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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 209r, page id 00068196:0413
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Duae Aequationes vel Formulae 814 X + 13aX + 12 aa XX + 11 a X + 10 a 20 et
24 X4 + 23aX + 22 an xx + 21 a X + 2070 debent habere divisorem communem secundi gradus.
Dividatu prior multiplicata per 24 per posteriorem multiplicatami per 14. Et divisor semper per
resimum, dones residuns sit  aequandus nihilo. ita enium attinus divitor qui est secundi guadis succedit
as n s
 qunti i sepemi
414 24 X) + 13. 24 a X + 12. 24a aXX. + 11. 24 a X + 10. 24 a
= 14. 24 = 14. 23 - 14. 22 - 14. 21 - 14. 20
+ A8 ax + 44 aaXX + 4+ ax + 4B a. Residuus per quem riditus 4X teque
 compendio 400. 33 4X + 00. 32 aa xp + ob 31
multiplicatus per 43 et fiet
23 qu 29  a
compondio scribita X + 2392 a
24. 43 24. 40. 43
+24 45X + 23, 43ax + 22.43 L Xx + 21. qu a X + 20. 43 a s
 24. 43 ax 1 29. DaxX + 24. 9 aex + 24. 40a)
Erit residuus (ab 22. 43. 43 xx (+ 21. 93. 43 ax + 2012. 43 ga, a
Qui dividere deblt dausorem paiem, mutsiplinetut i diriserpisepera
dividatur diifor novissimus pe multiplicetur per 122. 43. 4
A +22343.47 X.
22. 43. 43. B XX
in hac divisione, ut residuus evanesiat
=42. 2392. 415 +41. 2342. 45
24.470a X3 - 24. 41 43XX =24 40 aX
Enga X + 24. grea px tug. giax + Entoa
qremaex -qqx -qu. m a
t Residuns novissimus per . 43: a3. Et pro nova divitione fret
dividatur hcgar dirifor 43
+ 22. 4t. g2 9) aax + 22. 43. 43. 40 a fx
a  132...
+ 20. 13. 93. 43 aa
44 2 X a a
- 42. 2342.40
Murtiplicatur prior aequatiius per 40, et posterior per 41 et st subtrahatur a priore posterior, scet
et . 43. 1D . qrr esfe 0
-42. 2342.401
2. 14Xa240 42042. 42 (42
C80. 234243.
a
Engsia r, 1 . 9 p 20. 4) = 21. 40
Seu 1. 20. = 10. 21
2 , 11. 20, 24 = +10. 21. 24
sed quia etiam successisset novissima divisio sine residuo, si ordinassemus secundum a, et invertissemus
Et sufficit haberi duas aequationes
(+41. 2341. 43.) 40)
et explicando 40 A1, fiet:
nam altera quam ex destructione residui divisionis serundum X duximus, ad hanc reduci deveret
20. 4. 43 aa =0
processum ideo, etiam pari jure fiet 13. 24 = 14. 28
ipse autem communis divisor, nempe ultimus est
ubi qui expliceter primum 2541, fiet
+21. q
=-4r. 23q2. 4
oa
seu t22. 41. 43. 43. 9 
- 20. 43. 43. 43
= 23. 41. 42. 43
424. 41. 42. 42
+ 23, 40. 43. 43
= 24. 40. 42. 43
. - 91. 2342, 43
+ 21. 43. 43. 43
= 22. 41. 43.43
22. 43, 40- +20. 43
-42. 2342.40 - 40. 2342. 13
+22. 40, 43. 43
-23. 40, 42. 43
424. 40, 42. 42
+ 24. 41. 42. 43
sed hac aequatione carere possumus
10. 90. 13. 43. 2342.
inhric aequationibus serdatu
quia, nil juvat, praestat aequatio non explicata
nempe aeq. st in qua quaedam evanescunt. Ie
 im cralicetur aequ. 5i fiet
et jlanc ex pli corquae sunt 40, H, e Z
A. T2. S. B (N 12. 2.40. 43
ie  40. L. F. B3. 242
940. 41. 42. 43. 2347)
-20.20. 43 420. 40. 432. 23. 43
+20. 22. 41. 153- 7. 20. 40. 43. 2442
20. 41. 42.4743. 93 - 40. 43. 24. n
X. 42. 43244
explicetur, prsus explicentur prembra quae easden habent non explicandas, et 420. 41 42. 43 (23. 43 + 24. 42), quod dabit 
Haec aequatio dividatur per 43 (et ut quam commonssime
+20. 41. que  - 13. 23, 24. + 14. 23. 23 4 12. 12. 24 - 14. 22. 24,
20. 42.42, f. 20 13 + 124),- 15 10 2a +1 420 23 + 11 22 24 - 1 21 22
2 hy aq. s sit
+ 20. 43. B. 93 ac
27433 a a
rogd. 94. 43
= 20. 43. 43, 43 a a X
4 40. 2392. 43...
421. 45. 43. B aX
+ 20. 43. 43.13
+29. 40, 42. 43
formelium et irtuatium
422. 48. 43.42 aXX
42.  2342..
+21. 43. 43. 43 a X
= 2. 43. 43. 43 aX
1+ 22. 43. 43 XX
13qu. 13. 9. 24. D B ri to. n2. 43. 24 42