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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 5
# Folio 68v, page id 00068255:0136
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27) Hine patet etiam ib
S1. 113 aqu. p7 aricali 14 et valore 713. 313
0 et 7112 =0cessare valores ipsarum 73: 313, et binos valores
ipsarum 51: 313, quos quos, alias dedissent aequationes
11, 12, 13, 14 articuli 18, sed
loco eorum valorem prodere inde ras aequationes quatuore (723 12. 34 = (1mo) rG. 3pe 1712, 123. 312 e
ex 13tia, lire ex IIma 3 1 1723. 112. 323-1712. 123. 312 =0 vel e 28 ve
(1mo) 1723: 1712 = 1230312,:, 112. 323. et ex 13tia, (2d0) 1723: 1712 = 112. 323, :, 123. 312, et ex
12ma, B3tro) 1723 : 1772 = 523. 712, :, 5121723, et ex 14fa, (4 t0) 1723: 1712 = 812 13 :, . 523.712
Utroque modo colligitur 1723 = (+ C +)) 1712, seu vel summam eorum vel differentiam, nihilo aequari
ut jam habuimus cgrticuli 26 aequatione 9. Cter etsi valor hujus signi ex aliis determinam possit
per inventos jam valores ingredientium ipsius 1723 et 171E. Ex aequ. 1 et 2 huijus, fil 123, 312 = 112. 323.
seu ax aequ. (2 articuli 19 (6t0) 1252. 2372 = 235t.  1272 quae est aequ. 7 articuli, 26.. Et ex aegq. 3 et 4
ot. 122. 729. et substituendo valores ex aegus. initialibus articuli 19, fit utique
hujus fit 523. 7182
5). 12  (37) 28
125 seu 1254. 237, :, 235+ 127 = (8v0) 112. 323, : 123. 312 sed per aequ. 2
aes 1 (a) 31E articuli 19 est 115  112. 323, :, 125. 312 = 125. 237:, 235. 127 Ego
ex. aequ. 8 hujus fit 15 295t 1 1252. 237:, 2352+ 127 = 125. 237:, 235, 12. seu 125. 237 = 235, 127, ut
jam habuimus articula oto. Itaque aequationes 3 et 4 nihil dant, quod non jam dederitt aequ. 1 et L
Assumeramus autem ali  (aeterum omnis calculus ab aequatio articuli
18 inclusive huc usque erpori innixus fuit, sed felici, nempe in . 18. qu F aequ. 4
assumti A, 11223. 71223=51273. 31323, quod putarem permutando 1,5  9,  1 et 5 cum 3 et 7
unum ex altero prodire. In quo errami, sed feliciter. Nam hac una hypothesi assumta prodeunt omi
quae malto calculo huc asque indagavi Ae Nam per revera ex aequ. 13 artiuliia et 4 articuli 15, bit
13. 7 3 et 13 articuli i9 et ar 5 articuli 15 fit.  11223, 71225 = ) 2 15. 37, 125t 25, 17 + 2, 2
3E, 125 + 235, 117. 2372. Ergo posita, aequ. 1. fit 125 = 235, 127 + 237 = (Gto) 15 4 235, 123 - 299 2
quam aequationem effecibs expliate ponendo fies 15  (125. 12,+ 125. 2372 - 235, 127 (- 235. 237) = (125.128- 25. 233
 +95. 117= 235, 237) unde 2 125. 237 = (2), 235. 127 quae est aequ. 7 articuli 26, vel
297 Rocolligamus jam inventa (1mo) 125. 237 = 235. 127 per aeg. 7 articuli 26, vel  jam
aequatio 6 hujus.
+ en aequ. 4 artiC. 25 est 112 +512 = 312 + 712 Aa a - (2ho)
seu 323, 112. 123a - 15. 239 2 adot 125, 312. 313 a - 3). 2372 et ex aequ. 6. artic. 25, 113+5 23 = 3134 723
per aequ. 4 articuli 18.
Ecqts 312, _ 112. 122a + 15. 125 . 12 5e. 313a + 37. 12722 jam vero antea ex aequ. 8 articuli 16 vel
aequ. 2 articuli 19 l 1232. 312, :, 112. 323 = (4t0) 235. 127, :, 125: 237.
