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Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 83r

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: 0.77.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

One image of two folio pages side by side, registered by the library under both labels (also fol. 82v); this page is its right half.

The machine reads it as

  1. Hubita jam comparatione sedium veniamus ad earum additionem.
  2. sit a +b = 01 0iot a=
  3. 00 11 00 C
  4. vol 02121262
  5. et generaliter S+ 5+ 225 = 051305 = 05151505 = osis esis + osusosisisos
  6. c+d = 00
  7. obde di
  8. a+ C = 0000 211
  9. (O212) 2 (1202)2
  10. 99901111 00001111 = (04 14)2 (14 14)2
  11. sinior 2 (10)2
  12. CFP = 000011 110000I1II
  13. 0000000u 000000or
  14. et generalite 5+ 45 = (0515) 2 (1505)2
  15. 010101 01 01010101 = (01) 4 ((0) 4
  16. a+D = 9000000DIIH1III
  17. 00110011 00I O3I 30I 051 00 001I = (021) 4 (1202)4
  18. 000000000000000V1II 1I 1H11S
  19. et generaliter 5+8) = (0515) 4 (1+05) 4
  20. Unde tandem generalisseme unu Sts = (05 15) (150s) e
  21. caleus permet si omndams.
  22. (osisttt oles s
  23. s Lesisse orespes
  24. h+ C +d = o2 121202 + 0818 = o2IZIO2O2I2NOI, 0818 = o2nnOnoion
  25. ergantus ad tria
  26. 1b11b = 0414140414040414
  27. (d+ e(041414087 aria 1 e 14 i
  28. dt 1414i4 14041404, (21 D2 1404)2
  29. (.fisit + orsers = 401.s.7ossiosobis ositde sequestretur
  30. +25+4s= os es + (os. sis oste + 045 14) = 01isisos 1505ois
  31. f+ 2 + 2( asis = ((0si sC sos) )fa
  32. ((+ 25 + 8) = bosi) Act +08(∞185 = (0s.51505) 2(1505 6) 15)2
  33. (+ 2( + 165 = (0si5 150) 8 + 016)+16s = (051 si505) 4 (15050515) 4
  34. S+ 4(+45 =
  35. 11+214- 0001010
  36. qoe o
  37. ibno
  38. (Osissra sos)2 + oascas = (Osis (os s )2 fpotu li t it su quori g osias (ofis) 8 tutsoits. s
  39. (+ bis a5 = (0515) 4 + 0452s ss sist
  40. (74 (+35 = ((5. 14 (50()2) 2 + obsi8s = (O1s) (50s) (s0s ) 2(8, 1P, 10c01
  41. 5145+165 = ((05.5) 4 (1(05) 2) 4 +01b511bs((osisp (150592)2 (150()2 (0s 1s)e)2
  42. ssosse
  43. 8 1010 10 = (0s. 1)2 (1) is)2
  44. Et generaliter (L. 45 +4L5 = (0(. 5) 2(1 50s) 2) 2k + 08hs 1 8H = (( osis) 2(5o5) 2) K ((1505) 2C os 15) 2) K
  45. Et sic quoque st B + 18k) = ((05 15) 4C 50s) 4) Zk + 150H5 1 16t5 = ((0 si 14 (150 s) 4) k ((. 50(9 4 (0 ( 1) 4) _
  46. vt gaienaliter et generalissimepsrius. s. + 2hs + Ahks = ((05 .1) h (1s oh) 2K + ∞ 4htes 1ahls = C(0s. B) h C150() h) K ((11 osi hC a t hK
  47. Sed generalissime pro duobus sechseret (0sis ) 50(t
  48. Anergo peneralssine uo quatuor. a s +hte ) + Ctit s eit CC(. A Cqosse)A ( As aBI o ne AB, cuet d ed
  49. Et patet progressus in infinitum pro addendis in unum quotcunque sedibus diversis. Diversis inquam, nam
  50. si eadem sedes repeteretur seu plus semel esset addenda, nonnihil esset sariandm regulaque generalissima
  51. inmutanda, sed quia ita res esset paulo perplexior; et repetitio sedis in additione semper evitari potest
  52. cum eo ipso transferatur in columnam sequentem sufficerit regula proposita, quae generaliter sic enon–
  53. summae ex sede nova prioribus addita
  54. si catus siviei persi si casibus seriti ovae
