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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 44v

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: 0.71.

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The machine reads it as

  1. A = l -n, M =
  2. 2=M V = L - m) Trinl maxima, n minima
  3. 24 = 1 +11
  4. 31=12:, oor - 1N
  5. 23 =0d.
  6. post tanc significationem notarum assumtarum, proponitur aequatio
  7. resolvenda a 31 (24 -31) Y - 00. 11 (13 +31) = 1131 ( 221 31,
  8. 24. - 31 = (00+ 11) (0or = W (1) = 00. 11A, : , 00V - UM. Fiet 00. 00Y = 00. 1 M
  9. 411. 00V - 11. un - 00. 11X,:... . = 007 - 11 n + D0. 11(V - ( - 1), :, .
  10. Sed V- n - X ~0. Ergo fit 24 -31 = 00V - pn, : ooV -uM. similiter
  11. 24+31 = (00 - 11) (00r = 11(3) + 00I12, : . . . . F, et 00. 00Y = 10. I1 (M - 11. 00Y
  12. Luui = U +u. un +00. 1d, :.... 20dr + t +00. 1
  13. CA - n -1), :.... sed A suir = M. Eup est
  14. Ergo fit 23+31 = 09V +1n - 2. 00. UM, :, v0r - 1(
  15. dertio etium modo idem culculut obtineri pors
  16. facendo eorH.umG, F = GKH E. = 3
  17. Bor HF- 20c xoErrd =2odrvad
  18. =ooinoo oorcipu ie +2. soru ndo H.
  19. umiriu
  20. E = X5E
  21. IIueF = teor p oir suur ieniun f. odri od 1 2
  22. xtpurtncor viputuia +u lm m ooy R2 3 = (- 11 .)
  23. Hic vator obser vat popitiam inter 0 L 1I, Y
  24. = _. eoVLIL.M = 00. 11X, :, . . . . = 00r +1E n = 00.1t (A + (n tYio GxR _= ex VoVr + 00Y 1I N = (2 00Y. du. M 5
  25. 1. sed A + n + Y = 2Y, et
  26. Et sit 23- 31 = 0oV + 1en 200. IIV, :, coY - 1p
  27. (m 00Y - 1 n 1n t2. 0 m eB. MP F.
  28. compendio
  29. et ( FH60 DGHK -6) N n GF
  30. et Oor FH, - GKH = nN HNFG = ooVF - GK, H
  31. 10or 12
  32. +002 F -100rV =00. N aY 3.
  33. OSrr - 3.00uur +00. N Cn 1V-H 1 X 4 p L21
  34. GKH - + 00r Do -oi vou L obroVi (2 ) -0or I M P Y F. = =
  35. Numeratores ipsorum 24. = 3L 23 +31 23- 31 31 denominator commenis GK -
  36. Et excequ 2 sies, ereoud F V - 00. 114G = - 00. 1 Am GF
  37. Kk. H: K
  38. o inour tu mooun (N) -umC=
  39. 2Wvir ovrra bbau oou p. cur vo Ex AZ O IYII p F
  40. GKH= ZoV-o C)Loor ( L+B)-10. 1(mfEr):
  41. MH Sit A+YLI
  42. GK = (E0OVBOK COY I1e + (2l0OV OOHM = IIM, L1I M
  43. A , cVFI = aB 1aY + Hoc sutotum hintiplidemr per H fiet min - reit
  44. Fumoortuma -2. M M00 )
  45. post EH) =un, eree e oor oortoorue bost oena A-m F t
  46. pnoorummeum oou
  47. R3 2Q E n n de a .1BIXtoui
  48. a n
  49. oi o t NhC 2. aeie n 4 _o CALV,
  50. C0d 11
  51. pt
  52. nr.3
  53. taref = Hn, 4300 r- 608 + 4 00 1t cnt
  54. 20dH ZV+ ∞408. 11
  55. N +M - 2n AV sa t M st - in. d
  56. 87
  57. ot5
  58. MaFG= (up) aeotai uo od + 2.0o r ovua
  59. Aunar nit ( 2. IC a 00. 11 M)
  60. 2. 10. p
  61. Y n sit n
  62. X- VM.
  63. sem = in 2 is
  64. si esset m = d, sicret d A n et V =l et cuta ex differentia
  65. retinen debet _, et firet WMM F 2. 00. Cum L00 IL (aM -X) -2uoH
  66. praur por- C nt . m - 2b n. m
  67. Et fet qua oder +ddu (an Zbi d ( F0
  68. quod siciat i in datis sit n + V son . n + l. n =0 seu l = mns. 2 foletur
  69. sed placet eandem aequationem ultimam ad hac clia ratione quae
  70. rere, ut calcula melius fidi possit. Ex eq. 3. fit o0V F = KH - 1 M F, G
  71. am CC Lumoonr , = V, B8Y -200 1V +3, 0v. 11n
  72. quod productum multiplicetur
  73. FmaY 3 od. 11 P v0IIn
  74. L 2. 00.1 M adr Loom 00 vo oviim
  75. +00. 1 M a f + 3V =
  76. oor, arod oripi LL. 6or dB 1Y)
  77. (rimaer unin) frunoou
  78. aquando hos. nos valores, ipse
  79. ipsins GKH, et ipsius dorn
  80. fiet destruuntur utrobique termid
  81. qui valos etiam obser
  82. quod superest dividitus per I1, et aequatio ordigula
  83. o= 00. p nrar - veii nr (Omten + au p (3V + 4C) L 4 Co ur
  84. 1n = 0o1 (EntV) +00 1(2 2) - 400 =0
  85. ut prius jam. itaque huic calvulo
