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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 5
# Folio 67v, page id 00068255:0134
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19) Antequam evolvamus aeqq. 11. 12. B. 14 articuli 18,  explicemus aequ. 8 articuli 16. tollendo 512, 323,
712, 124. Nempe per aegy. 9 et 10 articuli 14, et per aeque 1 et 2 articuli 15 fiet (1mo), 512 = -(15: a) 23512: 123 et 523 15. a) 1eseg: 12
et 712 = BF  - B71a) 23712: 323 et ry23 = (7. a) 12G25: 3it. quibus insertis in aequ valoribus in aeq. 8 artic. 16 subistitutis
quae erat 112. 512. 323723 = 137. 523. 312. 712, fief -112. 15. 27612, 323. 37. 127152 - 12g. 1, 12535. 312. 37. 23712. seu fiet
N2. 3237, 235122. 12725= 1232 3122. 12525. 137 12 sen 12. 323;, 123. 312 = + 12523. 23712, :, 2352. 127 25 = 33. Xn:, 512. 729
et 112. 723: 123. 712 = 112. (12723: 312) = - 123. (23712 -323) se uE 129 13 12 = 112. 323. 12723,:, 122. 312. 23712. Unde per 2
5x3. 312,27512 323. Et Porro u12. 512, -, 123. 523-
S2Z12 23512, =, 1232, 12523 =(mo) 31. 712, :, 323. 723
eris 112. 723, :, 123. 712 = Ato) + 12523. 12723, :, 2351r 63712.
et 17. 512, : 312. 712= -112 (15: a) (23515: 123), : , 312 (37. 4) 23112. 323 = 112. 323. 15. 23512, 5, 123. 512. 3]. 23112. se per 2
(15. 12523. 23512, i,37. 12725,. 23712 = (9n0) 123. 523, :, 323, 723. Et 112. 313;, 623. 712 = 123. 312,: , 512, 72
(20) Ex aequ. 13 articuli 18. At per aequ. 17. articuli 14, fit - 7123.  21 1 4 712 St2. 3C5,:, 1723. 123. 312 - 121 . 143. 5  
23 12523. 23512, 12523 -235127:,  12523 + 23512
itidem quaeri posset, et 112. 723,; 523. 712 =. 123. 312, :, 5.2. 323
-(5, a). _. 12523, 23312, 12523 -2351, :9 112.123, 12523+ 23512 su
L7123, 125232, 123. 312 + 7112. 23518, 112.323,:, 1723. 123312 - 1712. 112323=
127 2),: 1723-1712 (1i2. 322 seu (+ 
. 12717do) 1Stosa
vel denique + 7123, 12523, 12723 f 7112. 23512. 23712, 1:, 1723, 23512. 12723 f 1712. 12523. 23712
vel + 1n3. 25 E x a u.  ( 
13. 712-1712. 512.723,:, - 7123, 123.712 +7112. 112, 723
Unde post destructiones 12523. 2ysI2,:, ~B125 23H23BI2 2, 1723. 123. 312 e 15 27. 23112 - 1712. 17. 13. 2952. 1275, :, 4 7p p. 123. 82. 237122 + 712. 112. 315. 12725
5: a)12523, 23512, 125C3. 23512, i, d2 423, 11523+ 23SI 15. 12925 72. 22712 15  sp. 22. 127 25
UIB EY aequ. 14 articuli 18 fit per ac
bel Denic 4t) 125a3 - 275125. 1 12523+235I = 1723, 12523. 23712 4 1712. 23512. 12723, :, 7123. 23512. 23712 +7y2. 12523, 12723
iculo coprobavimus
1723. 12523. 2371241712823512 12123
. . . . . . . . . = 17 2 3. 125 23. 2371 ( - 1712. 429. 
(6t) 12723- 23712:, 133t 25t12 = 1723. 23512. 13723 41712. 12523. 23712, :, - 7123. 23512. 234712 7112. 12523112723
erdantando 15, 3,7
5t) 1272323712; , 12123+23712 ( = - 7123. 12525,12723(L 7112. 23512. 23717
e 1723. 23512. 12723 + 1712. 12523. 23712
Et ex aequ. 12 artic. 18 fit per ∞eg. 6 artic. 15. ad instar aequ.q
tem illius coincdere numertori hyius, Itm   et nomina oqu   alis
123, 12523, 12723 47112, 23512. 23712)
Has Utamur jam egg. 2, 4, 5, 6 articuli praecedentis et dividendomultiplicemus aqu02 et 6. nvi-
in labenta deptris n aequ. 4 et 5 numeratorem illius coincidere nominatori hujiu
(200) 12523- 23512,:, 12523 t 235125
Ubi notandum pui aeqq. 2 et 6 no
1schCZ - 12525. 23712 15 - 23512. 12525 12725 4 235I2 12523. 23712 +2723
Sed nondum hinc aliquid magnopere apparet
12323. . ZZIIL. HB 4. 125C3. 27SI2. 23712.  +23 51. 25712. 12723 +23515. 21712
12515. 1272524 12523. 23712 127234 23512. 13523. 12723
+12523. 12723(12523, 12723 27712 4 23512. 12523.127154
si aequ. 4 et s eodem modo conjungas ut aeqg.
