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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 186v, page id 00068195:0372
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fiat 20. 100 +02 300 + 11. 100.300 = 402.  ubi 2 in fine ob duos 1 otales
10. 100 + O1. 30=8
Et 2. 20. 100. 101 +2
10. 101+01. 301 = 00, 411. (4 30101+02. 30 4 11. 101. 301 = 00, 912
scilicet permutatio interm, et.. O inhrinetalib
et aequando valores 2402. 201 + 411. 402 = 2 4012. 200 + 401. 201. 200  + 401. 4012 + 40,2 201
Ergo 200 = 12. 4  401) 201 + 411. 402 - 401. 4012,: 9012 +401. 201 qui tersins valor
si aequetur secundo, habebitur aequatio in qua 201 assurget ad gradum secundum. Sed videarum
an r deprimere liceat sed deprimere dem licet melius hoc modo: Sint duae aequationes
00. 200 + 00. 40]. 200 +004920
205 + 401. 201 + 413 20
2.00200. 201 + (929 00. 401. 200 +90. 4012 =0
ba 00. 9I1. 201
ubi aeqq. 12 oriuntur ex destructionibus terminorum
auserendo aequ. 2, a summa aequationum ieth fiet
(
sae
200 +201  2200. 201 = 4012- 402 seu 200  - 201
(5) CB -  401 +  1(401. 401 - 4. 402) sd si conjungamus aegqu. 4, 5, 6
 habemus solum duas
2
20) et 26) - 1. 411 + 1 Y(4 11. 411 - 4. 4 12)
200 + 201 vocando et 2001, fiet
se d sint interventus irratio seid a
Addendo aequ 1 et 2 et 3
20 et 4uo 4 200. C + 401. 200 4, 4: 201 + (2. 401. 411. 2011 201 = 4. 200. 201 + 4012 + 2. 2 e 
eu -401 (401. 200 +402) 4411 (411. 201 + 412) (- 401. 411 (401. 200 +411. 201 4 4012), aequ.
(D (401. 4u (200. 2101) + (20, an. 200 + 402. 412) + 4012 4. 4017 (401. 200 + 2 1. 201 + 4012)
ita res omnis reducta ad 200 ut 201. non nis
simpricem gradum facientes. Nam ordinando
401. 200 +401 402 qu. 2. 401. 411. 200 + 2. 401. 211. pu12
2. 401. 4112. 201
40B. 200 2. 401. 41. 200 + 4. 401. 912. 200 = 4. 4012. 401. 200 + 40 (. 402 = 4. 401. 4u. ton + 4 402 112 ( 4013 - ( pon
4113. 201 4912. 412
413. 201 - 2. 401. 412.201 4. 411. 903. 201 - 4. 4012. 411. 201 4 411441
compendio inde fiat 830. 200 +840. 201 +801 =0 et 690 200 1640 201 + 601 = 0
et loco aequationis 0- 200 - 201 - 1 (4012 - (402+ 412)) scibatur 200 - 201 = 152,  = 0 vel
generalius 630. 200 + 640. 201 + (60) = 0. unde fit - 200 =+540. 201 + 501, : 530 = 640. 201 +601, 63
ergo 540. 69D. 201 + 501. 630- = 530. 640. 201+ 530. 601. Et 20 = 501. 630- 530. 601, :, 530. 640 - 540. 630
Et pari jare 200 permulando. 4. et a3. fiet 200 = -501. 640 +540. 601, :. - 540. 680 +530.640
ubi jam explicationefacta et pro 630, 640, 601, ponendo +1, - 1, - X2, fiet iunde ut
200 = 501- 540152, :, - 530 -540 pt 201 = 501453015E, :. - 530-540 quos duos
C + qu (530+540)4012
6= 2. 501. 501 + 501. 5301522530. 540. 52   A (570+ 540) 501 (401 4 91) - (BB 0n 20) (210530 - 401. 340) 152 7
valores substituendo in aequatione rda, fiet
ubi magnum habevitur compendium, si destnatur 152, quid fiet
si faciamus 2.501.530 - 2. 501. 540 = (530+ 840) (411. 530 - 401. 540)
2501. 540 152
atque adeo 2. 501. 501 - 2. 530,540 (9012 - 402 - 412) = (530+540) 501 (4014 411) + qu (530+540)4017 =0
sed haec omnia forte brevius consequemur, utendo Canone ilum a me posito pro tollendis literis ex duabus
aequationibus secundi gradus  Redeamus ergo ad aequationes 1,2 et 3. Et per aequ. 2. erit
261 = - 401 . 200 - 4012,: 2. 200 +411. quo valore substituto in 0g. 3. fiet
+ 401. 401. 200. 200 + 2. 401. 4012. 200 +40121. 4012
= 2. 411. 4012
+ 4. 411. 412
Unde ex canone alibia me reperto fit.
