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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 75r

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: 0.78.

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The same scan as fol. 76v (00068196:0152), where its text is given.

The machine reads it as

  1. resolvendae
  2. 11Y
  3. 200 troZ + 20 q a 0
  4. dio ie
  5. 100l + 101Z + 101 lv + n2ol dZ 1 102l dv
  6. nodaque 0 per lmin, p addamus in unum fat fit aeq. 5.
  7. 202 ddv
  8. 200m +2omZ +201mV +22m 7 +202 m dv
  9. dioon Fdnoq + dtnV + yon du ton d + 1on ddque + 1o2nda
  10. dnon dZ do2n de
  11. 42oo pa ducop Z Fdrospo + 210p AZ + 2oip do + 220 p dz F 202p ddr
  12. Aerop sqZue idrorp dr
  13. t ooah + 310fzue 1301 fV + 320F dZ Y302 fdv
  14. =dyogz + 13o1gP+ 310g 4Z 1 201gdv +320gdZ + 302g dav
  15. aequatio tractabilis)
  16. Assumatur jam fO + gdO tah = (6 - 0
  17. et sit = 310Z + 301V + 320 dZ + 302 dv
  18. fet de (8 L d3oZ F d3o,. B + 31dz +. 30. de +3rodtqe Bodar
  19. fiet eg. 9. tractabilis
  20. identificentur jam aequationes C et . Utetiam ipsa N95 fiat tractabilis
  21. Habetur h per terminos absolutos aequatos
  22. Aequandli daque et ddo coefficientes habemus n etpperus
  23. (10) 202. 920 - 220. 202
  24. fit p = 3209 -120n, : 220 = 302,g - 201n, : 202, quos duos valores aequando fit 2c2. 329 - 202. 129 = 290. 3 org - 220 0 2, adeoqe N = 20 170- 210107
  25. dgrogaqe +d3olgd
  26. quo valore ipsius n substituto in prie valore ipsius B, fiet p = (202. 120. 320g 2 1907. 3209(- 202. 320. 1209 + 220. 302. 1209,: (202. 120, 220. 102)20
  27. enim _ p = 102. 320 = 120. 302gquod non diffeit a priore, nisi
  28. 102. 120 - 120. 20X mutationesignorum umeratoris simul et nocaleris
  29. e
  30. permutando 10. et 200) ex M fier
  31. Compendu 1eq. 1B t communis denominator, 120. 202 = 102. 220 sit = 13 = D0. 1002 fit 1 2 L . 3o- 20. 10g et p = noqua tor e9
  32. inde eodem
  33. modo
  34. 110- 0 t -1000Y
  35. 120. 202 - 102. 220
  36. eodem modo 3015 + hoju -dioin - droip = 17 = 00t et ob Z, fiat nol + 20m = x 18 = oor et ob fiet 101l + 20im = 19
  37. quo supra invenimus n et p, invenus l et m, et et el pro 120; 22D, FD 102, 202, ndo 3 20), 302n, B, fit
  38. 101. 20
  39. 201. 110 - 21010, = t M = 10. 201-101,210
  40. et compendio sit 110. 201 - 101. 210 = 22 =00.2001, fiet 1 = 23 = 201 Y - 210t, : 2001 et m = 24 = 110t -101Y, : 2001
  41. superest ub aequemus oefficientes ipsius dz, et coefficientes ipsius av. ubi compendii causa fiat 10 +d120 = 25 = 1120 2+ + 220 = 6 - 2120 101 + dp.A. = 27 - 1210 201 4 42od - 18 -240
  42. et jur I +dhon g - 1210n = 2210p = 30 = 00 . Ergo obdue fili2oltiom = atgult2oem = voV
  43. 1002
