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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 194r

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: 0.86.

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The machine reads it as

  1. 10X + 11 =0 20X + 2120 10. 21 - 11. 20270
  2. 20X + 2IX+ 32 =0 41B2IX L10.220 Ex 5 et 2.
  3. equa nova
  4. 11. 20X
  5. fit (ut ex + et 3 fit ceq 3 nem pe in 3 pro tC, ponendo 10. 21 - 11.
  6. et pro Et pontior 110. 22, et sicC: 10l 21. 21 = H. 10.3 10 20. 2
  7. Ex 5 et Y fit aeq. nova ut ex 2 10.20. 22,
  8. e in 3 pro 20721, ponendo 10. 21 -11. 20, et 10. 22
  9. et ex aeq. 3. sit 10. 10. 22 - 10. 11. 21 = 11. 11. 2015
  10. 20X + 2 X + 21 X + 23 =0. Unde ex 2et L. f1 + 1O. 2IX 4I0. VX H 10. 2
  11. X + 21 =0 tollendo fit:
  12. 20)X+ 2IX + 2240
  13. 1Ct equ. 1 aequ. 2 dat
  14. reg
  15. (SH 1 X + 12 seu X + 1222
  16. tx 22
  17. H-2
  18. Ergo ex aequa 3 (per 6 po 2t ponendo) 2. 22 121
  19. fit. 13. E X
  20. IaX +H o ax+o
  21. fite Ex 8 et 1. sit ceq. nova, ut ex 4 et 1. fit 6. Et in 6 pro (10 X + 11X + 12 = 0 20x + 21 = 0. multiplicetur aeq. 2 per
  22. 11. 20.
  23. 20, 21, 22, ponendo 10. 21 - 11. 20, 10. 22, 10. 23 fit
  24. inde ex 6 fiet 10. 10. 10. 23 7010. 11. 22 + 10. 11. 11. 21 - 11. 11. 11. 20
  25. C1) et
  26. 10X et aequ. 1 per - 20, et producta invicem addendofiet
  27. +102IX
  28. ita s ( detur 10X + 11 =0 et 20X + 21X + UX+ 3Y14 -11. 20X - 12. 20
  29. fiet 10.24 - 10, 1. 23 + 10. 11. 22 - 10. 113 21 + 11320 =0
  30. Et ita porro in reliquis
  31. Aliter ex + HX + 12 o 2X F uXFLE8
  32. plicando pr crucem per. 10 et 20, fit 410. 21 X 4 102
  33. aliter multiplicando per crucem ner 12-22, fie
  34. divisip omnibus pex post additionem, fiet: Al3. 20X + 13. 21 =0
  35. = 10. 22X - 11. 22
  36. et conjungendo 6 et 7. pro aeq (10, (2) 1). 2d =0 fiet alia, si pro
  37. on e cun
  38. si pro (10)
  39. 20)
  40. poratur
  41. (21)
  42. ponatur + 10. 21- 11. 20 10.22 -12.20 12.20-1022 12. 21 - 11. 32
  43. unde fit 20 = (11) et pro (10) 61) - (11) (29, fiet:
  44. = 10. 12. 21. 21 - 10. 11. 21. 22 - 11. 12. 20. 21 4 11. 11. 20. 22
  45. + 10. 10, 22. 22 -,, 10, 12. 20. 22 = 12. 12. 20.20
  46. qui calculus est memorabilis, quia procedit sinem
  47. omni destructione.