=0 seu compendii causa 00 + 8t. 200 + 82 = 0
cui conjungende aequationem primam, quam umfor
mitatis causa sic scribemus 70. 20047. 200 +7
80. 10. 82. 82 + 70. 7. 31. 8 -10H. _ =0 ubi res plurima
+72, 12. 30. 80
71. 71. 80. 32 =71. 17. 80. 
= 20. h. 81. 82 =0 sed fortasse
2. 70. R. 80.  tantum +70. 72818
H. n. Ve. B fiet s
coptraheretur, si fieret 1B. et - 7280 =0. restaret
et optimum quidem videtur
aq ita foret 412 =  + L 401 41 - = 40i, ob 20 = 0
fatis ert ad contrahendum facere 82 vel 80 =0
82i GI = + 11 + 11.71 - 4. 70.72),: 2.10 seu 8 g = 401 + Y(401. 401 = 4. 402),: 2
401 + 3 (40i - 2409)
70. 82. 32+ 72. 81. 81 = b1. 81. 82 = 0
4012. 4012 - 4112. 401284112 (2401. 411 - 4401
2. 401. 4012 - 2. 411. 4112-401. 4112+ 4 (.3, 401. 411 -  405)
401+ S(40- 4. 402)
seu 4012 = 4112. 4012 - L 411.401 + L 411.401
Hinc aequatione plana habebitur 4012 N llideamus j 411. quae cum 4012 sola ex ha cinculum radicale est
Aia = 2. 401.9012 - 2. 411. 4012 (= 401. 413+ (2) 401. 4112 - 41. 401
bendit ad cubum, quodest sisto altius
 sed videndum an ex ipsis 402, 401, 411, , 4012 possitit inveniri quantitates 100,300, 10130
Nam 20 = (00 . 81) 461 - (10: B1)100 301 = (00. 1) 411 - (D: () 101 sid musus
et quidem plane. Et apparet rem succidere
Ex qua et unde 2. 20. 100. 101 + 2. 02.  qu (oN: 31) 401. 411 + (00. 10: 012) (101. 401 + 100. 411) + H1. 100 00: 01 ) 41 br1. 100 (10. 8,) 101
per et
nteg adhibitas ubi pro 100, 101, substiturndo valores fit relatio inter ipsas
assimulas 401, 411, 402, 4012 nam sufficientes adsunt siliceret facere
Si liceret facere 902 =0, diretur 300: 100 ex datis et fiet 200 = - 401
esset aequationi I. Hinc ex aeq. 2 fieret - 2. 401. 20) - 40, + 411. 201 + 4012. Unde fiet
201 = 4012 - 40i,:- 41 + 2401 = - 411 + Y (411 - 4. 412),: 2
ex 402 et 412 habetur
hons satis factum 300 + per 100, ita
quod si faceremus
et ficet tandem
habentur 20, et 30
101. sed praeteren
4V- 4. 412 =0 duretur haberetur 301: 101 ex datis
4012 -, 401 = 4112 + 2. 401. 41 sex A6 q0c qui q gr unde elici
poterit ratio 14 ad 101 ad 100. sed intis Haec succedent modo ne fiat 300: 100, ut 301 ad 101
vel 301 ad 100, ut 200 ad 100. Et primum si sit 402 = 0 f et
di
2; 100 = - 11 + H(1 2- 4. o 20.02), : 2. 02. porro ob 415 - 412 = 0 fiet 10. 10124 01. 30 i + 2.10. 01. 101 301 2
4. 10. 1012 +402. 305+ 4. 11. 101.301 sit 4. 20- 10 = 3 Et 4. 02 -0 = 39 Et 4 . 1= 2. 10. 01 = 2. 31. atque it
neque fiat 101ad 100
g in 31. 1012 4 33, 301 +, 313. 101. 301. unde 201. 161A = _ = 373 + YC3132 - 31. 33)
nisi egitis cesibus
100 sit 301 = 112 101:
semper in fallor niabilibus coincidit cum
bre substituto, . 000. 1  100
+2. 401. 411. fro1310. 10d. 100. 101 +2. 62. 112. 102. 100. 10141
e ea a ui is