  44. paeterea fiat compendio 320f + (310 + 4320) 9 - 1120n - 2120p = 29 - 004
  45. Quos duos valores ipsius l exaeqa 23 et 35, et ipsius m ex aegg. 24 et 36 aequando fit 201. 1002 Y - 210. 1002 H= 202. 2001-220. 2001Y u0 10ort - 101.1002 A ho. 2001 102 2001 8
  46. 120. 202 - 102. 22
  47. 1B. 202- 102. 220
  48. 110, 290, Y, 101, 201
  49. ubi numeri sunt dati sed literae debent explicari Quae libet harum quatuor literalum novissimarum continet n et p, quorum valores supra inventi continent 320 et 302 incognitas
  50. Unde rur sus habemus l et m, pro
  51. sed non continent 310 et 301. itaque si ad calculum absolvendum sufficerent hae binae, pro duabus 849. 37 et 38, non opus foret devenire ad explicationem num seu valores lite
  52. rarum n et B. itaque majoris comprndii causa, in aeqg. 16, 17, 29, 30, faciamus dion + d 2op 00 β, t _oin + d20ip = 00V et 120n + 2120p 00R et 12on + 2410p = 00 p
  53. Et ita jam explicando Y, t, 8, V in aequ. norissimis 3738, ope aeqq. 16, 17, 29, 30, et 39, 40, 41, 42, fint ex aq. 37. sequens aequatio 43. et ex aeg. 38 sequens aequatio 4
  54. 1002. 201. 310f + 1002. 201 d3109 = 1002. 201. 00B =1002. 210. 301F- 1002. 210. d3019 + 1002. 210. 0072 2001. 208. 3205. +2001202517209- 2001. 28 00-200+2 20. 3 12 f. 2001.20 39 . 00 n
  55. 1092. 110. 3015 + 1002. 110. d3o1g = 1002. 118. ∞) - 1002. 101. 310 f = 1002.101 d3199 + 1002. 101. 00 so = 2001. 120. 3025. + 2011 1205, 701 (9-2av1. 129, eo p- 2007 1 1 2. 30 f 2ogi. 12 f. 1. 9 420o1. 104 0 9
  56. troons BA
  57. Quarum duarum aegg. novissimarum, ope invenire oportet 210 et 301 possunt autem haebines aequaliones ad majus compendii redigi, compendiote comprehue
  58. omnia, in quibus abest 310 et 301, si hae binae literae incognitae suffictunt, quod tentabimus. In aequ. 43 fint: 1002. 201 0β3 vor. 210 vol 4 2001. or rof t 3roy). 1001. Wul eot. 2em. la ro
  59. Undi ex ceq. 43, fit (1002. 201 f- 2dol. 2029) 310 + 1002 1019 d310 400 1. hrog - 1002. 20 f )301 - 100 2. 219, 1301 p0 ili aivor map Meni te e 2e t. pe a i ut 4 20or 100 t 2 1 a
  60. A
  61. Unde exaequa fit. (200. 1079 -1002 101F) 310 1002. 1019 d310 + (1002. 10 f - 2001. 1209) 301. 4. 1002. 110y d 30, 007 V
  62. Videamus jam an ex his duabas aequationibus una componi possit, in qua absit tam sot, dat tam d301, quam 301, ita ut supersint solum 310 et d310.
  63. ita enim habebitur solutio desiderata. Nempe aeq. 4b et aeg. 4 dividatur quaevis per coefficientem ipsius 3ot nempe multiplicetur aequ. 4b per 10 et 48 per 2∞
  64. et de inde in unum addantur ita ev anescente d301, per se, superest, ut evanescat 301, fieri X (10, 220. 21I - p20. 410)9 +610.210 - 110. 20)51002 f = 0
  65. Itaque reen tentenus aliter coua ex aeggu. 46 et 48 facere tractabilem multiplicvndo ibam per b, hanc per c et dende
