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Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 73r

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: 0.76.

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One image of two folio pages side by side, registered by the library under both labels (also fol. 64v); this page is its right half.

The machine reads it as

  1. id cnfendo aequabiones 4 et s articuli 8, eum aequationibus 7 et 8 arti culi 7. habetur
  2. quaedam depcressio. Nempe multiplicetur aequatio 7 per 4, et 8 per s, fiet ex priori
  3. multiplicatione Sircgl. 31213. 5123,:, 7121, 3. 14213. 7,223 = 51224 (112+ S12) : 712253(32+7,2). Sed hrl: 1113 -521
  4. et ita in pluribus. Ergo fit: Sin13: 71213 = (1mo) 11223 (112+512) : 31223 (3121712). Et ex posteriore mulbiplicatione nempe y8 per
  5. Cq.5. fit 523131. 32313. 51223,:, 723133. 12913. 71223 = 51an 1 (123+525), : 412233 (33+723) unde factis destructionibus
  6. fiet : 52313372313 = (2d0) 112 23 (1234523): 3129 (323+723). Eropa harum aequasionum 1 et2 articuli praesentis, Et
  7. ex aeqque 4 et sarticuli praecedentis fiet 3ng. Im t) li13 . 31213 = (3tio) Si2e3 (312+ 712) :72 .3 (112 + 112) et
  8. Et eodem modo labebita
  9. 12313 = 32913 =51223 (323+713): 71223 (123+523). His igitur quatuor aequationibus continentur inventae jam
  10. 10) Tollamus jam earum opelitums 113, S1g, 213, 21B. idem Explicanto pa quae pertinent ad 113
  11. relationes determinatarum. Comprudio pro aeq. 1. serilamus sirs M. Explicemus
  12. non sertinent; ex equi fiet _ st nSt, :, 3ec. 73= 313. 712
  13. seu 12 S3a 113 Sisa ex aeq. 1 fit H~ Seza - 13. ra 3rETIZ. NeL 213 112. 7512
  14. Ex aq sit (200) insua- IB 503a L 313. (13.752 313. 72525. Et (x ag. 3. (C
  15. et (3to) _2 Osa + 1c3. Sra= 312 713. 5712 + 313 712 5712 Et ex q. 4fit (4to)123 sisa tnSga 32 5xyf 313 Y. 57
  16. F112. SB = WX3(A1I. Sez = 51223 et ita porto SuE siiis. at . m. jujis a seinvilem agg 3 et fieta Auferatur etiam aequ. 1. ab aq. 3 fit V13 sua ( m9 (71 Y51)S3 +(BHCE 11)313. 712
  17. s
  18. et auteratur postremo aequ. 2 ab eg. 4 fit 2. U3 523
  19. 3 l 73 In 313 EX ex aeq. 2
  20. t (2d0) 123. 3s. siz - 523. 3323. 118 - 303. 11237 13 713A 313. Et ex a42 ft (otro ) 1. 712. 51g + S12 mu s3 B3,2 MM2 1 X2 31, 3
  21. e.772.535B13. Proquibus
  22. A 7 M. VE S1 Sir. 33i2 114 reC m. 313, preoite sit bmo) 15. 13F1. 513 4 13513 + H. 713 L0,
  23. Et ex eg 4 fit (4to) 123. 7123. 51 n a
  24. 3F 2L53 + 13. 313 + 24. 713 =0 et tib) 31. 715 +32. 813 4 53. 313 + 34.713- 0et(4to)9 1tyr 2B3+43831 17B
  25. jam earum ese liter 113, 513, 313, 7 13. Et ideo in aegq. 123, 4 articuli praecedentis
