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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 5
# Folio 72r, page id 00068255:0143
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Extractione igituo fucta ex aequ. articuli 12 sejundum articulm B3, fiet
12. 512V + 129. 523Z= Sir23 ((11223CU - mm.) I. p (1213. 12913)). seu per compendium
H2. S12V + 128. 323Z + 109. 100 a =0. Et pari jure ob 8, p- 0 fit, 312.712D + 323. 723Z + 200. 200 a0
quae duae aequationes debent multiplicata ut debent coincidentiari, ne per eas reperiatur
Y vel Z, vel veZ. et fiet  112. 512. 200 aV = 123,523. 290 a2 100. 100 a 40 quam aequatio
nem jam identicam reddendo, fit 20: 105 3121712. Mp et 208. 100= 323,733,:, n35 Unde
15) Omnia ergo rducta sunt ad aequationes 5 et 6 arsiculi hujus, itemque  3 et 4.
1. 2, 3 g articuli q
vgrte tamen adhuc se imstendia quaedam
et  semper let u3 vel siem T1213, S12B, (1413, 52313 solum
comptendia
tantum extra haec t occurrit 13. 5C3 in valore lationali MI3C iC. 313 + 13OSAZ et 1X5B. 2
qud seli et  ieatoribus P, 
e . et H2B i si3 n sI. sit mBsB = I S) an ergo praestat tollere 113513
quam caetera. Nempe 11213 = 112. 513 + 1γ. 512 et 1213 = 125B- 113.512 ergo addeado
11213 F51213, :2) =. 513 = 123(3 +52313; 2 2. 123 Hinc 123, 112I3 +H3. SnB = 112. 123 Gru2My
1213 - 51213, 2. 512 = 113 = 12X13 - 52313; 2. 523AIc C5. 11213, 52.51213 = 5I2 NN , 5yV
monisin
quod si  velimus tractare eodem modo fiet:
mess meneurs erdussus
1213 = spH + (231 - si5 - 11. S13 = + 3. 523. (27- 195711215 2. 8. m B
4112. 512. 1532 112. 12. 52313)
et Rationalis aequatio destructis irrationalibus erit
utim ( us ib videguns an aequationes  4 articuli 9 possint
u
jam 
Ex aequ 1. s  fiat - 112. 513 + 13. 512-
-312. 7B3 + 313.712
fit 12. S13 + 113. se2 - 571
-123. 513 + 113. 523 - 1323
1312. Ex a9. fit 2, 3 73t313 723 3123
B pro 1, sit  1 a + r2bl. L  0 pro 2 sib ad 2a
129. 511 F 13. 522 - 5 23
pra dsic Matp = 3 pro
pro 4 sit na- nd 21 40
Ex isit na + 12b = 10 (1d + 14).  Et ex 3 est na - 12b = 30 (13d - 140) Erg. 2. na =  ( d 312C) 
deniqu pro 3 sit 4la atrb 3 30
2. 21a = 29 (22d 1249) + te su d un BC)
Et eodem int ex aequ. 2 et 4. fiet Et eoder
2. 12b 2 (0 (1d +14C) - 30 (13d -14 e)
222b   (23d1240) - 48 (3d-24e)
similiter suburendo ab aeq.). sustichendo aeq. 6. fit
et ex aeqq. 2 et A pari jure
Ex 7 et 8 fiet: (12 13,  + f 13, 22 24, 40 23d) d = (2 te 14. + 28 14, + 2 14, - 4e24) e 80
Et eodem mod ex getiosis (2. B n - (3e 1u- renn +. 40 21) d  = (- 1∞3. 1472 4 0, 4. 22 + 28 1412 + 20. 24 12) e
Eiqu ex 11 et 12 fil (10. 1 2) + 30.13 21 - 2a. 1125 - 40 241) (- 1014 2 - 2 19 21 + 20. 24. 12 + 40 24 12)
1apat - 30. 1722 - 20. 1712 , 40 11 n  (- 10 1 4 21 + 30 14 21. + 20. 241 - 40. 4 1)
prasabit Addantur in unum egus  et c2 jam 2+ 2 = sar 123B
11223.51225 (inise
2. 11213. 2313
et deni
Et subtrahendo
=11223.51225, 52312 (l mon)
= 312. 712. 1001. - 323.723. 106.. = 100,. 200ad
etiam  112. 512. 323.723= 123.523. 312. 712 seu 12. 512:, 123.523 = 312.712:, 323. 723
x articuli B3. aq3 et 4 quaecamus 51: 113, et 713: 313. Nempe ex aeg. 1. fit 51 F 4 Scus 5i + 4. 5u s.
4. 1123. 125. 512. 525- 11. 123,. 512 625. 1225. seu
((12 a  mte (4. s 51s
u2. 125. S1C. 325 = 112. 123. C. 312. 512. 123=Z
112, 123
determinatione consequamur
11223, 112. 123( to) 112. 125, 512. 523 H: aa piet
seu (4to). 112. 113. 312. 5(3 = 11225f. ) atih- H
faciamus 4.113. 123. 5123, 523-112. 123. 312. 523. 112257
4. 112. 123. 5p b23 11223 = 112, 123. 513.523f.tah
et fiet SeZ=  (112. 123. n2. 513 0(f. 2H) f seu =)  512. 51Z (f - 24). Et ob G, F-C pari
Mg. 12. 13t 31223 a: +ka -99  et (7mo) 713 = X1. 724g- 219.
turc fiet (670) 312. 323. 312. 123=
dum tamen res pentus ad rationales redacta est quia 12 173, Si2. 523 latent in 1122
112. 123512523(4aa - B) ~ 112. 52374 123. 512,2. 112. 123. 512. 523XA. Unde transponendo
fit. f112. 123, 312. 523ff = (9n0) 112. 525 aa + 123: SIkR = 2. 112. 143 512. sB Hk, ergto
tandem fit f f- 112. 113. 512. 523  ffi12. 523la 4- 123. 512h =4 51223k.
 Si faceremus () aha -Y = 0 seu f= -2R. quia ob eg. 5. non
licet
Ergus faciamus b, aAA- fs, Cd, = M. 523A + 123. 3. ita nulla fit nova determinatio
et x asg. 9 fiet 112. 123. 512. 52317 (112. 523 ab + 123. 512 ab seu =) 11223tb seu per n et 12
un fit B. 123. 512. 52 = (1310) bb, 4aa - f. Ergo res reducta est ad aegq. 5, et, 11 et 13. quod
jam seto com jam bb, ata- s compendio vocemus  B Nam  majus esse debet quam ata seu
d ps  quel. 10 113. 123. 512. 527 est quantitas
au atoremjam ex aequ. 1  sit B = B
112. 525 ab + 112. 52B  ab B) B 112. 515 + (P. lb) 112. 523 + B8. as bb
30 + 4 aabb3: 4habb. seu 12. 523 ub (B 2ab) ( (+ aalbb - β: etb
sergo ex 4 et 18
jam 3β2 b SB. qua et B aabb dabb sbb et B  b fona _, ergo fief
tanb
  a ia oses it siasit e s
sis reduci potest ad rationates
uie art asnse