et  prodit idem nempe aequ. 1
(22) Quo brevior autem imposterum sit scriptura pro
et ex aequ. 1. articuli praecedentis fit: 200)
12523, 23512; 12723, 23712
Conjungamus jam et aega. 2 et 5 articuli praecedentis, considerando
 tm i ifferre signas,
523. 275. 127 + 1712. 125. 237 ideu podis si dividas aeg. 
712. 235. 127 erq cpant.
Ex his jam fubus equatur nibus articuli
deu piait quod aequando et 
(lujus nempe 2, 3, 4. solvi possunt omnia
eadem praesturi possunt quae ex aequs. 4, 5, 2, 4, 5, E. arliculi 20. quoniam ex eo quod composita diverso modo
et fis oteo dividendo s per aegr fit 
susterestat aequemus aeqg. 2 et 4, quo case
7123: 7112, et 1723. 1712 quorum valores substituti in aeq. 4 dabant aequationem ali illis liberatam
7127. 115. 127 47112. 235. 237
Haec ergus ut praestemus pro, aequ. 2 pa artic praecedentis per constendrum scrbatur (e
1723, 231.12771712, 125. 237
ndicum  est leas non nisi tribus aequisollere
100, 210X + 100. 20, y. seu X: y = op. 20. it o 2
+(25 + 235, 127 + 237)125.127 + (125- 23531271 57) 195. 137
Et pari modo ex aeq. harticuli praud. 1 B 4 (ir5 +2)5, 127. 23 ) .3 5. 127 4 (125 335, 12 H . 11  25 57 4 ande X - + 31 4d
noK LIBV,: 210X+ 201y  100, 200
indi Adeoque restituento priores quantitates 2
1(125. 235, 127 +231) 235.127,. Cu p2oG 17 - 1 ) 125. 13), uti tip 2 et R - 7123 (t  - 7112
articuli, 20 icet enum illa non sit comved homoschetia, tamen vel ide
quae obssant, aut prodibit quod sicebit duplicare percuutando et
7123 et 171E tolli in aeque. 4 artic. p 22
et ex aequ. 2 et 3 713 = 9 7112 (17A= Z 1723
D-struS, etcL 6, D, 8. Gsehabent
ata meVI mostimoci
25 1u, (125 - 236, 17- 257) + 23 5. 23, (125 F235, 713, 6- + (125 + 235, etc
Cinsirk niress, urtn) F 135. 2Bus, antIE((125H235,127-237) 235. 127 4 C125- 225, 127 1297) 125. 257
1((125 + 235 177+ 297) 15. 127 4 (125. 135, 127 - 237)235. 237
ys127 (V2st2y5, 17 - 237) 235. 127 425 - 135, 127+ 237) 15. 2y, )
5. 27.G +u5. 235. 23F + 295. 237. 127 f. 235. 251
4 12s. 23 (125 - 237, 127 + 23)) 235. 127 + (123 +235, 127- 237)125. 257) cue
odeamue an non nihil contyahere liceat C = +, 1251. 127 = 125. H7. 237 - 235. 125. 127 225.12i2t 
D = 1252 127 +125 127. 237 + 235. 125. 1272+275. 125. 127. 137 +125. 235. 237. 127- 125.95. 23,-235. 257. 11 1275.9)
8 = 7, 25. 275. 127 = 125. 235. 127. 237 +2352727- x352. 127. 237 + 125. 237. 127412522372- 235. 125. 237. 127 -235. 125. 237
 = 125. 235. 1272 4 115. 235127. 237 -235t. 127 - 235. 127. 237 4 125. 237. 127 f 125. 237 +235. 125. 237, 127 = 235. 125. 737
rnnsae fr u2 23512. 25712 um n am mst
(12523. 423512, 12723+23712)12523. 127234 (2523 - 23512, 12723 - 25712) 23 512. 25712
cem prodit mo) oratroon 
y123 4(12523 -23512, 12, 23- 23712) 12523. 121
Qua bavi, autem imposterum
137I