  26. Ex Ya 1Daexplicemus terminos ubi 13, compeudiole exprimemus as rubi non est 13. fit (1mo) H12. 513 G2. 1iga =
  27. Z 312 IN 21 M. 13I 4 1312. 312. 73 -1312. 712. 313 et Bdo 1∞ 1235Ba-523. 113a= 132932713-1325. 33. 313
  28. et (3tio) 112. 513 a + G12. 113a =, s3I2 12 Sg. 5712. 317,71345712. 712.313. E(1) 123. 513a 4 523. 1134 =5733,323713+5723. 73,313
  29. Ex 1 et 3 addendo fit 2. 112. 513 d= (1313+ 571 e (2 (+ 13n)7B+ (+ 512 1312)712. 313. Et subtra
  30. fet ((10), 1a 3 fil 2512. 113a = (64) (5712- 1312) 312.713 4 (571241312)712. 313. Et ex 2 ct 4 fi( ad
  31. 2.123.513a (5723+1323) 323. 713 4 (5723 - 1323) X23. 313. Et gubtrahendo 2 a 4 fil 2. 523. Ha =(657 23-1323 )123. 713 H(51234323) 725. 313.
  32. ubi unde ex aequis et 7 fit (5712+ 1312). 123. 312. 713 4 (5712- 1312) 123.712. 313 = (9no) 5723 + 1323) 112.323.713+ (5725.1324)112.723. 313
  33. Unde fiet (1b ino) (1323 - 5723) 112. 723 - (1312∞ 5712) 123. 712( 6., ((13224, 5723) 42. 323 - (1312157 12) 123 31 = 713: 313
  34. Et ex ggg. et 8 6 et 8 fit (712 - 13n) 523. 312. 7(34 (5712F1312) 523.71. 315 (5725, 1323)512. 323. 71345723+ 123)512.723.313
  35. se unde fie (12mo) (1323+9723) 512. 723 -(1312+5712)523. I,: (1323-5723) e2 313 - (13. 2 5 n2)523312 = 713: 313
  36. iea unde semiliter pro 1312 et semilibus ponendo i habetur 513. 313. Et notaridum ut ex duobus valoribu ipsi rviin
  37. 513: 313 fieri novam Ane 2. 13
  38. 1+ sed fortusse brevique propedilicebit, refinendo H3I et similes, nempe ex articuli 9 aequat nbus 1,23, 4
  39. sis set 13a i fima) 1 Et B1. S et S23Ca = r 1325. 113B et tu) Mra = 571 3113 et dem
  40. Ato) 1231hA 5729. 32313. E 9. sed ex articuli 10 aequatio 1,r 3, 4 alies fabrica vimus vable
  41. D et d destructis jam irrationalibus in Aquatione articuli restat sequeas aequatio
  42. 12 2. smepsues Gt4
  43. mm
  44. , 1323. 11213 -51223. 512B3 - (a + b( lan)(a- lisl- n
  45. 123. S12. IIZ. 1121y12313. - 123. 322. L12a. 12313. 123137
  46. Btam abL bm = Lametbl = (M2. 523+ 13, 4) (In 527 11 4. 51) (1. - insns
  47. 2 112. 512. 118. 529 4 2. H2. 512. 173. 513 == 2. 112.512. 12313. Ergo coefficiens ipsiu ev
  48. est - 112. SiZ. 11213, 12313 et coefficiens ipsius ZZ est - 125. 5233 12313. 11213
  49. ipsius vZ duo quae per L conpanximus, sunt 10213o 12313. 11225
  50. jam in coefficiente
  51. Ex reliquis tubus nemeris
  52. doefficientis il si22(II2. 512. S1323I + 123. 523: 512131 + 113. 513 512281). quae explicando
  53. de bos ae dad
  54. pro quibus substituendo valores, ex aequationibus 4 et S articuli 6, et aeque 1. et 2 articulia 7, prodibit aequatio (M. 51, S1223. W SEC. SIB231 = u2 H 2h. 5+32(+13.
