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Leibniz-Handschriften zur Mathematik LH 35, 3 B 3, fol. 12r

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: 0.80.

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. 13v); this page is its right half.

The machine reads it as

  1. 1-1
  2. RM = a
  3. na art liansf. ab.
  4. 2ab
  5. Ex Regula nea generali in veriundi quotientes fractonum periodas
  6. cujus Numenatar
  7. ivedeter id est 7) t per eum sividendus est nu
  8. doncc prodeat periodus. Sed ne opus sit dvi
  9. sione actuali, regulam hanc inveni. Ad numerum datum addatur 1 fit 1000 ei
  10. 111I11I
  11. dimidium 100, erit multlicalor perpetuus. jam qu periodi quaesitae quotias ultim
  12. est semper In sposito scilicet, ut semper assumi potest. Numerum cujus fractio qaertur
  13. esse imparem). Is ducatur in multiplicatorem fit, 100, scribe 0 vet ne +0. Hoc
  14. dic in multiplicatorem fit 200 scribe scriptu habes quotientem rum retine 10
  15. transs abtac -abe
  16. Quobentem novum duc in multiplicatirm, adde retentum fit _ic, scribe o pro
  17. apotiente tertio retine I_. quotientem dertium duc in 100 adde retentum fit1
  18. scribe 1 retine 0. Et ita habetur periodus.
  19. 1860000 f0100 100 100 eM.
  20. demultiplicatus per primi
  21. sit numerus
  22. D.D Ct acstr
  23. firbus a ax
  24. comprobabimus operando acto
  25. n r l
  26. quotientem 1 dabit ddHat
  27. retri
  28. idem esse ac si eadeba multiplices per deeunt et productum
  29. et, abr bh. bh. am, quod adde ad ddu
  30. semper dabit periodum quae sitam, multi si multiplices per 10, et addas1. fit periodus
  31. manifestum e
  32. Et patet nvera
  33. debet 1 vel l.
  34. ergo bl + am dabil b+ a = Pab+n lenn- btanab
  35. quaesita, cujus ratio patet quia ascubu
  36. et ab + ab
  37. eum et bm t an = C + ba Hinc fit p= in p sit et + bm = an + ab, saq u de
  38. e de b. a L mult
  39. ab quod transferetu
  40. musferctur in locum sequentem, et de vel restabit da aliab adeoque sit p= C+ a - 2ac
  41. a
  42. anferetur ab ii locumse quentem
  43. eut c + a 4
  44. idem esse ac si
  45. poro m. a ad m-
  46. et + ab + ab aa -2 ab + a b
  47. ub quod patet, non posse ire ultra 1
  48. eta = cta + hac seu ata = eta -rac
  49. pux quo scribru 2 ab + c+ a ad
  50. labi
  51. et set P alt ab c a
  52. ambsi ambo 1, nompe, a et t
  53. c
  54. et et a - 2ac + ab = p+ ab. + aB= 4 bC
  55. est in lrane
  56. aa + bl = 2 ab vel aarbb.
  57. aate
  58. p estin el + db + an = cl t abl + a + abb - 2 aab
  59. M= al =a n + 2.. = bl + am = bl + aa = b + a =aan h
  60. fiet a + 2 ab = a a + bb et n= aa + bb -2ab, et ab transferetur
  61. = 1
  62. el + ab taa
  63. pat
  64. et ale c+ a + ab jam a + c = aat at
  65. in columnam sequentem.
  66. + ab = 2ab + ab =
  67. entransferetur XC-
  68. rabit quatto qu
  69. en sequent nlis est erat quadzacio, qui
  70. tab
  71. rac
  72. 2a+
  73. len
  74. iic
  75. ipt 2ab (ad +cc- 2ac) + a + c+ 4aacc
  76. b - 2 abcc +4aabC, adeoque
  77. ransferendo ab + ab (aa +CC - 2aC) in sequentem, fiet p= a +C + 6aacc
  78. 2a
  79. a + C
  80. a
  81. = 4aC - 4ac + aabb = 2a b - 2abcc + 2a a bc
  82. seu fiet
  83. p = a + c (+ 6ac) - (8 aC (F ab, - (2 ab =2 abC) + 9 abC) seu p a +6 nb- ab
  84. conjungendo primum.
  85. la et ab, et post addendo c. Nempe p+2... = c abt a + ab + C
  86. x (1 uab rati) seu PF a + b - 2ac + 2abc
  87. seuqu au ab tabet
  88. et paosn
  89. 100
  90. 00
  91. quotientem n quem scribe et reliqua retine, ita apparet et ila porro, s
  92. = A Xb-ab rab i (+ 2aacC = 4aC L 4 dc + aqusibe a
  93. reliae
  94. H3.a
  95. 00
  96. ux additis bl et am, habebis tertium
  97. quod deb Multiplica a
  98. pocier
  99. +d (uib. ab acrabus absolvi debet a
  100. ad esemp
  101. nnib
  102. tau
  103. in
  104. e Multiplicator, id est dati unitate aucti dimidius
  105. FY1Y 1
  106. NA.
  107. scribe a restat
  108. )= a+ a) b (14) aCaEd ( an bo ab. ac tab.
  109. nayf. ac- abc
  110. Hac +ab
  111. pnttum
  112. Mhi
  113. 2a
  114. paginae 18 ascripta est, oritur haec pro dgadicis. Sis numerus , vel 111 dyadice
  115. numerus inde finitus:
  116. Paob resa ab)
  117. anab reab
  118. P2
  119. queab
  120. e
  121. fit
  122. Aliter idem
  123. at atab = a ab. jam . addi debet c, fietque a + ab - 2 ab + a b
  124. + ec = 2ac + 2abc + 2ac = 2abc, et reservando ab + a c - abc
  125. ut ante
  126. in sequendem col. ifiet P = a (F ab, - D ab + C = 2aC + 2abc,
  127. q+2... = dl + Cm =bn Z ap + ab + ac = ab c = d + hc s Ab) + b - (2 1b. A
  128. a( ab F ac= (2n9 + (2abC (+ ab + ac) = abD = a + b - ( + ac - abc +
  129. a+ b a tb 2ab + b ob aub reservetur sb, manet atb. 2ab primum atb
  130. et atc- abc etiam ergo erit erit q gubfab +2ab
  131. = 2ab = 2ab, + ac + abc - 2 abc 2. (a + b- ab) (ac - abc) et in sequente honsferetur
  132. (a F b = ab) (aC - abc) adeoque Gia +b - fcb + (aC = abc) - (2 aC + (2 abc(- 2abC -+ 2 ab c 4 2ebc. 2 a l1
  133. ab non excedit 1
  134. +b-ab attabe) + acuabctab0 ab
  135. ravond eo tet aedi ala at anerare uti seri ae steatari
  136. ervetur
  137. ed cb a
  138. in it d H. al
  139. eudnea bu an
  140. euda eu luan
  141. Apepuap.
  142. eu
  143. n h l
  144. f11C
  145. 15)
  146. 1ab, per bxo

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 B 3, fol. 12r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068253:0023?run=74