  86. cum prioribus fidi potest. Et hic
  87. novissimus etiam in progresso ipsa
  88. servabit harmoniam, quia utrumque
  89. aequandum per se harmonicum es
  90. ne compendio sit 2(n + V: M = 13
  91. 2V+ M, 00 : n = 15 00V: n = 14
  92. et fier 13 - 13. 112400. 1511- 44 00 =0
  93. fiat n1 = 41 + L13, et fae substituendo
  94. 400. 15. 13.3
  95. AI+ =Z 13H- 2 13
  96. 400.15. 1+200l5. 5
  97. ad. 14
  98. = 44. 002 bo. 41 + ∞4I + aaq -0
  99. et sit 41 = 9t sa ( aaqu + s(qu . p a )) ei (C aaga eleaa)
  100. 2 A∞0.
  101. A 99. 4 = (4. 13, -36. 0015. 15) +417 0d. 14. 13 +51 ct. B B 2. 91 14 13
  102. =(2, 1d t. B+ 001 5. +3. L. 15 od. 54 ae, 5 . J. cd Ab . 1 4
  103. sit in Hyp. et Etlipsi glatus lusoe 2t useu a Bmapor ut 72 1B
  104. distantia socom diut ad exem mujorem pt
  105. =- di. et dz - - d_ a XN = dx. u i1.
  106. (4X- eed, X-qqu sit 4.
  107. 1z du GX , x.
  108. a +-b
  109. fiet d 7 abaxi saxi X- b, X Tansum erus
  110. opus erit ut consieamus ssax, Xub, X. Erit
  111. uo
  112. et n - m = A = t H = C = A , sen l. B = c- b -
  113. etCautem est major quam b in Eillipsi
  114. dque ( a ta (4 x :, 2 x - 494)
  115. eque g 4,4
  116. Vel dz- (ax
  117. sis2 G. 2a tirt cu = X ((ax, X - a e, X - a)
  118. sit ee: qu = b et fiet dz = - dx da ( (ax, X - b, X - a)
  119. G se rcR 4i e 0S. I(arI, V) + 2 od. 1 (4) + C)- 5 00K
  120. et
  121. Zordinata au minotam stdes Elemento
  122. t ra fi
  123. ut cor, (0dy 1) 2d t (e r t eoituc 2teL 2. ouse e (. qei (3) l ar
  124. uy en quire
  125. et vrulure ipsorm Lux
  126. 25. 41
  127. Evrs-am dei= dZ ((4 eet V: 149 912. fial 27=
  128. 6C2. +8 = 2r + 7
  129. eei noc um
  130. quiH
  131. d t
  132. quaenon consentiunt prirbus iitaque taculi sunt repetendi
  133. ii FG e
  134. eri
  135. d0et 11, V et _
  136. a1. A 4 2, 41 1 B. 3 - 13013.9 (20-
  137. i
  138. subus ∞dr = 2i00stI + 3. donitui V, obr ubsit, 3. ooule) cris e at hilsi a pit sit a gro unilulo, fieti
  139. A0o
  140. quod multiplicando per hfiet siver00 Lo0Y0. t B odr vor ip
  141. oF6 40=
  142. aa
  143. Undetandem sit 11h =, 00. 1. C2en+V + 00. 1 (2Y+ ) - 00r = 0 a4) + aB = 20. 1213- 00 5. 157 0015. 14. 13405. 14
  144. terminns summus coptineas 1B, et aequatio fiet plana. Sed hac ubi non est in datis
  145. KH = fcrN or ( od s u = 2 ∞V. OB. IIY)
  146. upt Ciroo upi ciei
  147. VIN = XFM trEYI
  148. em 4B(3.4113.3) + 3. 41. 1329 4 133:279
  149. 4000 00V
  150. GIAN + 40dit + LWVrC-40dr
  151. effici non potest
  152. (I = qL 2(NAV
  153. rs a
  154. +DOV, FA
  155. gra tam ob harmoniam, quam ob consensum F
  156. Pt p gp - X = 2p Y +
  157. + = X + = l- n - n + m
  158. fit 0 = i (a +2C 400 1An+V+
  159. FG
  160. n+G = 4M + X p. 8 = e
  161. L -
  162. fa stabit:
  163. et dividendo per 400nr, fit
  164. le
  165. oppar
  166. Y= N = Y - nn -
  167. qoor F t, - (1 1) 1 300rr = 2. 0d n H st oB. )
  168. aex
  169. e.
  170. et dour
  171. erit l- -B, n =-a m0
  172. A= n = -a V = l = - b R =I- n =- a - b
  173. facinmque a = 2b fiet A = = 2b, Y = - b n = b
  174. (D) 1Cp (00. (VtC) 4B5. 1CWVHM) 4 00dY =0 ut supra Wt = - b t = b
  175. ErtA; M = - 1 2N F; n = + 1 V: (1 =
  176. Ut supra. quae aequatis aulchre Harmonica est, nam et ex ciq. fient xtq a 1 - 1r fB - 11 + (, et fit 11 = ( vel 11.
  177. permitu 11. et n permutari possunt cum 00 et V (sunt ergo tes radices huous aequatianis, 1, 1, - lranesu duae aequales
  178. sit 112 1 fiet 31 = - 7 -2b:, = 2 = 1. et ZL geaeatiur ( si a = 2b fit 12
  179. IY= A =C
  180. nam . bo
  181. test munehi H
  182. salva aegeitione
  183. val juctitiam inter
  184. infncil ta i
  185. b infinila
  186. tno =
  187. d
  188. de nit inetae

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 44v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0088?run=74