  55. tum quo sedes nova
  56. repetantur secundum numerum quo sedes nova supremam priorum
  57. renet si casibus prioribus si casus priores per rum primum ip
  58. tiari potest, it
  59. cum oppositi p
  60. quiod exponentes metitur. Unde patet etiam quomodo puncta anjeantur, quae notant tranclationem in columnas ba
  61. cnenaliter ubi Ad estn catibas (. trans certur in opposilis in columnam sequem
  62. supremam priorum metitur, repetantur
  63. 10 000
  64. fiopt os eisoes M o 3 hnsi cusonn oi ik osiB Ces oB)HK)Im (ote E is ite in ce alotes esors
  65. sertis = (05 1sth (1505) h
  66. (0(os)h (osesIE
  67. AchsAhiK) = ((0) isth (505)L) K CC1505, A (O (11 ) H) K
  68. ((0505)h 19515)H) K ((05, () h (1541) h)K
  69. einitio tamen, seu in ea additione, quae tI
  70. (+ s ratius M) ((C0 5. sh (1 ( os )h)K ACC. 505) h (o sish)K) L (CC. 50)H (os. s) HK ((oS. 5) M C15051) L) L prioris
  71. (Cofas)h(osos) 2) H CCoses) h (osts )h)K
  72. ((0F0))h (051 5)h) K ((OSiAhCCIpSHK) 1 ((osiBh ((pS)h) K ((111() h (sos) LX
  73. ost(s R e ofas Tass )Ch Cssh) K (Tosis A E. Ld) B Z) L
  74. C ofos) h (osos) h) H (( Bsos) h (0ses) ))L (esos) h (0sos h) H ((0 fos) h (b si s) L) 1) L in secundas
  75. Itaque generaliter culumna secunda tatis summae opponitur primae, et ceptis primis casibus numeros, ubi oppositio pustula res 1, sed est o
  76. phis-. Hs
  77. Regula generalis
  78. = (0( .() . (1s es) in prima columa suam multitudo hm no coefficiente comprehensa
  79. transformatur in du
  80. ubaeque simul comprehenduntur uno
  81. ientes quot addendi
  82. Cxtralis = st ia(tales y = 0onm o B dli 1 =1 vtiroch odeo pd coefiliente naco; ita, ut tor sim cosicit ot, fiat 11. e
  83. a
  84. 00 1u0 110000 oovodiso
  85. cobi C(ahstahk segtiX Isriblikelms = (((osist h (st) k (. (o 1h (op ) H K) L(((.50)) h (us s) LIH ((Os. s) k (150s) H K) 1)m (CLC, s0)) h Cot. Bh)K (Bs. 5)M C so s A B) L (1. 1al. os a LLBVB a )
  86. le000vo ovemI
  87. (6sei t e sti k. ot. uC isis) )L ( os syh C. sis a 1k CC s iB Ceso s ti X) () in AL COsi(s) hC t. ) t X (. s.pta (1sos h.119) LCer. s h (.50) hi ka is t6. isti1 m
  88. B cy 50 a 4
  89. C Oc, 12,, 12, 22m 12, 23, 27, 349, 12, 23, 23, 341 23134, 34, 45,, l2, 23, 231 341, 23, 34, 34, 425, 23, 34, 34 451, 34, 45, +5, 56, 111)
  90. a 20 51 11 21 10 oc 2 2 21 49 1001 62 e1 11 10 11 10 109∞ 31 10 19 4 19 44 9 21
  91. iemperascenditur, dum
  92. prima ad columnam propositam tansit, un
  93. 1 ponitur non nisi ultimo loco. Etita et
  94. pro ausimento ex osos fit o ex ofit
  95. ex asososes fit osolosis
  96. osoliteta im prmocat eneintsio medtetu
  97. ita potro
  98. eum excmf. 63 est nies ut 5. ncmpo in pariois smma lauaerum it impindis ua us
  99. 52 est ILIIo dat 5
  100. Aumerus lacipdans notas
  101. minuta iact nmerum notam loci
  102. ita tandem regulam habemus pultherrimam.
  103. paru us p at pt edis uge tate, d mcteut sita st a b enteti tue
  104. am col pir
  105. de sig aut
  106. hinc + 1.) rest. 22 ausad u g1)
  107. ntitr i brpe t utibr 110210 lisi put.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 83r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068255:0165?run=74