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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 135r, page id 00068197:0269
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Quaritur modus efficiendi, ut productum ex 10 ~V + 12 et 20VD + 22 aequetur Bto
Cipse r= 31e 4 32e + 93, :, 40e+ 2. 40 4e + 45. fiet 1F= 1St 02SI Net OI
asa Eodemmodo licebil explicare 3ovrt 12.
porro ut nt prvtentus ext plicationis ae
XId ZL. SEEECXBIIEHOS
fiet 10b0+12 - 11 4 q ebqo Cr p V E. Heip. qi
408+4. 1d4 e + 6 40 2i e 1 4. 90 n C  41
Ut ae ergo productum ex dectis aequetur qu Eodem modo explicabimus 200  + 22
Ut ergo prodactum ex duohus sic explicatis aequitur quadrato, oportelit numeratore,
in se juricem ductos aequari quadrato; svia
finge v= 30 e + 31C+ 32, :40C+ 41 e r 42, siot Nam irrationalitas ista non nocet, cum caeteris
peractis resolvi possit
+ 10. 31. 318 F10. 2. 31. 32C +10 3232 : 405 + 41C +42
Bd 10. 31. 30C + 00. 2. 31. 31 e2 + 10. 2. 34 32C
et fiet 10VP+12=
+ 12. 400 + 12. 41C + 12. 42
pastemus si jim C (valoris i ipsius 10vV +12, aequetur quadrato, idemque fiat cum nlore ipsius
Ntn spator
utique productum valorum aequaevitar quadrato, quia
netrobique neminator est idem videamus primum compendii causa, an liceat quaesitum
nulmeratore valoris ipsius 20B + 2
assequi ponendo 30 =0 in aeq. 2. ita 10. 31. 31 e +2. 10. 31. 52 C 4032 32 aquabitur Ctr
100 eC + 101 C + 102
a C + 2a+ bb
a = 100 b∞ f102
ab 2 (100. 0d = 101
12 40 D 12. 41
et fiet 4. 10. 31. 31, 10. 32. 32 = (2) 2 10.31 32
12. 40 .n 12. 42
12. 41
12. 42
et fiet 40 = F.): 10. 3,. 32 +1. 42 = 4. 10r31. 31,, 4. 12
(6
Sed similiter 402 (D 2. 20. 51. 32 + 22. 4) - 4. ~. 31. 31 20. 32. 32+ 22. 927:, 4. 22. 1. 5l. 51
(2) 2 10(3r. 3r4 12. 41 = ( 2. 10. 31. 32 +12. 91 - 4. 18251. 31 10. 32. 32 + 4. 20 31. 31. 20. 312
quos duos valores aequando fit
4. 10. 12. 31. 31 = 4. 29. 22. 31. 31
quod si compendii adhuc majoris causa, quia sic licet, cocissemus ad huc 41 = 0,
=
fivet 40 = (4. 10. 31. 35 = 4. 10. 31. 32) (4) 10(62) 31. 42,: (4 12)
quid si compendii ad huc majoris causa (quia ita videtur licere) sccissemus aDhuc 41 = 0
fieret 40 = (4. 10. 21. 32 = 4. 10. 313 32) -(4. 10 (12) 31. 429:5 (4. 12)10. 324 12. 42
seu 40 = - 10. 31. 42,: 10. 322 + 12. 42 et rursus 40 = - 20. 31.42,:, 20. 35 12. 42
s
quos duos valores aquando, fieret 10 20. F 10. 20. 32 + 10.22. 42 = 10. 20. 32 +12. 20. 42
sed ita  autetrem non licere, fieret enim 10 - 20 10.22 = 12. 20
quid si 42 fecissemus 0, fieret 40 = (410. 352 32) + 4, 10. 1231. 32. 41 4 132 41( 410. 31. 32)- 4. 10. 12. 31. M2, :, 4. 1012. 32
et rursys 40 = 4. 20. 22. 31. 324 12. 417 - 4. 2022. 31. 42,:, 4. 2022. 32
quos duos valores aequando
fieret (4, 10. 12. 20. 22 52. 4D1 10. 122 41 4. 10 12 20 2 31. 32. 41)- 201 0
4. 10. 12. 20. 22. 31. 32. 41 + 12, 20. 2X. 41 - 4. 10. 12. 20. 21. 31 42
c 4, 10. 12. 20, 22. 31. 32.41 + 10. 12. 27.45 = 4. 10. 12. 20. 22. 31. 42
fiere 
C10. 22 = 12. 20
Ergo rursus esset 3 =20
Quid si in aeq. 6 et 7. faciamus 32 =0 fiet 40 = 12. 41 4. 10 3i 35 - 4. 10. 12. 31. 42,:, 4. 12, 42
aequ.
et rursquse qu = 22. 41 (488235 52 = 4. 20, 22. 35 92 : 4. 25. 42, quibus aequalis fiet 10. 12. 22 = 12. 20. 21
: 4 10. 12. 32 + 4. 12. 42. = 22. 41:, 4. 20. 2232+ 4 23. 42
ubi eursus 12. 20 = 10.27
quod nonlicet
seu fieret 10. 22 = 12. 20, quod minus adhuc procedit,
adeoque A. 12. 20. 22. 38 (44. 122. 22242) = 4. 10.12. 22 324 4. 12. 22. 42
fecissomus 40 = 0
feret (4. 10 31. 324 4. 10. n. 31. 32. 41 + 12. 41(= 4. 15 35 327 - 4. 10, n. 31. 42 = 0. seu
sed potius licet facere 10 = 20 adeoque 41 vel 42 farere = 0
22 = 12. 41 + 4. 10 31. 32. 415: 4. 10. 31 = 22. 4,2+ 4. 20. 31.32. 417:, 4. 20. 312 quibus aequatis,
id est 10. 20 = 12. 22 ut semper
ethoc faciunt ut arbitrer idem generalite futurum ex aeu. 6 et 7 adeoque eas non procedere
fier, 12. 29. 41 + 4. 10. 20. 31. 32 = 10. 22.41 + 4. 10. 20. 31. 32
sed ujus tammen experiendium.
non procederet recarre retinenda esset quantilas 30, qu sed quea tunc
retur ad quadrati quadtalum faere
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