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# Title: Ad majorem Dei gloriam. Theorema Arithmeticum (shelfmarks Leibn. Marg. 88, Stück 5; Leibn. Marg. 88)
# Folio 7, page id 827668708:0009
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Non ergo possibile est inrenire rres numeros primos incer
se, quorum differencix, quadrari, ec differentix quadtato
rum, quadrari.
Sed Aa, b, c, tuerine assignati non primi, accipiatur eorum
maxima communis mensura: gux profecto difterentiarum
a = b, b = C, a =- C, COMMUNIS mentura eA quadratorum,
iplaque quadratus numerus est. Ideo enim a, b, non lunt
primi, quia a, relolutus in primos, re hac hpg, ec brelolutus
in primos, re tiac hps, habent aliquem componentem com-
munem, putahp: ec differentia a - b, est hp g -- hp5: Ouxe
non porest esse quadratus, nisi ec hp, SEquadtatUS, e 9 - 5,
sIE quadracus: alcerum enim sinc alrero non (ufficit. FC CirO
iplorum a, b, c, communis maxima mentura quadeatus, qux
dicaeur h2.
Ec dividaneur a, b, c, per h2, ve hanc primi numeril, m,
n: ec differentia, quadeari a = b, b = c, a = c, dividantur
Per h2, VE Aant l = m, m - n, l = n, paricer quadrari nu-
Mmeri: item a2, b2, c2, diridantur per h4, ve tiane quadraci
l2, m 2, n 2: e differentia quadratorum, quadraci a 2 - b2,
b2 = C2, a2 = c2, diridantur per h4, Ve Aanc l2 = M 2,
m 2= n 2, l2 = n 2, quadraci numeri.
Sed hujusmodi priminumeri l, m, n, alsignari non possunt,
ve ostenlum est: ergo nullomodo poruerunt astignaria, b, c5
quorum differentix a b, b - c, a = c, quadrati; e quorum
differentiae quadratorum a 2 = b2, b2 = C2, a 2 = C2, qu2-
drati. OMare, ec.
LVAN ZDM sic erronea propositi nostri Problematis allata
solutio, quaesiti tres quadrati sequentes indicabunt.
52357727962243 35097474586243 5755474489249.
Latera 2288168
1873432
2399057
Intervallum primi es secundi quadrati est 1725965337600.
cujus quadrata radix est 1313760.
intervallum secundi es tercii quadrati est 2245727030625,
cujus radix 1498575.