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Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 69v

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: 0.81.

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One image of two folio pages side by side, registered by the library under both labels (also fol. 68r); this page is its left half.

The machine reads it as

  1. Quemlibet jam valrem ipsius 513: 113 repertum in 8gy. 13 et 14, articuli 18
  2. aequabimus valori invento aequatione 16 articuli 14. Et similiter quem libet vactorem ipsius
  3. fient aegq. (1) et (2) articuli hujus. Unde so ex quibus consequitur aequatio qu (3) hujus quae oritur ipsos
  4. duos valoris in aequ. 13 et c4 articuli (8 aequando inter se. Et a similiter quemlibet valorem apsius
  5. 713: 113 repertum in ag9. 11 et 12 articuli 18 aequabimus valori invento aequatione 6 articuli 15 fient
  6. 094. (4) et (5) articnti hujus. Ex quibus consequitur, aequ. (6) hujus articuli, quae oitur ipsos duosvalores
  7. in aeqq. 11 et 12 articuli 18 aequando interse.. Et has 6 aequatiomes distincte scuibtre supersedeo prate
  8. 3 et b. ubi videndum an non compendia prodeant Nempe ae
  9. 0 aeq. (3) R. 1123. M (23. 513. 312.712 7 17 2. 112. 512.323. 723 + 7112. 7123 (112. 523. 312. 723 + 123. 512 . 523. 712)
  10. C15) 1723, 118. 512 323. 723B1 712. 123.522. 312. 712 1712. 1723 (112. 523, 323. 712, f 123. 312. 312. 723)
  11. et -71 23 + 1723 2) = 1212 - 71 et
  12. sed ex aeq. 8 articuli 16 est 112 Si2. 323. 723 = 133.523. 312.712
  13. et -1712. 1723 f 7112. 7123(2L - bis 12+512, 323+713, 123+523, 31 2 F 7 (2
  14. lurgo ex aequ. 3 sic explicata
  15. 1234523, 3121712 1124512, 323+723
  16. Lit ) 12. 513. 312. 712 + ()12, 512. 317. 723 = (2) (1124 51, 323 +123 4. 123+ 51Z, 312+712) (112.523. 312. 723 = 123. 512. 323. 712) ̀ qu. 0
  17. Et pari jure ex aequatione 6 explicat a debet oriri aeq. (11.) nitilo differens ab aequ. 10. sola permutatione
  18. +523, 312 +712
  19. 112+512, 923+723
  20. inter 1 et 5 cum 3 et 7 in notis initialibus, sed ita pulchre evenit ut aequ. 11 et aeg. 10 coincidant
  21. quoniam aequ. 10. eodem se modo habet ad 1 et 5 Ut ad 3 et 7. Unde cum aeq. 3 resultans ex 1 et 2 idem
  22. Det quod aeq. 6 resultans ex 3 et 4. consequitur aega 1 et 2 itemque 3 et 4, revera non tam pro quatuor
  23. quam pro tribus aequationibus esse habendas. Unde ex his 4 aequationibus possent excerpi decussatim duae
  24. ex 1 et 2 aiticuli hujus
  25. et eis conjungi aequalio 10. commode, etiam sic procedere licebit, ut loco aio psiqus 713: 313 per valorem
  26. excerpendae, consideremus dividamus ex vt a si C D. S. sIE S valorem primum
  27. aequationes 13 Ipsius 513: 113 ut fiat ceq (12) hic, et nursus ax artic. 18 dividamus valorem aequationis 12 ipsius 713: 313 per
