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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 202r

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.

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The same scan as fol. 201v (00068196:0398), where its text is given.

The machine reads it as

  1. CL A55I5 FRIMA
  2. alerilus 1 10 X + 1 2o 2oX + 2a = 0 sp. 2ox u nA = (o2oB + 10ua fit 10. - 11 20 = 0. elter 1B 217 11 21) = 1 20XF 11 21a) fiet idem
  3. lalus son 10X L Ha =0, 2OHCFINXF aA Do (IB 2OXXSH I. EOAX = (B. 20KDHIB LI AXHIB L2aa fit , 1B. H aX + 102 aa 20 quae conjungatur aepatim 1. frot 10. 10. 32 = 10. v. 21 4 111. 2020
  4. eq. A si pro 10 gubstitua permutet 0 et
  5. Aliter 1B22A XFH. ma) = 11. 2oNT + 11. Uo VanD (., ve 12oi = F quaesi compimgatur 5p
  6. q lum havetimar te di ddiu
  7. puitaeq. 4. Hinc duplex processus her irit
  8. at esqu. llmnam callauli (m posito 22
  9. ciluus 1eXtIa = , 20XPXt 2NX + 23a=0 (10. 20X + 11. 20 axx = (10. 20V Ho. 2axY F 1v. VaaX + 10, 23 a seut 10. 21 ayY + 10. raaX +. 1B. 13 a La consendi 2op tyax aa
  10. putiontum
  11. un l nlepire s
  12. ncauli prrecedentis, si ponis ho-0 et pro l p2, 29lice, nonas 2o, X1, 22. Eotem modo ex aeque ultina pasculi pre b.
  13. 3) calculi
  14. pentinaequ. d
  15. Aequationes quartae calculi (2, 3, et. consentiunt inter se in eo quod ex Ata calculi alicujus fit quarta calculipraxim e a u sipliando ilam per X, et adento 10. 2C a. Et ita paht etiam quomodo quintae ex se invicem criantu, et ita pur
  16. 10. 10. 11. 22 + 10, 11. 11. 21 = I1. 11.
  17. 10X . H
  18. sequationes 3tiae calculi 1. Ed, 3ti, consentiunt inter se in eo quod ex Htia Ealuli aliujus, sit otia calculi prorime sitelianto vtamm per X, et adendo 8 B
  19. poncido (20), (21) (22) calcili hanus, et fit
  20. remotae a primus nempe 3tiae, quantae, quintae _c. a se invicem ducantur Vibeamus et quomodo a se invicem ducantur Uttimit
  21. Era
  22. suamncaliani
  23. Quaramus praeterea residuis
  24. tet berdiaa
  25. s
  26. iit aua
  27. divitor 10X + 11a
  28. noru ntrcdae rattis 2tit ua
  29. e Resid. )- poero
  30. penmetimae, et antepenultima
  31. comite decurem lessum t hae mat
  32. et Residuus Cum
  33. tione altina salub
  34. pisisur 10X + 1
  35. uinistox t LlaE + DOaX Y2
  36. e - meaet -e ut
  37. Caeterum aliter et brevius poterit hic tolli litera X, si ex aequ. 1 fial X = - 118 et i valor
  38. unc aequationem conjongamus cum sequentibus
  39. I0XX F 1af + 1244 = 0 2OXX + 2IaXF 22aa = 0 (10207X + 11. 20aX + 12. 10aa = (10. 20Xx) + 20 21 ax + 10. 22a4, fit. F10. 21 ax
  40. sibstituatur deinde in aequatione secarda
  41. CLASSIS SECVNON
  42. Sed tunc transeamus ad aequationem 10 XX + ( IIaX + 12 aa,
  43. alculys primus
  44. tit ex lalentosecundo clastiis praecedentus sidio 22 (oi) 2t 1 (t 1) 20 = 0 _ ubi explicando 1ou lt, habelatur equatio fine p.
  45. Unde ex eae C et 2 fet
  46. 10. 22- 12. 20 ( 1021 41. 20d a X ad xarsus = fi. 2l 2
  47. in hoc calculandi modo id est laudabile, quod hoc modo non a
  48. Lode
  49. calculus secundus 10xX. + H1aX +1 2a4 =. 20X + 2XX + 22 aax + 23 a =0