  55. ubi interpretanda 3, B. t per a9. 4. 5.6 et quide
  56. +123 52L5I231923, 1133372
  57. L123. 512) 1272515
  58. 8. 512. l1213. I122Z V = 523, lgg3. 71223 Z = 312. 3121B. Suues V. + 31. 32313. Si23 Z =)- 112. 1.213 fin2, Vel13. 12sis. In23Z + 3ahug siu, . 79tus. Sicese) et edem modys 123. 523. 51227. (2 131 9
  59. plura inveniamus.
  60. 71223 (G SI2) N3. s 3B. 712
  61. 512Vyt _. SBPH + a3. 513 VZ + 100p50ot-er mon =6
  62. =112. S12. H1223,. Iu5. 1113 (B. 1p112. 513. I12rZ. 112. 12313.
  63. + Ig. S13. 1123. 51213. 31123.
  64. por coefficiente ipsius yv. vel Z
  65. obso vetur infra artia
  66. S12 23 (912(712) Ar. 523, 327 a siZ,
  67. aequationes per A2B et Aimilibus Nam addendo E et 3 fit SiB.
  68. (1t0) W1 tsyn in (aF
  69. f112. 512. 5123. 11212. 5213VB + 112. 512. 31223. 11323,5B23V.
  70. +n3. 523. 51n3. 1117 51213.
  71. = ab+ am +blm
  72. G(Sie 75IB23.7 4 (5, 23F1325) 313 723
  73. Hini ex aequ. I. fit (imo) nc. 3312. Sih- Si. 3312. 13
  74. pro quibus breviter scribama
  75. 13= l p. 113+1V.
  76. ysPh
  77. valorem Y) sic scribertuus, 114(3. 5121) v 4 11323. 5143Z,:, 81223. 5I223. Inde fint
  78. ft 123 hg3mi=Ds
  79. u2. 522 3.. 723 = 13 sn. nq addantur aequ, h et 4 fiet 2. 12 5a = (6to) (572317525) 3C3. 713 + (3, 23, 15 a1) 313 223. Aeferantur etiam
  80. ex a
  81. Andantur aegu. 1 et 3. firt L. iZ sca (to) (S +Y51) M sA ((5)(2 7612) 313 n Semiliter
  82. Qfiet 17.S1 Ec, Se, ., SIE h segit= 5ri. lt ex aq. + fiit 1 sp 113. 5e5, , 32g H3. D
  83. = Hll bitur ∞, D- 0, tantum pra 1 vet 5) et compendiose scribe
  84. s
  85. 63523. 52312. 513171
  86. (uddatur 11213. 1233. 1225 ot1 12. 92 I4123. 513 f,112. 525
  87. 113. 512) VIB. 523129. 51
  88. i
  89. 51223. 112. Si2. 51323I = 112. 517+ 12 5_)NZ. 523
  90. 1 ssu). 125. 51 lu e
  91. Su. S12. p2. 52Z. 115. 52t X
  92. 12. 5Ic112. 529. 17551
  93. ur. st2. 127. 512. 17
  94. (+ 123. 523. 129. 312. 113. 51
  95. (∞IL. 523. 123. 512. II2. 51
  96. 172 . . S2MB. Se
  97. 4 123. 52. 112. 58. 115.51
  98. B.Z. 123 513. 525 (112. 175. 5. 513 + AE 13 512 siz s
  99. ot pS. 113. 513. 233 12. 117. 125. 512. 513. 523 eU9
  100. .f 115.13. 123. 512. 513. 35 113. 125(. 31B. 113 2. 112. 11) 14. 5 512. 57
  101. 127 12. 1132. 512. 523363. 125.113. 532 in 113(123. 512.52
  102. idat msu
  103. an fi sii in in sr hnuns ns ffshtun ns saisis
  104. (VS1 1123. 5253, H3 Se5IUI3. s13 L 2 1ssi (L113 +2 1. n3. 523 513
  105. ues su t E r.tet (
  106. s i
  107. seu Bsmontus A3 3t +
  108. is
  109. est aest r
  110. 11235
  111. Slohis 1 127

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 73r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068255:0145?run=74