  28. valorem aequationis 14 ipsius 513: 13 ut fiat aequ. (1) hic. nempe rursqualor novo ipsiq. 13. 7B3; E3 Hos duos valores
  29. sed aequando cum velore ipsius
  30. aequando inter se fieret (15) quae tamen videndum an non redeat ad aeq. 10. hicjuse
  31. 113. 713, :, 513. 313, ducto ext 17 aiticuli 14 et ex ag. 6 articuli 15. habebimus aegq. (17) et (18) hujus ita
  32. aeq. 15 non coincidit cum ae. 10, poterimus conjungere 494. 10, 17, 18 onquam sufficientes ad omna determinanta
  33. videndum tamen an non ex i’et 2, itemque 3 et 4 huju non possit fieri aliquid simplicius quam aequ. 19, 17, 18. imo
  34. re considerata apparet nit posse fieri melius; ob aequ. 8t articuli 16 nobis profuturam. Nempe dividento aequa per aeq
  35. 112 (2) 2123. 112a723 = 2112. 123.712. sed per aequ. 8 articuli 16
  36. fit 112.723, 1,523. 312 = (1440) 123. 712 :, 512. 323 = (1gno) 17. 55. 18t ex aequ. 12 Denominator voloris
  37. ati aequ 1 articuli 18 per q aequ. 13 ejusdem fit
  38. 2. 323,512
  39. scribi poterit 7123. 112. 129 (53 : 17) - 7112. 123. 712 (53.17). Ergo jam praeclaro tam exitu evanescit numerator aequationis 2
  40. de primitu denominatorem, et it
  41. tos
  42. jam ex articulis
  43. = (17mo) 171= (pero, 31 1d. 727. a qua
  44. Et ex equ Himc itaque aequ. 15 est denitica nec quicquam faci
  45. (12. 123. (12523 +23512)537(12723 - 23712) 12723. 23(12
  46. (312), 323. (12723 +23712), 15 (12523 - 23512)12523. 23518
  47. 523. (312
  48. =15. 4) 12523: 112 (21mo) et 223 = (3724) 127235, 3 12 et ex eq. 17
  49. articuli 14 e st 523f
  50. qu. 9 112. 127232373 : 312. 12515. 15
  51. unde ex aequ. 17 tandem fiet
  52. 123. 312 (12323+29512) (12723 - 2512) 12523. 23712 = (2284) 112. 323 (12723+ 22712, 1252. 22512) 12723. 23512
  53. non differt aqu. (18.
  54. 723: 523=
  55. je, aequatis cum aeq. 17 articuli +4, et aequ. 6. articuli 16 oriendis, et fiet - 7123. 342. 523 +7112. 323. 512,:, 12. 323-
  56. +2251Z ubc Ro esta
  57. 1712. 123. 312 = (1mo) (51. 13 L) - 15. a () 12523 - 23512 (12519 - 13512) 2, 12. 123, 12 315G
  58. ubi pro 523 et 512 substituendo valores (15: a) 12523: 112, et - (151a) 23512: 1237
  59. ex aequ 1 fie 2 00 equ,
  60. + 7123. 123. 312. 12523 4712. 112. 323, 23548 (2 3t0) 12523. 23512 (12532 23512)
  61. + et stiuendo 3 et 7 fet 12523 + 23512,, quas Aegq. 23 et 4 seponamus et
  62. deu 12. 1C13 (21 2523 = 123 23712, :, 323. 385 1 at a qull ent Eili s egrienti dug +123 s
  63. (2sto
  64. ex t. eZ isto B523. 21712,: 52723 23512. 12724
  65. (113523 + 235I2 C, 127 (3- 23712
  66. under rereausi
  67. seu 12523+23512, :, 12623- 235(22
  68. 223+ 23712, :, 12725= 23712
  69. 12628 a Eeden
  70. 2tme ) 7123. 112. 323. 12) 23 - 7112- 132. 312. 23713
  71. fiet: 7129. 123. 312- 1252547412. 112. 34. 23512
  72. 23. 112. 323 - 1712. 123. 312
  73. et27 437(2, 1725. 13. 3M - 1112. 1123 13
  74. Ar9. H nug un r f1235 17 27r2 eq