  50. unde Ex his priorem applicemus primae datae inversae, fiet 18. 16. 23 p
  51. rrunt depressiones
  52. x)Hisorvaret (2. 20 aaX = (10. 20X1
  53. ax,
  54. et pradbit (18. 12. 20XX L 11, 2. 20 aX + 1212. 20 aa = (0. 12. 2oXY) + 0. 12. 21 ax + 10. 12. 22 aa, sed aequatio quae ita prodit coincili
  55. Rarsus et posteriorem Minvensione _ (1) ex inversioneortam appliaemus primae datiei
  56. quod si ex aegu. Micte data, et rda inventas ada modum
  57. Calculi rdi
  58. nec 2dae ditae ntra gradum 2dum Ego aequationem pristem datam, et ap. ) conjuaga
  59. + 10. 10. 22 X +10. 10. 23a 20
  60. sinilite raeqrationem priorem datam et aequo 2) conjana
  61. 10. 12, 22 X +
  62. seu = 10. 1
  63. = 2. 12. 20
  64. - 10. 12. 20
  65. + 11. 12. 20
  66. I. conjungere ejus inverso
  67. 1o t H.2 B
  68. (10, 12. 22. 27). 13. 1 2 = 10. 12. 21 22) . 10. 11L. 2i C 10. 12. 16 23 10. 1. 1 20. 27 + 10. 123. 20. 2 1U15 20 22 16. 11. 12. 21. 23 X10. 18. 21 5 410. 4. 12. -10 15. nat. 2e A ie tv s. litivor .
  69. eeu. -10. 1.25 (+18. 12. 22.2 (15. 12 2. 13) + 10. 11. 12. 21. 23(-157, 12. 21. 22 10, 15. 2824) 410. 112. 1223 + 10. 11. 12, 2822 = 11. 122.20. Qu. vatione defantuse esanctis destuendis divisa per 1 prodit
  70. FI. l. 20
  71. +123. 202
  72. 418. 1E. 35
  73. . 2 2
  74. a3 + 11. 20. 23)=0 tatem videlum
  75. 1X. 12. 20.2
  76. sererali vin, lie iti dita aeqpuatent 104 rX = B e roA A 20 puX +2EXL + 127d + 24 X retis pstumus touim X, eoum in aequ. postriore pro a prerer = unde fiet a
  77. = 20 - 19 + 1gue n - 1 13 4 1 24 - 1825 + et e vel 18. 20 - 10. 18 al + 1. . 22 + 18. 10 3 33 - 11 10 24 + M aente periveniatur au plae qui ex terminus altimus.
  78. se sint jam dutae aequs. (D. +. HX + 1 BXX - 0 et 20+ 2VCL LZXX + 23 X + 14 X + 25 X + 26 X + etc = 0. Eit XX + = 4 g0 ader - u+ sini
  79. quo valome substituto in aqu. aleradata fist 20 B. v + V2- N 23+ 1 2 1 - 1 25 + erc
  80. 20 - 1 21 + 1+E 12. N 23+ uit 18 25 + 1tg s 1 17 + et = (a2, 21 + 12 23 + 12 75 + 92 27. Quo si jam detimus vnere trationalem, fiet
  81. 20 - 11. 20. 21 + 2, 1 + 42. 20. 22 - 2. 18 20. 23 + 2, 1 4+ 4
  82. 16. 104 8 2 11 2025
  83. + n 2121 - 25 .F2 212 + 2
  84. Unde t deptrum latus aequationis in sinistrum transfereudo, fiet:
  85. +2 1ror 286 - et
  86. + qeate vu - 2. 1 + dta 23 + 2, 1E 3 v 24 - et
  87. 20- B: G8 1. 2021 + 2 ( 19 62. - 2 (L. 13 20. 1.
  88. (24 3 2
  89. 81 ) L. p8 Zu2e
  90. A sertet sujus lex habetur ex conideratione numerorum 20, 21, 22, 23, etc. quea quorum
  91. hic ponuntur quadrata, et biniones. e quoties hujus numeri inota dextra est
  92. impar, ut cum est 2t, 23, 25, ex. pefficiens habet factorem H, H3, 1, etc. Cum
  93. Quoties nomerus cujus neta dextra est par, ducitur in cum nume
  94. 64. 196 23.23 - etc
  95. + 2 511t 12024
  96. 1610 e 3 223
  97. Numerus cujus nota dextra est impar, ut 2, 23, 25, habet in eoefficiente 11, 11, 11, etc
  98. par ut re. 24,26, ex habet in eofficiente t, 112 412, 114, etc
  99. Hine si combinetar par, v. g. 22. 26, coefficiens est productum ex 11+ 42, in 115+ 42