Accedunt jaem qu ex
 ex aeqq. initialibus articuli 29, vel ex aequ (H B. 13. 14 aegg. 9 et 10 articuli 14 itemque aegy. 1. et 2 articuli 15
valores sequentes 5i = (56o) - 15. 235 : 123a et 523 = (6to) 15, 1252: 112 a et 712 = (,mo)  ~ 37. 237: 323a
37. 127: 312a  Deinde ex aeq. 17 articuli 19, 513: 113 = (9n0) - 15. 1125. 235, 125 -235,:
et iD 713 313 ex aequ. 6 articuli 15 fit 713: 313 = (10 M0) - 37. 127. 237, 127 - 2373 :1, 312.313, 127 +237. sed
et in q. ex aequ. 10. artic. 16. fit 152. 125t. 2352 :, 372. 127, 2992 Hm0 s A : H H = (+223, Imon;, ester. 123 139 C
et 723 = Bv0)
= (51225. 1L3  100 H 200MM, :,  2 H213. 13 13 id est per a94. 5 et 6 articuli 1(7, 
articuli 17, (11E 232 (100l-200 mm, . 113. 513): 31223 (300 nn -200mm, : 313.713). sed per aequ. 14 articuli 14
2y 112. 123, 125 + 235
or quem valorem inserendo
in valore ipscus IN: AI fet et duos valores aequando, destinitur utrobiue 15,37 et fi R 125. 235, :, 127, 237
et per aequ. 5 articnli 15 est 11223: 312232 = 152, 135 - 235, :, 373 127 -23
= 313.713, 125-2350 (105 - 200mm) :, 113. 513 127 2- 23, (300nn -20d mm) seu fit tandem 313. 713;, 113. 513 = (11 mo
12) ((125. 235, 125-2371): (127. 237, 125- 2351)) (300 nn -200 nm, :, 100 11- 208 mm) fuide quae scripta pagina aversa articuli 261)
sed  ex aequ. 1. hic, sequitur esse 125. 235, 127  - 237 = 127 3377 125- 235 vide calculum peractum
pagina aversa articuli 26. seu est  12720237,:, 1252 235 = 127-237: 1252 - 2392 seu denique
et Z13 per aeq. 9 et 10
et similiter
113. 513(5 - 15. 115, 125. 235, 125 - 235, 29, 112. 1239125+235 = - 15. 1152, 125, 235, 125- 225 3: 4 112. 123, 125 - 255
 et post per aeq. 13 fiet
odnna adonn
3172. 71s (6 135. 112. 15. 127- 13 
152 313, 3232 125-2354 = 1124
325 ponendo per aeg. 4, 123. 31 : 112 ert 115 1233:, 315. 325 = 112 5:, 312.seu fiet
,2s. 277 sobma. vpu d 31 2. . 1. g
ex qui artic. 16 fiet
iults insiquis qu s canticuli 17. fiet 12. S12V + 123. 52)E = 11229 Spoll 2orum, c2. 113. 513), ubi
1300 nn -200 mm, 15=it. uu
1t, 12y 522 vatorem per ea 14 articuli 14, et
ratorem ex aqu.15 Exius et ponendo
(275 ergo fit S13: 113 = 15. 125- 238: - 12. 13Irr
et pari modo 713: 1132- 37, 12 - 237:, 312. 323ser et per ( 11, aequ 15 sit as 8 113 51 = 1, 13G 125 155, 12 13 
per pro 133 substituem
125 235 12 +295
q et a est 513: 1Z2 -15. 125. 235. 125-232: 1112. 1231 1
(12, 31Z, 523, 71, 712, 723, consideremus, ex aequ. artic. 3 esse _(m) 213 = 519 + 313 7 13 13
512 + 312 = (280) 312+112 et 223 = 523 +323 = (3tio) 723+123. Hunc explicando inventos.
et C2 r3: 513, (21) 15 27. 323 i 155
Ias duas aequationes conjungemus cum
93 235 4 31 213. 323a  37 125, 15 1 1 13 valores iteram ipsarum si, 523, 812, 723
(30) Habilis jam valoribus
prodeunt it pli summa aequs. 1 pro literis 8, quantiratibus 8, seu potius pro rationibus, 7. Quia in ae99. 2 et 3.
et similitur l 212-
uticuli 29, quibus si acceda
erticuli 29 signa sunt apubigua, adeo ex aequ. 2. fvi ibi, facianus  112f + sif = (4to) 312 9 + 7129. posito 9
valores in artic ag fiet
et 3. conjungemus cum tribus aequ.
itatem signo affectam, adeoque gy =1 g, idenque ff =. et ex aequ. 3 ibi faciamque  12yh +513h (sto B2k 1r23A
 itidem sunt unitates signis affectae
512 = 2(2- 312 et 712 = 212 112 substituerdo in aeg. 4, fite
3EB +9) 2(f-9). Hinc si f et 9 sint sig nondiversorum
odem modo (7mo) 213 = β27 -123) (h+K): (h- K), unde
112 F, +212F -3l2f = 3129+ 219 - e129 seu 212 ver
 conscatit aequationi l’artiali 2g. posito inroe intria ex aequiat u et 
125+ = 235 : 1252 235 2 17 = (12mo) 127- 237: 127. 237 Unde tandem fit (13tro) 313. 13, :, 113. 513= zoonn- 2odinm, :, vooll. 20 en
nisi faciumus 125 23t =0 et n 23X a0 quod minus se jam in hac eu Ex hac aeg. tollamus
et 315. 713 = 37. 3134, 127, 237, 127 - 2574,:, 3122. 3257. 127 - 251. Unde per aequ. 12 o
itemque 115. 5132 = 15. 113+, 125.3359 (25- 2357, :, 112- 123, 125 -235
 Z 12N. 127 esC
100 l - 200 mm, 37
fieret