  75. 12727 Toestuendo ubique 1igi B3, fiet
  76. (1251 1 (23312), inum n +
  77. manenim
  78. 12523. 23712 171t
  79. a
  80. =(272 (23712
  81. seu 2Z. hur. 25 S12. 1371 = seu 13 1s 23 f 1
  82. vel Yi
  83. 1 (sis)
  84. L 112. 92. 232 17
  85. 11 123- 23512 X a) : 123 3. 112. 123 + 1252 65. a),: 112
  86. H SI ZBa 127L3 323. 37
  87. 312+712, 1323+723 = 312. 32 a -23712 15 (2. 375:, 31 4 5 a t. 725. 313.37
  88. f312 a, 112. 285(2. 12723, 123 (312) 12523. 23712 HE 2572 (3123h.1. X35IX. 12723 :, (31da. 15. 312. 12525 2p112 + 1272 3. 52 57. 113(19 1251G X(112. 112. 1 2512. 12713
  89. Sen f 12. ct. 128. 12. 14523 ~ 3B12. tereBESI 2 M. 31. 2s En A has EsuIE.n reS. HE. Msi. AEYEa H 12. 128. 37 ag 3 3sr2. 1425. 23 2
  90. teur
  91. 351323A2 nSL3. 12723
  92. ed per aeq. 25 323 = + 123. 3(2. 12523, 23712, 7 12. 23512, 12713 quo subst luto sit 312. 123 a. 12523. 23712= 112. 312. 25715. 23M. 12723. 37: eue qo
  93. 512. 712 A seu
  94. 2a = 2351R: 112. 15,:, 112. 12Bat 125 . 123. 15B L 11I 45I2,: 11345,8
  95. 3. 212. 723 + 13. (512. 323. 712 = lis 112. 723 + 123. 712 (Exl ergo (29no) al sernetrum geluditur s15pE. 22712 + 21512. L2p.
  96. 12322(127~). 712
  97. pr anenter
  98. ulbamus et p2At 13 + CB in eadem eu. 10 funt jam 112 = 31Y. 120 1E. a et 523 (1 ee. 12) is. a aambus
  99. 19.7 123. (31: 4) 237122. 313
  100. eL:, 12s u Zmmnunrhtn us. 2n
  101. es + in as seufps)Binm cm
  102. Ear. 12725 = (ob 25 hic) 4 12. 922. 12725d. 12523. (237 12 = 4 12523.
  103. 12 magu
  104. m 2
  105. Nunc superest ut coy. 10 evolvatur, et ut alterutra 23 vit 24, sola. Et pringum pro aqu. 10 tollamus 512, 523,
  106. 53. 2 et ibi habebimus inter alia +13 Z
  107. et 712 = 65: a) 2351 enfunde 123. (12712
  108. 2.73 1(2 (37. a) 127237312
  109. qq. 23 et 24, et ope aeq 2b
  110. 2
  111. utAI. . 2IEy B 22. 1
  112. 351226s tuendo valaem ex aequ. 25
  113. unde ubi pro 3F 123. 312
  114. 173812. 23512
  115. qu. 25. fdebuis et jam institur articulo ficerente post 6 post eg. 8.
  116. 723+ 23712
  117. 123, 711
  118. 27iZ. 112. 93 1212 _ -2112. 15. 3I2. 23718 1ngrg. 23712 (12733 -25712) Se Redeamus jam ex aeq. 22. proqua consideremusquod
  119. 1723. 112. 323 = 1712, 123. 312, hujus
  120. fed ex aeg. 14 hic pe
  121. 112. 323
  122. placet tamen ad huc a actu ipso exhibere aequ. 1. hujus articuli quoniam hactemis quator aequ. ex . 11. 12, 13 articali
  123. fiet: n seu
  124. ipusa
  125. 113(713, : 95B. 313 = (20mo) = 17: 52 vel distinctius 113.713, .9 513 315= e3. 5o C. nisi a alitums ipsum paatmerato rem
  126. 13. 712 7112. 42. 723, ubi in dem de nominatore rursus ob a9. 14. 15 pro 512. 323 ponendo
  127. ex aequ. 12 fit
  128. 123. 712 (53: 17), et pro 523. 312 poneldo
  129. et

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 69v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068255:0138?run=74