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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 127v

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: 0.63.

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The machine reads it as

  1. 83
  2. iudo
  3. 3
  4. 2 6:
  5. s
  6. i e
  8. et e
  9. s
  10. C et c
  11. 1
  12. t 5 1 eo
  13. ut = D
  14. EX+
  15. 3 F
  16. = E 5.F.
  17. = id 10
  18. 32 2.2t
  19. EE
  20. 8∞
  21. = 5
  22. 5 112d
  23. 570
  24. E Ese
  25. 5- 1
  26. + 350
  27. F5
  28. ux =. B)
  29. ∞L. C
  30. 2 a2
  31. E 2
  32. E u
  33. + cL=
  34. 1 = = E
  35. XbE.
  36. b0: 60a = 10. 3u_ S gota - a D0. b1 a = l10. 31 F 6)
  37. +
  38. 5+ Y
  39. +
  40. e e
  41. 2.=2
  42. c
  43. 12 3
  44. E En X
  45. c 8
  46. 5 1
  47. o + las
  48. 8
  49. 53 F d
  50. = 1
  51. 5 83
  52. a i 3
  53. ∞ das
  54. 8+8
  55. 15)C
  56. 85.3
  57. 8 d) 5p = X ∞ F. = L
  58. s
  59. 05=
  60. 8 29a
  61. E +t 2 3e
  62. Se
  63. 8 83F e. = 280
  64. Ne Ex his ratiu . g0: 10r30 = G a. 2 = ir: 31. quid si etiam foret - 0
  65. t - 8
  66. 00
  67. E
  68. (0 d1: 8
  69. Lc
  70. x his ratio 00. 40 :, 1030 = 00. 4+,:, 11. 21 quod si et sed et Ct 00. 41G:, 10. 21 + u. 20. itaque daturtatio
  71. etrum inter
  72. uiicic onstans intest h ba a
  73. G8, adeoque X fiet constans contra intentum
  74. et a O3(Z a at 5 = a (24. Est autem (G - 20. 2OXX + 2. 20. 2 + 2t Uaa
  75. O eatr + lu 2G- 40nX +a lax a q ad et 56 - 6ona + biax + 6r aa. Undere
  76. interpretando fut 20. 20 XX +2. 20. 118 +2 a 60apaat 00. 6 ax + 00 62 a p ibe a 2oaa
  77. alteram tantemus rationem, fintus +el
  78. sed ex aquternntundo, ftat n
  79. + e
  80. C2= 1 = ∞ = E +d
  81. 3F5 :
  82. sit 00 60 = 10. rop. + 00. qul,: a Eprins) 20 2o aa -00. 4olp,: ap
  83. ssepctia ab habintdinischen amt
  84. t. 2 c
  85. et e
  86. 2
  87. 10 1XX 110 raper usi an 0o. soatr. t ae biaax + 00. bra
  88. ao tinsre ommune illo
  89. aaitu
  90. 5 ute
  91. et
  92. et
  93. 8 det
  94. 5. dd ∞ X
  95. d
  96. 5
  97. et 5
  98. i
  99. 5:
  100. 3
  101. ia Diet pro 20 20po, 2.20. X
  102. roctilxi
  103. nC 40 4 a2 p trrcngum e a B sto l. 2ut. 142 = h. A Sia 26 p 1 a 1. n 10 :
  104. absi bbra M2F Et 00- 52a = 11 31 aP +004 21
  105. Et similem caceum indituendo pax m aqu. quae drato, simibs habe latur valares iprorum 40, 4l. 43. F Intum aua l, p, ponendo M, 4, et
  106. siet 40 = H31 a4 20a4 - 10. 30197 : 29100 et 4 = 214a - 11. 3199, : 29 m 00 et 4_ = 2. 20. 21 aa = (10. 31 + H. 30) 17, : 2 moo Et binos valores
  107. ipsorum 40, 42, 41, aequambinter se fiet 2020 aa lp = 10. 3049 p = 20. 20 a a 9 - 1030 ppogn et tote 10.30: 20. 20 = jaa t p. - qni : B 4 pg (pn - 91) = 11. 31 : 21. 21
  108. ex 19. 31 + H. 30: 2. 20. 21 sed ita productum ex D et D habet constantem ationem ad 30. Ergo et inter se, et , ut O ad 9, et D ad Q, et 50 ad 20; etc. adeoque
