit 4136 60 2s10. 30. Eo ipsy es fil A 2 A. ( 2. 414 00 - 40 = 109 1r11 2060- 46
  60. seu 242. 10. 30. 41. 602 1031 + 11. 3, 40. seu 60 = (010.2 2 40. 1054 11 30. Ergo ex 2E et 31
  61. fit = 10. 31 + H1. 30:, 218 30 quod mihi suspectum. Ergo calculum osumemus
  62. qui s rectus, tantum opus est tolli 60 ex ag. 28. C1t
  63. axil = 00V + 0i v +0∞ v. + 013ov +013 N (h6
  64. abulad
  65. ld
  66. O6 = (8 + quqov tuo qiv + alsIV +Z Mor p n or Hit
  67. viro
  68. 0. 3 cum opus sit tantum ad
  69. (10) e (15)
  70. 435, 10. 30 +aigoiog + 4190 )1 31
  71. 00740 +4130. 10. 30 = 60+6,30. 10. 30
  72. ol J.1B 41, +13O10.3Ituso = 2. 60. 61 +613010. 31 + 1130
  73. o= 41 4128. 1. 3 ab= 61 + 6130. 11. 31 - ad
  74. 015o22, HX. 40 26130.60 E 6130 = 10., v. 30
  75. Q= ut 10 tantum pro charactenota 4 ( 013t 2. 4130. H2 2.6130.61
  76. va
  77. (9
  78. C2
  79. Ex aeq. 18 fit 6130 4130. 4: 60 Ex 19 fit 6130 = 4130. 41: 61. Ergo 43: 41 = 60: 61 seu 61 = 41. 60:40
  80. initio numeri ponendo (, ut pro. 430. 10, fict 613060.
  81. (
  82. Ex 15 per 20 fit 40 + 4130.10. 30 = 60 + 41,40. 560 10. 30) Gurpercont n, fit 45+ 4130. 1. 31 - pb= n. 60. 40 + 4130 41. 60 11. 31 - ad
  83. Et ex 16 per 2o 22 fit:, 2. 40. 41 + 4130. 10. 31+ p1. 30 = 2 2. 60. 41:40 + 4130. 40: ( 1031H11. 20 Follamu 4130, fit nod
  84. Exaequ. 3 3 sit A136 =63-40, 60,: 10. 101- 40 se 13d 6 Exaq. 24 b 41 b0- 40 + ab- ad 40. 11. 3160- 9
  85. seu ex depresfier fit 60-40 , 11. 31 50- 49, 41, 10. 30 + ab - ad 40. 10. 30. poroo ex 2b depos fit H3 - 60:, 1030
  86. Ergo exaeq. ed sit 24) ( ) p 21+12(C 4 2, 41, 60(60-40(60-40740, 10. 31 + 1139, 60: 10. 30
  87. cntus in aeq. 30 fult
  88. 41340 10. 31 f 11. 30,: 2. 10.30, quae aequatio vatis facit, pria
  89. falsus. Superest jam aeq. iqua moas substituatur vator ex ertirt os qu C 11 seu ( demes
  90. a
  91. sib o Co p 4) 60 40 + 40 ab- ad i1. 31,60- 40, 10. 36 m 18
  92. evanescente 60 fit
  93. 41parilfit (40) 1o sit11. 502165. 4d + 10. 40 (40, ab. ad 2 4. 10140, 1. 31 (1) 60-40 seu
  94. fit A 1 45 ab ad, : 66. gd q 1. so. nst pmu 1d uti si faciemus 1ontt So= v0go 1 31
  95. fierret e 0 4 2903040 rabuad: 100 et haberetur b0, sed 40 maneret
  96. arbitraria ubi tet 60 et 40 serve et respectu ab ad servare rasdem teres, ut si pro 60 substi-
  97. tuas 40, a et contra, et pro abs 60, a 40, abut 4b et ab substituas 60 et ad; et vicissim,
  98. re natio qa ante quod tamm non apunt unde uisa cluitus huc sutrecta
  99. ermem admillum in aeq 2C ubul scrintem eo 3 6o 1d cum sit scibendum. Unde jam 10. 3le11.30 = 1on1 + 11.3C
  100. revem esse
  101. +2, 10,70. 11. 31
  102. Ergo ex 33 per 34 fit 10.31 + 1130 =2103] 8130, 68.40 4.10. 307ab+ ad seu 10, 51 = 11.30,: 10.30 1, ab+ ad:, 60-48
  103. quae aequatio revela servat leges homoeoptotorum. Id est si permates 40 et b, cum 60 et _ d, nihil mutatur. quo in quo
  104. aliqua calculi comprobatio est
  105. sit 9120 40 2 + 53 O. 30. 203 =00 et sirv.m2t + 53E. 32= o2 + ac et s12B oatta. 2 53IS. 50. B
  106. 2.5120.5320.20 36130
  107. ja ingentat
  108. Pt
  109. et 201
  110. Habemus ergo 21 per
  111. et sO= 00, 0.co 3316 . 10 ortac uns -55ib t sit. 51 26 =-002 E1 +D taC. 30. 20, :, -10. 203(21 3a
  112. 2,5120, 5320 219131. Ex 42 et 43 fit 21. 2620131: 0130
  113. Et Ferruc. r, 3. D-00.1. 21 407 tac. 10. 203:, 9u2 2 - 30. 20. 11 21 F 10, 20. 31. 2
  114. c a stind Es. 1 idi v
  115. si explices
  116. p0. 11 714 or tac1o. 20 30. 21 + 31. 203 01. 30. 24, (10. 31 = H. 3
  117. er s ter ue ae
  118. u. 4+
  119. 31F
  120. i
  121. arte ie tie ti

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 336r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0667?run=74