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# Title: LBr. 454 · Augustin Thomas à S.Josepho
# Folio 22v, page id DE-611-HS-957479:0044
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Restat ut etiam priorum duorum tam summa, quam diff.s
it
nempe 4X + y2
X + 47
Summa 5X +5y = E
Diffa
3X - 3y = V
Hic neque quadratorum neque y numeri sunt quadrati. Proinde
C
Bachetus, Fermatius et Billy hanc duplicatam aequalitatem
rejiciunt ut menodabilem. Duae fortassis etiam ausa fuit
insigni Mathematico Bononiensium Petro Mengolo existimandi
Problema hoc in numeris rationalibus esse impossibile. Fg0
vero contemplans utrumque terminum tam. summa, quam
diffa superioris constare tam summa quam diffa corundem
2
2
quadratorum, nempe sumam 5X = 4X + X
diffam
3X = 4X X
Item sumam 5Y=
2
y +4y
diffam -3y = Y =4y
2
ita in methodum nirdi adaquandi quadratis superiorem
a
Substituatur igitur Z - 2y pro una incognitarum quantitatum X.
(N. -2y desumptu est ex ultima radice a
X = 27 serc 1X = 2y, diviso 27 per 1. cujus assume
monsolutionis interrumpamus. dabimus infra per Lemma)
stabitque superior duplicata aequalitas per substitutionem sic:
Suma 5X +5V = 5Z -20Zy + 25y
Diffa
 12ZY + qu
a
3X = 3Y = 3L
25
9
3002y +225y2 =H.
duc plrucem
Diffa 452= 1802y +225y = D. Subtr.
Diffa 302=1202y. Ruejus Producentes it a
quaerendi. Radix La ex 225y est + 15Y vel-15y, per hujus duplu
=30y dividatu -12027, it 4Z una pars producentium; demum
per 4Z dividatu 302 1207) habebitur altera pars 15Z - 30y