  109. et 218 ad GE, et ila fieret constans
  110. contentum
  111. gamus diversos modos et Hecusa calerer probum essee, vel ipsa prosut, etsi deside taca contrntia reductia ne lastat
  112. Quodsi conjungamus diversos modos, _ et quoad l, aequemus Beq uni producenti, ut DQ alteri; sed quond m aequemus 94 uni pro ducenti, et OD alteri
  113. ert 40 = 20 (10 a a - )pp): 200 pl, et rursus 40 = 20 aa - 10. 3099,: 2gn 2. 00 9a. Et fiet 10. 2oaagm - 30. 20 pp qui 20 20ca pl- 10. 3099p ita
  114. videtur rumpi incantamentum reductionis ad constantem, nisi restituatur ex necessatate trium aequationum auxiliat ideamus Eritpa jure
  115. et 42 = XC1a a - 3Ipp): 200pl = 21. 2104 - 11. 3199, :2. 00g. Unde 11. 21 aaqm -31. 21 pp gm = 21. 21 a a fl - 11. 3199pl. sandem d pari
  116. rursus jare, ob 4 - (10. 21 + 11. 20)aa - (30. 21 +31. 20)pp, : 2. 00 pl = 2. 20. 21 aa _ (0. 31 F 11. 3. p, : 2. 00 qm. unde n0. Et cagm - 30. 21 ppqu 2. 20. 21 a apl. 103 f l
  117. Ex aegu Cexnovissime prima est 30= 20(20 aa pl - roaagud: ( 1049 pl - (20. pp qu) Et ex secunda, 31 2HL 1 49 21 (21 aap l - 11 a a 9a) : (149p l - 2ipp auo)
  118. qui valores substituendi sunt in aequ. 3. _d qua Hto et 1 H. 20) aaqu 2 con ccapt vocemus 0000r, et ex aeq. 3 fieit 5opu (el t n t H p (X 2o2
  119. a= Unde fit 20p9 (20opl ionnqn nL CH(1gl - Z1pn ) 21 (21 aapl naa qu) qu (10gl rapn) = 00 aY (nau pl - aagn, 109l - 2 0pn)
  120. ivaq
  121. aapus
  122. Si aequ. 3 dividatur per 20. 21. reducetur ad 10720, 11: 21, 30-20, 31: 2 ide ope aeg 5 et 6 tollantum 30: 20, spe ipsanm 10: 20 est 31. 21 ope ipsius 11: 2
  123. et prodisit aequatio ultima in qua solae erunt binae quantitates 10: 20 et 11: 21. Hau Harum loco seribamas pro 10: 20 seribagnis 59: 00, et pro H1: 21, scrilamus 51: 00. +taqu dividam
  124. et perpa. ita CX aeq. 3 fit 5 (5B +51) aagu (0: a0 +91 2) pp an = 2 aapt (50 e) 50 +5) (aa - (20 + 31) pm- 2aa l - ( 31 + 51. 3.) 9 Hic lex est
  125. unimmnrinturis iata
  126. avoto
  127. _ H permutentur cum 3i B et pra, itemque1 et aequi forme ex 1. et 3. permutentur cum Leq et 4b. r Ex aeq. fit 3n a a L Z aam:, 5 gl - im perpe d
  128. 16 aat st aa :, s1 gt - pnc. compondi causa sit F q Ausu - g e pn = ah. Et in aequ. 6 subsituendo valores ipsorum 0 et 31
  129. ex aeqp. 7 t 8 fiet 50 +419 -
  130. 2eaf - at
  131. + ne-
  132. Sias- a
  133. J_) ah = 2aC- (. ae - 50 a9. 5 + ac l taqe 50) af Hie 50 e3 servunt inter se legem Homngeneoru
  134. 5o af =A
  135. EbF ah
  136. nceus ens partes id quibus plures sunt ductus sinctia Dubit (+ 60. 51 Cf 50. 51 f9 P00. 00R
  137. itaque si divellamus aequationem ( 1 in d
  138. litora lextiolateris pende
  139. -60C-509, 51f -0olisu ( 10, 2 (50f - 0oh, 51f. - 0oh) 00 = (00. 51- 50. 51, 51 f- ot.
