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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 201v

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 is also registered as fol. 202r; its text is given once, here.

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. suamncaliani
  22. Quaeramus praeterea residuns.
  23. tet berdiaa
  24. s
  25. ex au
  26. 10X LIIa
  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 + I1aX + 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. - 10. 12. 20
  61. -10. 12. 21
  62. + 11. 12. 20
  63. similite raeqrationem priorem datam, et aequo 2) conjana
  64. 10. 12, 22 X +
  65. seu = 10. 1
  66. = 2. 12. 20
  67. I. conjungere ejus inverso
  68. 1o t H.2 B
  69. (10 12. 22. 23) 10. 1 . 2 =10. 12. 21. 22), 10. 1. 2. 2 (C 10. 12. 16 23 10. 1. 1. 20. 23 + 10. 123. 20. 2 PoV. 15. 20. 22 -16. 11. 12. 21 23 +18. 1. 2t 3 410 4. 1. 4 - 1e se M 21. 2e to site ro quiao 8. listi ton e . 3
  70. agn. 10. .25 (+18. 12 22. 19 (1 5 12. 24. 13) + 10. 11. 12. 21. 23(-15, 12. 21. 22f 10. 13, 2824 410. 11 12. 23 + 10. 11. 12, 2822 =11. 123.20. Qu.aqvatione defantus destnctis destruendis duisa per i prodit
  71. FI. l. 20
  72. 18 20
  73. +8. 12. 25
  74. . o
  75. Geerali via, ien usi dita aequatont 104 XBE, = B e ron A 2B AuX L2EXL = 13 7d +2A X +etu pestumus touco X, soum in aequ. posteiore pro X poreraer - 1B. unde fiet a
  76. = 20 - 19 + 1gue n - 1 13 4 1 24 - 1825 + et e vel 18. 20 - 10. 18 al + 1. . 22 + 18. 10 3 23 - 11 10 24 + tc aente periveniatur au plae qui ex terminus altimus.
  77. se sint jum intre agus. D. + IX + 1BXY - 0. et 20F LIY F LEAX +23 X + 14 X 425 X + 36 X + et = 0. Eit XX = io adege N= 2 1 + sia1
  78. quo valome substituto in aqu. aleradata fist 20 B. v + V2- N 23+ 1 2 1 - 1 25 + erc
  79. 20C - 1, 21 + 22. sl 23 + 1 1 25 + re s l 17 ten = sa2. 21 + _2 B + 42 95 + 82 27. Quod si san detimus tollere irrationalem, fiet
  80. 20 - 11. 20. 21 + 2, 1 + 42. 20. 22 - 2. 18 20. 23 + 2, 1 4+ 4
  81. x
  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 H3, uti revera assurgitur uetra 123
  113. videndrem ergo in applicationequ generalis (anonis ao speciem temper justo altroea destruantur
  114. iscubica. ita seme cubando et seut quid anto aequaturera ratomlem liberam . X logtqutum
  115. atexemaltimae ete. Nempe allima calculi propo alicujus dabo
  116. nea et ut suceit divieo fit l0 usante
  117. unde per
  118. utto ex e aeqam alisuno eru
  119. F1ClI. 23aae)
  120. Coincidet Residu issue a
  121. potens sero compo-
  122. netur ex on
  123. equationtl ultimatur
  124. calculorum praecedentium
  125. tiplicario fiss)
  126. primo sollere velimus nimis alt
  127. hultie fers
  128. io. 12 ux t un ax ( H
  129. t o ita eleganter evenit, ut dum in und
  130. et fiil +10. 10. 22
  131. in 20X + 2IaXX + X+ 25a, item cum 20X + 2CX +. 22aCL +25a X 24a
  132. eaa stio
  133. XX) F 10. 11. 21aX
  134. pt avierus n
  135. rexFua
  136. easse HeumX
  137. 12. 20a
  138. eptinum
  139. papaer
  140. ut t opu 2. iacentus
  141. tionis prim
  142. 42) + 10102E ax + 10
  143. oru at
  144. 2. 2 = 12 12 204 121. 21 ax ( 1
  145. vel atiqui termini destut
  146. = + 10. 10. 237f- 10. 11, 237
  147. 2d a 20
  148. simplex in altero 12 assurpit ad
  149. nota ulaeti palicata
  150. divitentur per
  151. 1220 redit
  152. raa 2.
  153. modum classs
  154. seu fiet
  155. Ehratum et co est sumples
  156. sed quia it utoblu alagit ad p a b
  157. 3 savit ad quadratum et iL es
  158. habentar nili 103 et
  159. =0. se
  160. 10. 22. 2C
  161. destuentat aeliqua
  162. abest H, et renqua
  163. a et fiec
  164. si esset 11 20 fiuet Et proinde
  165. X = 126 = 10. 222
  166. - 20. 12 ac + 21 ax + 2 - 0 seu
  167. XX = qu 18.2 p rgaa = - seu 1 1 o. 2. 20
  168. 1o aa o exsecta eia sndet quanmenticnem
  169. 10. 22 aax + 1B. 23a. fit 10
  170. 1923 AX( 10.12. 2344) = +. 10. 12. 21 XX + 10. 12. 12 ax (4 10. 12. 23aa) Unde podit ade
  171. mcedenti
  172. uddettis proe
  173. 2. 10. 12. 20. 22, hic autem est solum 10. (2. c8. 2
  174. 42, 21 + 2. 42 ∞23+ 2. 82 2125 +2. 41 227 1 2. 47, 2129 + ex
  175. vs + 3as
  176. +2. 48 2327 +eu
  177. 155 8 2525. + etc
  178. (V1. 20. 25
  179. 3210) 15
  180. 1.425 E1. 24
  181. 18.61) 11. 20. 27. Fib . 8. 1a
  182. ut pu. 26
  183. 1 + ) 3.24
  184. Seb videtue hic altius assurgi quam oporiat, ex. gr. cum non assuru im ultra 23. videtur
  185. perveniri ad 116, et 106, cum lamen non debeat assurgi intra

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 201v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0398?run=74