  48. Sit 1023+ uX 4 12X + 1320 20X + 2X +X + 23 270
  49. multiplian rucem fiet
  50. + 11. 20 X f12. 20X F 132
  51. Multiplicando in crucem per =Het zo. Multiplicando in Erucem per +3
  52. fit +HI. 20X F 12. 30X +13. 20
  53. = 10. 2 = 10. 22 - 10.23
  54. fit: - 10. 23X = _ 23X - 12, 23 (4
  55. +13. 20. + 13.21. + 13. 22
  56. unde ex aequ. 8 calculi proxime anterioris ses nova
  57. (11)
  58. (22)
  59. (12)
  60. (20)
  61. (217
  62. ponati 11. 20-10. 2. 1220 -1012 1320.10. 23 = 1023,1, 2 =71. 231,3. 2 =13. 23+13. 22
  63. Si pro (10)
  64. ubi vursus coincidunt 2 (12) et (20), ut paulo aute 11 et 20
  65. Leges combinationum: si duae sint aequationes secundum
  66. quarum ope tolli debeat x, una dimensionum a, altera
  67. dimensionum b. Necesse est in nova aequatione
  68. ipsa litera X carente, coefficientes aequationis dimensionum a
  69. ascendere singulas ad dim. b. et contra. 2 coefficientes
  70. ordine sumti retrorsum, eodem modo se habent, ut coeffici
  71. entes ordine sumti prorsum. Sen quod idem est si coeffi-
  72. cientes invertantur dro a substituendo L, illi in horum
  73. locum succedunt et ricissim: 3. quaelibet ex coeffi-
  74. cienlibus aeqvationis giic dimensionum a significeta
  75. B (item b) significet = a ( - b) reliquis
  76. literis significantibus 1. aequatio neva in qua tollitur
  77. Sublata est X, sedet sic explicuta succedet. Ratio
  78. est, quia sic sulcedunt aequationes datae, penindo X = 1
  79. Ergo succedet etiam ex ipsis derivata 4. Quodvis
  80. membrum constat est dimensionum a a +b.
  81. et summa ciphrarum dextrarum facit ab. sic si
  82. in aeq. ex AB 10X + UX etc = 0 et 20X + 21X et = 0
  83. 0
  84. rursus in ultplicetur aeg. 2 per
  85. 10, 21 - 11. 20 et aeq. 3 per
  86. -20 et fiet:
  87. (0. 21. 21 - 11. 20, 21 + 12. 20.2040
  88. es dimentionum 5, et summae b, nam 10323 seu 10, 10, 10. 23. 23
  89. dat summ. 0+0+0+3+3 id est 6, et 10. 12. 22 dasum
  90. 20X + 21X + 2220 multiplicando pencrucem
  91. jnvicem addendo, fit +10. 21 X + 10.22= jam
  92. ope aeq. 1 et 6, fit aeq. in qua absit x ut ex aeg. 1.
  93. substituemus 10. 21 - 11. 20) et pro 21 subistituemus 18. 22- 12. 20
  94. et exaeq. 4si et+ 10. 19. 13. 22. 22 - CB2, 10, 10. 12. 20. 22+, 1212. 20
  95. = 10. 10. 11 21. 22 + 1.X 10 11. 1220.21
  96. ∞ 10. 11. 11. 20. 22 = 11. 11. 12 20. 20)1
  97. . + 18. 10. 12. 2p. 29 -. (2.)10. 11. 12. 20. 21851 9
  98. et divisis omnihus per 10, fit tandem aequatio (s)
  99. (10. 10. 22. 22.5-10. 11. 21.22 9.f. 21, 11. 220.12,=0
  100. 12, 12, 20. 20 l = 12 1 21,20
  101. 10. 12. 21. 21
  102. seu ordtuando 10. 276- 10. 11. 21. 22 + 1 20, 22
  103. 2. 10. 12. 20. 22. Groba: d 4
  104. sit 10 X + 11X + 12 = 0
  105. (2)
  106. 2.19. 12. 20 22 = 11. 12. 21. 20
  107. ponendo 10.2 - 14 20 10. 22. 120, 10. 23
  108. calculi
  109. Itaque ex ag. 8. fit
  110. in nova aequ. 10 ascende
  111. combinationes possibiles. ita quidem ut mumirum habeat
  112. at productores ex aeq. dimensionum a, et contra. Summa
  113. id dim. 3, et 20 ad dim.
  114. naecidentis fit
  115. 10.0+ 12323 oto 1. 1 12 20234 10. 10. 1212. 2C. 20
  116. 1B. 112 12. 20,20 2. 10 11 1912. 2021 1 ( 10. 12. 13, 21. 21
  117. 10-10.10. 10. 23. 23
  118. 1o 13. 12, 12. 21. 21. = (2)16.11. 12, 12. 20. 2 (+ 11. 11. 12. 12. 20. 20
  119. 10. 10. 10. 12. 22 2L - 2. 18.10. 12. 1220, 22 + 112. 12. 12. 20. 20
  120. = 10: 10, 10. 11. 21. 27 + (. 1. 10. 11: 12. 20. 23
  121. = +0. 10. 11. 12. 21. 32 (+, 10, 11. 12. 12. 20. 2V 418. 11. 11. 12,,20. 22
  122. redditur dimensionum ratio redditur ex eo quia aliotivi in vgq.