  100. Si combinetur pari par m et impar, V.d. 22, 25, prodnctum coefficiens est productum ex 114+ 42, et 155
  101. eisere
  102. denique si combinetur impari, productum est coefficies est Vg. 23. 25, paoductum coesficiem
  103. quidem deberet esse iP in 15, sed to seu 118, sed tamen ab eo detrahitur A2, quod homogeneum illier
  104. ox 18
  105. (A 121. 25
  106. Fi pu 2+
  107. +H 277
  108. n1 Y21. 27
  109. fr. 26
  110. +111, 723. 25
  111. (1. 3 4 28
  112. rt 113, uto revera assurgitur nelra 123
  113. videndrem ergo in applicationeq generalis (anonis eo speciem temper justo altioea destruantur
  114. esculica. ita semel cubando et sen qua uno aqpunturem ramonem tiberam a logesitum
  115. ntepemaltimae, etc. Nempe ulima calculi props alicujis dabis
  116. nea et ut sucetit divieo fit l0 usante
  117. unde per
  118. tt ex se aegrm alissuno exp
  119. F1ClI. 23aae)
  120. Coincidet Residu issue a
  121. easse HeumX
  122. 12. 20a
  123. potens sero compo-
  124. netur ex on
  125. equationtl ultimatur
  126. calculorum praecedentium
  127. diplicato fie)
  128. primo sollere velimus nimis alt
  129. hultie fers
  130. io. 12 ux t un ax ( H
  131. et 0 ita eleganter evenit, ut dum in und
  132. et fiil +10. 10. 22
  133. in 20X , 21 aXX + 2aX+ 232, item cum 20X + 2X + 22aC f25 a X 124a
  134. eaa stio
  135. XX) F 10. 11. 21aX
  136. pt avierus n
  137. rexFua
  138. paprer
  139. dutu et leo 2. inaentus
  140. tionis prim
  141. 22) +10102E ax +10
  142. 102 at
  143. simplex in altero 12 assurpt ad
  144. nota ulaeti palicata
  145. modum classs
  146. Eratum et co est simplex
  147. sed quia it utoblu alagit ad p a b
  148. tui vel attqui ternuni destrut
  149. = + 10. 10. 237f- 10. 11, 237
  150. 2d a 20
  151. divitentur per
  152. 1220 redit
  153. raa 2.
  154. 2. 2) = 12 1 29t 12.1. 21 ax (F 12. 1 22 aa)
  155. 3 savit ad quadratum et iL es
  156. habentar nili 103 et
  157. =0. se
  158. seu fiet
  159. destuentat aeliqua
  160. abest H, et renqua
  161. a et fiec
  162. si esset 11 20 fiuet Et proinde
  163. X = 126 = 10. 222
  164. - 20. 12 ac + 21 ax + 2 - 0 seu
  165. XX = qu 18.2 p rgaa = - seu 1 1 o. 2. 20
  166. 1o aa o exsecta eia sndet quanmenticnem
  167. 10. 22 aax + 1B. 23a. fit 10
  168. 10 1.33 ax (( 10.12. 23a4) = p 1 0. 12. 21 XX + 10. 12. 22 ax (F 10, 12. 234) Unde pront - 0 12.
  169. mcedenti
  170. uddettis proe
  171. do danir per 12. sel nam caleati paeceduts
  172. ido omcnia per 13.) sed est dificullas, quia ibi est
  173. 2. 10. 12. 20. 22, hic autem est solum 10. (2. 28. 22
  174. 42, 2i + 2. 72 2 23+ 2. 85 2125 +2. 42) 727 +2. 147, 21. 29 + ex
  175. vs + 3as
  176. +2. 48 2327 +eu
  177. 155 8 2525. + etc
  178. (115 20.25
  179. 3210) 15
  180. 1.425 E1. 24
  181. 18 101) 1. 20. 27. Liib. 8. 14
  182. ut pu. 26
  183. 1 ,t) 3. 24.
  184. Sed videtur hic caltius assursi quam oportat, ex. gr. in cum hon assurgi tur ultra 23. videtur
  185. perveniri ad I16, et 106, cum tamen non debeat assurgi ultra

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 202r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0399?run=74