  66. Sed hoc non licet, quia ita eo unisuit s. g, et urire aeqvatio in datis
  67. Comporendo et efficiento ut coefficientes ipsius d310, et 4301 sint aequales, et ipsius 310 et 301 sint etiam inter se aequales iun
  68. enim aequationem fier tiae stabilem alibi ostensum 3t. Et fiet (2ag 12 ) b Evrofc
  69. (1002) 201 (9b = 1002, 101GC = (1002 2109b + (1002) 11oGC et ubi cum evane seat g, habetur ratio b: c
  70. Eiquemus jam et coefficientes ipsorum 310, et 301, fiet
  71. 1 corf 1002fab - 101C) + 20019 (102C - 2026) ) 1002 f(110C - 206) + 20019 (220b - 120 c). Ubi loco b et c substituamus
  72. Nam fit C: b = et = 210 + 201,: 110 + 104
  73. quae ipsis proportione respondent e et fet 1002f (1 29(F 10I. 201 = 101. 210= 101. 201)) + 2009 (02 20 (t o2 roL 10 2o2 (101 20D) = teoz ff2o. 2, 9ruo 20s = 110. B 14. 200,
  74. 1019 (110. 220 + 1. 210 - n0. 10 - 1 20201)
  75. cesse copstantes, se
  76. itaque faciamus non quidem coefficientes ipsorum du dio ut dio
  77. tu t a eorb or:; 40b + WoC = ( 13. 1
  78. m 2 + 13. 201:, 12. 10 4 12. 101 L et in aequ 50
  79. sed ita cum utrotius destinatur f, ehunescit etiam, 9
  80. pro C et b, substitcamus proportionales fiet 12. 1002f (2a 3. 12tC) 1 12. 20079 (102. C - 20 6) = 13, 1002 f. (11oc - 210b) + 13. 20079 (220b = 120C)
  81. 3 HC
  82. in fiet
  83. Eatob
  84. ay + Y = 0 quae rebditur
  85. 12tb tote
  86. tequatio 49 ex 46 et 48 (piost multiplicationem pe respecive per b et C) compositis formata, compendio scribatur fin im 3Id + n 301 + p d310 + 4 3 ee t h = (aB..
  87. 2e:
  88. ee
  89. 3P1 - 181. 1.
  90. naaum ntculi instituto inveni enveni prodire et in datis efficiendo mpZ n. mg - np. = gdp - pdque si jam ratio p ad 4 fiat constans, se veluti 9-
  91. his positis reperi posse tractabilem, seu aequationem istam aequivalere huic sd + ndB + Y. si fat O = E310 + A 301
  92. = 12p dp: B3, seu tandem 12m = 13n C et 13 12 p = 3
  93. 2 12p: 13
  94. quod epistemcis in
  95. 100if (. 110. 201 ( 13. 101. 208 - 12. 210.104 (B 201. 10r)
  96. quod tentemus efficere in aequation qs, composita ex aejus 46 et a8 Ept autem m = ex 5eg. 4b multiplicata per b et 48 multiplicata per C, eritu
  97. 9- voeg Eferne F. anf 210
  98. s et mp. n 12p: (3 = np = 12dp 113 er ( 12 p dp. 13
  99. m = 1002f (201 b - 10iC) + 200) (102C - 202b) n = 1002f, (10c - 210b) + 2009 ( 20b - 120C) p = 10029, 201 f. 101c 9- lvorg,
  100. -= 12. 201 +1, 210,:, 12. 101 413,110
  101. super est jam al faciamus 12M = B3n
  102. -1 20. 11
  103. 1002. 1f (C (01. 12. 4091 201. 1, 1. D =101. 12 201 -101. 15. v0) + 2 0v1. 129 (102. 12. 201 + 102. 13. 210 - 202. 12. 181 - 202. 13. 10) = 1av2 1f(no. 12 o (+V0. 17 9 210. 12101 f21O. Iu 10)) 12os. 3 (ervo 11 .