  123. (I1. 11. 12. 12.20. 20)
  124. 10. 1c. 11. 11. 21. 23 = 10. H. V. 11. 20.23
  125. Et odinando
  126. 10. 23 ∞ 10. 11. 22. 23 B +10. 11. H. 2. 23. F 11. 11 12. 2022
  127. - 2.102,12. 21. 23 0. + 510. 11. 12. 20.23 =11. 13.12. 27
  128. + 102, 12. 22. 22
  129. 10 = 10. 11. 12. 21. 22 412. 1252. 36 1
  130. . - 8, 10. 12. 12. 20, 22
  131. 12, 11. 21. 20 8 = 2. 12, 10, 22. 20 12, 10.31. 21 12. 51. 11. 22. 20
  132. + 3. 12. 11. 10. 28, 20 manet, teu si ibisi respondet. Nemper
  133. duabus datis, adeoque nec in datis servarentur s homogeneorum
  134. tet 2 sequuntur
  135. a = 11. 11. 11. 2022
  136. 4(0. 12. 12. 21. 21
  137. Examen antistrophes coefficientium ex Lege=
  138. pro 10. 11. 12. ) 29, 21. 2223 debent prodire idem quod nunc
  139. 23, 22. 21. 2
  140. Notavimus duobus punctis membra sibimes avr, S pEFOYTa.
  141. (+ 18. 23
  142. 1132122) + 1∞. 20
  143. autem seu valor dimensionum manebit a+b. cujus valoris rutio
  144. 22 F1X. 20
  145. et 20X + 21X + 22X + 23 =0
  146. ∞10. 21 X + 1022X + 10. 23 =0
  147. - 11. 20 X = 1X20 X Cu
  148. pro (20)
  149. (2)
  150. +10. 18. 12. 29, 23 +2. 10. 10. 11. 12. 20. 23
  151. 2. F 3. dmonda est rufg 6.
  152. Et secundum hanc legem fiunt omnes nembrorum
  153. = 11. 20X = 12. 2C
  154. et 2 tacta fuit aeq. 4 et in aeg. 4 pro 20,
  155. O =
  156. Nola suendi ommia - 1. Acepto 1- - 2 et 20- - 3 + D Bg 3
  157. nata cum a sit 2 et b sit 3, fiet a +b, 5 et ab, 6.
  158. ideo ni membrum quo dlibet ut 10325 vel 10. 12 20. 21
  159. seu DtX R 10. 12. 12. 22 dat summ.
  160. Et excrac lege 4 Hic exglicata pce
  161. 5. Lex Signorum + 10) -1
  162. (3)
  163. musti- aeq. 5 per 10, et aeq. 1 per - 20 et producta
  164. 20
  165. O3
  166. po
  167. coordinemus et secundum hanc legem
  168. (-10. 11. 23,22
  169. (+ 10. 11. 23, 21
  170. l- 127. 1 20.21 l+ 1R. 112 20. 22
  171. (-2. 10. 12. 25. 20 + 3. 10.11. 12. 20. 23
  172. l- 212.10. 20. 22 O
  173. 10.12. 22.22 = 10. 11. 12. 2. 27
  174. l + 12.10. 21. 21
  175. - 113, 20. 23
  176. absunt combinationes: 10. 152. 22 113. 21. 22
  177. 2. 112. 21.
  178. perinde est igitur ac si adesse ponerentur
  179. praefixo signor dient ia sividi alliqus posse 12
  180. posseper 2
  181. ratio h23 Ssi sepriui a t reiqueque p racius 20=0+
  182. fiet. 123. 20, 10. 123 = 2 124020.70 detent
  183. 12 H20.2t omnia
  184. Hinc excluduntur obinades, in qua situnt ab sunt 12 et 23
  185. vel in qua simul absunt 10 et eo, sigua autem et
  186. numeri praefixi utique ut in calcalo praecedent
  187. Hinc ex
  188. rcte
  189. peurmut
  190. d novus, supplendo tamen eos in qurs
  191. X + 2. 21 X + 21, 2
  192. + 1. HtrX t H. 21
  193. + 12
  194. stre a

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 194r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0387?run=74