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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 175r

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 machine reads it as

  1. b, yre
  2. (20)
  3. Et his vec-
  4. si vellimus facereagu bu= quadrato, possumus fucere nu - qra
  5. et ytb, ote etiam aq. csto unde necesse cnt vel yb, et ytc a quodlibet singulatiu
  6. aequari quadrato sivel unum quodque aequari quato facto ex quadrato proprio, in formulam communem
  7. Ad hibetimus etiam Ldlm et Lrl. Xon et txem. X.n.
  8. yel sit 10, _Am sit 20, et nen sit 30; et similes quantitates per x et Cognit simplices per X, conti–
  9. undum e
  10. Eateris sit jam lay = 12 so 20 + 113 f10. 30 + 123 + 20.30 + 10vea () et quadrando fiet = a r esse roigna
  11. 18o 100. a a
  12. di
  13. 212 f10. 20 + 213 sio. 30 + 223 120. 30 + 200
  14. = 2.30. 113. 123 110. 20
  15. 1. 123 s10. 30
  16. o
  17. . 212. 212. 10.20 4 2.30. 213. 223 11020
  18. ad. 22. 207
  19. 6. E. 2
  20. oei a ins ad 3+ b.
  21. Odate
  22. erit y+b, ytc quadratus, si
  23. Eme
  24. neta esit it compendii causa
  25. neunt literae sequentes, ita pro 1120X + 1121 per compendium scribamus net, atque ita in
  26. et a, (5t) 112 112. 10. 20
  27. . 122
  28. 2
  29. simplicis, sed gradus compositi, ut O et )
  30. 10. 3c
  31. es 93. et itn yse qudut)
  32. Pieid , e eodem modo grlv)= OBa+ DBC: 5D
  33. G: DD. ubi 6 et e sint gradus
  34. quaelibet autem it t nota , 6, 8, 8, etc. continet
  35. formulam quam ingrediuntur h0. 20, to s10. 30. +20.30. It ex 7 et 9 fiet 00a + DD 588 et
  36. 30a + DDc = 88 88f
  37. pro a inaeq. u vel1r scubemus E, fiet Dh + 33b= 58 et
  38. eodem modo et ex 12 fiet OOh + DDc= 28.
  39. Ventamus jam ad aequ. 1. actu ipso exhibendam, ut quia pari jure et modo deinde procedi poterit
  40. cum aequ. 12. sit
  41. fit 65 312o. 3120. 10. 20
  42. 0. 3C
  43. 3230. 3130. 20. 30
  44. 300.300. a a
  45. (13tro) 6 = 312H0. 20 = 313 1o.3o + 323.120. 30 + 3000a ergi quadiundo
  46. + -303130.3230. 58. h0: 20
  47. 2
  48. 323 110. 30
  49. 0
  50. et (15to) 8 = 412 ho.20 L 413 Y1030+ 423 12a30 + 400 a
  51. sed quid id prolixius fortasse sufficiet facere (3to) tay.
  52. (5t) Z = 1.22
  53. 90.20
  54. unde feri test ex i15 fieri potest 568. quod
  55. comparabile cum 03h + DDb g ap. 31.
  56. 112 10. 20 + 13 A2o 3 a = (41) 3a et fiet
  57. 21 110.30 + 200a
  58. = (610) 3B. et quia (3mo) yrb- deo vb.
  59. et (8V0) ytc = Odh + DDC,: DD et multiplicando yt b per yte fiec gG+by + bc = B (6t) OYhh + 00DD hb + D bC: 5+
  60. et debet fieri quadratus numerator fieri quadratus, ita tamen ne sit b = c
  61. It C 4 -
  62. + 1234 30. 30. 20. 20 hh
  63. 6. 112. 125. 10. 30. 20 hh
  64. LM
  65. bc3 = 2137. 10. 10. 30. 30 bc
  66. 2007 at
  67. 4200. 213. 10. 30 bc
  68. h(b11) OD, 12. 21710. 2030
  69. 123
  70. 123. 4330. 20.10 F h ete)
  71. 112.200. 1026aa
  72. 123, 200.30. 20 aa
  73. 4. 112. 123 2l5. 200. 10 20309)
  74. a
  75. 4. 112. 1233.3020 hh .. . . .
  76. 4. 215. 20ca lo. 30 b. (10. 30
  77. 4. 213. 202 bc
  78. 2.112. 213. 20410. 20,
  79. 2. 112. 13. 200aa 28)
  80. jam exts erit
  81. 99 = 112. 112. 10. 20 = 2. 112. 123. 20 s10. 30
  82. 3D = 213. 213.1030 +2. 213. 200a L10. 30
  83. 200. 200. aa
  84. 1 pro 10n 20. 30 scribatur rectus
  85. =. SIto a 4. + si to 30
  86. 2. 125. 213. 2ma. 30. 20 y hBrc) 10. 2