  104. Ergo si 12p = 139 fiet 12. 201b = 12. 101C = 13. 10C - 13. 210b seu c
  105. enimus proportio
  106. et in valoribus m et n, pro b et c, substituamus quantitates quas mv
  107. Fietque
  108. itaquex solis 310 et 3oc rem consequi non licet, sed adhibere postet adhuc 3 320 et 302. Itaque redeundum est ad aequa 43, 44 ibius explicant (), A, er
  109. sed video ne hoc quidem prodosse, et similiter eancdestiniae f, unde et evanescit
  110. 1do2
  111. Et 00B = D d1o1. 202. 320 = d 101. 220. 302 + d201. 120. 302 - a 201, 102.320, : 00. 1002. Compendio sit 120 d 201 - 2e0d 101 2dD, et
  112. d0p. 302-20d1.3le: 00. 1002, et 90d = 1129. 202320-1120. 220, 302 +2120. 120. 302 - 2120. 102.320,:00. 1002. compendis sit H20. 202- 21208
  113. per 39, 40, _1, e2, et per 14, 15, fint 00 β -7 d10. 202. 320 - di10. 220302 + d2go. 120. 302 - duo. 102. 320, : 00. 100
  114. . 2 20. 320 2020. 302: 00. 1002. 5t 00 s=, 1219. 22. 320 -mo. n2o So2 + 2210. 120. 12 - 2210. 102320, : v0 10o2. Compendio til 1210. 202 - 2210. 102=- o2so, et uo tuo. 121a no = 201
  115. 001002
  116. 29 + 100 2. 201. 10d2. 302 = 1002. 2001. 202. dyrog F1 2v2. 2001. 2w d3 029 = 0
  117. et fier 00n O210. 320 = 2010. 30∞: 00. 1002. H. jamvalores inventi ipsorum β8, γ, A, e substituantur in ae q9. 43 et 44
  118. 8.
  119. et fier s e
  120. der 22o = 10d2302,
  121. et 103 1701 2o d101 =od1 et fiei Y
  122. + 1120. 290 = 2120. 120 2020 et fiet
  123. et ex aeq 13. fist 1002 (1o2 201 f - 2001. 2∞ 9) 310 + 100n Vo2 10N 7 1310. + 10ve ( a mrogu 301u ar a E. veg 13a=
  124. 410c
  125. L200i
  126. 2001. 202, 202036.
  127. e ex aj. 44 fiil 1002 (2vo1 1029 - 1002. 1015) 310D 1 ver. 10l9 d 310 +1002, 00 2. 105 ,30j u 21uc2. 10, l341 +1 col. 1. 2081. 715) - 1092. 110
  128. 2ool. 120
  129. 510. 310 t 5o1 d310 + 520BBI Hor. d 3e1 . a5 30. 320 fs_3 d920 +5 ∞. 202 1504 d3o L
  130. (10. 310 + 601 43, 0 4+6i0. 301 +602 1701 + 827. 320. 603 432 +640. 302
  131. et 301 = 21320122302
  132. 30. 90,320 +50300d320 +540. 00. 302 +504.00 dse
  133. at in +501. 12 ..
  134. 502. d22.
  135. 2
  136. +
  137. 502. 2.
  138. +604 dy 23
  139. et in aq G Huimus 510.H.
  140. vates, ut haten
  141. pestinestin
  142. Q tor roq ivrdvus -Morar reci tvoiseo
  143. 630. 00. 320 +6038320 +640. 8.302 +00t. 00. d3026
  144. 610. 1.1
  145. 601 di ...
  146. 120. 2
  147. ot du.
  148. quatinae ripnict
  149. 4 10
  150. 11.
  151. 601.11...
  152. 602. 4...
  153. finni ras coefficientis est
  154. lieis olsitns
  155. o u ton
  156. Ex org er iomprdu fint
  157. 15964 fint
  158. 5ol. di . . 4301. 11
  159. L a2
  160. 502. 27
  161. onanus ce ad ad siat S . E puirae fl 1542
  162. pic
  163. susiee pana ia
  164. 1 310 p. 320 + 12. 302
  165. 6o. oo
  166. 210. 3og + 2og1. 20. 2010. 3
  167. 1201d8. 3c03
  168. o ec aiio
  169. 50i deZi 601. _ ... -0
  170. 6or 822 . 602.22..
  171. multiplicotur aerg. 68 per 60
  172. im ab abtera tollendr eomnesce
  173. teram aeguatua
  174. 43e0 in aeq. prod
  175. s 40. 001 510 m2 25odi d d2 C, . A40. v0 + 610. 12H Bo,
  176. 604. 00 +bd1 12 ++ 60Z. 22 Py 5oq. 00 +5o1. 12 + 502. 2
  177. sien bor. (526-50) = 50r (62o. 602) s
  178. ane alipel
  179. o1. 12
  180. C+C
  181. lio
  182. ide dir. 2 0) (
  183. enr ood oor ieu) (.
  184. ior vornog
  185. neu roeta et ratebitur ita 320, Ergo et 302)

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 75r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0149?run=74