  140. -(00C- 519, 50f -0uh)
  141. Requatio 10, compendio 52ga +h = D ) 00. 50 ef _50. 51fg 40
  142. 20052lf 42. 50. 51f
  143. +00 sigh 12. 00. 00 e
  144. indu
  145. ab
  146. 00. 50. 51 gh(= fu sv. 51. 5259 +00. 5+ s1 Pf F 2, 00. 50. 19h = 00. 01 529h = 5051. 32f9 +00. 52. 52 ef + 2. 00. su. s1 (t 9 = v0. 00. s2 gh = 7
  147. sed Terit Sacefg +00. si t et
  148. - 50.5051 fg +00.5050ef-00,00 50 eh
  149. Et fit tandem 50.51
  150. 00. 51 91
  151. 00. 51. 50gh.
  152. f-99n +2C, : g, 9h - e
  153. itaque tam Z quam 7, non alia habent ingredientia quam SD, S1, et 50+51 = 52
  154. +800. 5051 ef = 2, 0050. 51 ef
  155. Th = f, ex priore sint (50+51)g00e = 529, ex posteriore 2.00 ph( - 201 50. 51f
  156. (20029) 2.00000C
  157. 200e uie
  158. Erog Euoegus
  159. vabemus ergo absoluti tam valorem ipsius 50 + 51, equam ipsius Si. Unde problema est planem. Si sit ab et 50+51 = C, fit S1 = ab: 50 et 50+ 31 = C dat 5050 + ab = G0C
  160. t 50 = =C _C+ L H(CC - 4ab) unde si Et 5t = EC + L d (cc - 4 ab). st itiaqe si s0 et si desideremus rationalles, opus erit ut sit cc + 4 ab est autem sie
  161. C a erg e ec= (D eB et (quod dedet aequari ipsi 4ab) - D, eth ggh trees,:(qgh es, Et fit egh _ees et n os ggh erees, seu
  162. 3ef +est egh + gyA jam e= al q f = gl ia g anep h - pm: a. Ergo ef Il et gh - na et fiet H(3e+ h) = mn (etq) seu C: = gl9M tll, :, 3l- num
  163. est autem p=ata, ergo erit 4 atChata m: (gmm hll, - +mppll. a L) (ea m pel ap). Ex seu q= aa p, 3H- mm,:, aaM- pllm
  164. sed quia ponenda ce 4ab -0, fieret 10. 20 = Non licet autem destrutre irrationalitatem faciend cc = gab, nam fieret 50 =C-5
  165. = 11: 21 quod nolim, ob caetem quae inde consequentur. Itaque sec videndum an (CC= 4 ab possit fien quantitas rationalis ope. ipsarum p et 4 quae ad huc sunt arbitrariae.
  166. eut aeerque- 4e. efh -gyh +ree Fd = AH quadpto, et 1 - eth- g9t+ 2 ees = H.H. Est autem e- at f- a g-am h - jm Ent eft ef = U gh = mm
  167. oh- ef
  168. Et fiet emm et = hll + gtum +(2 eH: emm= ell = KK. aa seu aa emm- aahll = emmkk - ellKK, et fit
  169. oh- cet
  170. e ga, gnim -hll, :, mon (KK = aa) =H (KK + a a) et explicatis e, g, h fint d: q = (aamm-PBl ap) tum (Fr -UCKKtaa) Unde tandem fit
  171. g= a, mntetea nm (KK - aa)= U(Fir. +ad PCaamm ppIC). quae est quantitas rationalis ubi p et R sumi possunt pro arbitrio. Sed quia
  172. homonim ieterins non ntin silire alato, it poinde, do ver norentum na ua reoiannus lait, ot numeris tandem comprotudus
  173. vertatur
  174. s
  175. ∞C
  176. 1 = +E
  177. s
  178. E5.
  179. 2 +11
  180. PE0
  181. l.
  182. e
  183. didis
  184. es=

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 127v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0254?run=74