  87. 2. 112.123. 213. 102430
  88. 173, 123. 30. 20
  89. 2. 42. 51 110.30
  90. 112C, 31 ut appa
  91. appareat esse grad
  92. Si 112 vel similes sint constantes su 5 sint 120 seu contineant X. assurgetur in Memoro ratio-
  93. 42. 42.
  94. nali ad gradio X unde comparatitiae aequationes 5, et in irrationalis vefficiente ad gradum
  95. S1. 51. 10-30
  96. X, unde compantitae 4, summa 9. literae assumtitia, in A2 sunt 3, in st sunt 2 in 10, 20, 30
  97. erunt 3, ex 112. 123; 213; 200 sient saltem 3 summa 11 vel si velunque negligere
  98. apsas 112, 123; 213, 2 lanqua aequales unilati, licebit in ipsis 10;20; 30 assumdre 6 arbitrartas
  99. et fient itidem H quod posterius est maxime spendiosum
  100. sed cum haec sic sulis sunt prolixa, redeamus ad Methodum magis anclyticam
  101. et videamus primum un liceat d0h + DDC aequari quadrato ege et facierans
  102. OTh + D L -c in OTh - D t -c = 9Ze sit e = 159. et faciemus C th + D sc = GH et
  103. similiter O s D L.c = 8 Lg. Ergo O Mo + D F C. 5) = O M: 9) - D A c.9) sed ita O et D datio ict abe
  104. sit O = n2 tro. c0 + 43 troo + 1y t20. 30 + 100 et D = 212 toro + 217 l1o. 304 223 fro30 + 200,
  105. fiet ac th. s) F 212 H c: 5) = v2 sib: 9) 2n H(c. 9) seu 212 = 12 (. 9) = H h. 5)): ( f(. c. 5) H c.g
  106. Ergo altius assurgendum Non ergo licet ODh + dDC aequare quadrato, si tam O quam e sint
  107. ssimplicia. sint jam ambo composita et fiat 00 (C) (D) h + D D (2) (D) C = quadiato P2 (2) (8) 1sg, et
  108. fiet OD) th + D() S.c in 0) O (0) Ih - D () L.c = G (9) 1g
  109. ubi ob ratione
  110. jam dictam non licet facere O(D) th + 3() tc = ipsi C (0) th = D() LC multiplicato per datam
  111. itaque oportet O(1) Th. +D(D) S.c aequari quadrator ia ob ambiguitatem simul utrique salisfilet.
  112. quadratum sit popq f. veniendum jam ad explicationem ipsorum O, D, (0), 6 4. sit
  113. O = i Sio.ro a 113 sio. 3o + ag 120 30 + 100 a C(O) m. 2n 10 h6. 13 er. 30 0. 20
  114. (C) 2n...
  115. (1 op
  116. 2
  117. 313
  118. 323
  119. 623.:
  120. 523
  121. Contrahendi calculi cousa forte licebit facere 1
  122. 113, 213, 3(3, 613, 100, 20d, Loo 600; Si 513
  123. 0
  124. 3) = 6u..... 6
  125. 500.40 +513 l1830
  126. demva
  127. 00a
  128. e
  129. vinque
  130. V. 10
  131. 123.0ode.
  132. 100
  133. as 104
  134. idem calculis institmetur,
  135. pro 1, 2d, potis v, 21. 31
  136. 13. 213 1
  137. an 1020 + in v3 20 l l. 1 3
  138. 123,. 223. 302D h
  139. ien oret 3. 6o.
  140. IH - S13 512. 316 + 2 513 costet sia30
  141. 500. 500. q
  142. 513. 512. 1s
  143. 313. 613. -C500, 500 15
  144. M au et X on. mp) S I
  145. 123. 23 . (ih 313 biy (1 1. C 2.500. 500. H sf
  146. 1it n h 3 3 135
  147. 8
  148. 3b = L 131
  149. unius et secund
  150. X; et pro _2 et
  151. et similes potest
  152. scribi 1120. quia
  153. possunt intelligi
  154. gradus uleius.
  155. Hoc, et pro 1t ponatur 1, et
  156. pro Gs ponatur (G) et pro 500. 40, 2
  157. ponatur 100, 80, 81
  158. +
  159. ng
  160. pu
  161. mm iol eoi
  162. aota in duta tete quroa e ti ti an tatre siili t ab dproc
  163. cea
  164. 123212. 21 Th 323. 612. 21 Y.C
  165. 175 C2. 813. 00 quos
  166. equationes oparatitio 20
  167. num
  168. a2 lo2 2 B 20
  169. atere
  170. 123. EE1b 523.612= 55

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 175r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0349?run=74