Dear Julio,
thanks a lot for your hint to the footnote in DES I, p. 421 which I
overlooked presumably because I was so frustrated by his remark, that Roth
"wrote an unimportant algebra in which he treats of equations of the third
and fourth degrees". DES contradicts his own judgement of the unimportance
of Roth's algebra in vol. II p. 474 by refering to him as the probably
first who formulated the fundamental theorem of algebra. What DES meant by
"treats" in vol. I p. 421 is not clear. Roth gave in the first part of his
Arithmetica Philosophica Cardano's solution of the cubic equation
respectively of the different types distinguished by him. In the second
part he solved the 160 (at least mainly) cubic problems posed by Faulhaber
in 1604. In the third part he had formulated about 90 problems leading to
equations of degree four to seven without any result not to speak of
methods and ways of solution.
Interestingly DES does not repeat in this updated version of his account of
Roth in vol. II that he was born in Ingolstadt c. 1580. He gives only the
year of his death 1617. That Peter Roth died in Nuremberg in 1617 is
confirmed by the parish register of St. Lorenz which says that he was
buried on April 25, 1617 in Nuremberg. Faulhaber confirms in a letter from
May 12, 1617 to Sebastian Kurz that he was informed by Kurz about the death
of Roth. This letter from Faulhaber to Kurz is now in the Bibliothe\que
Nationale in Paris.
I shall contact archives in Ingolstadt in order to find out if Roth was
born there and when.
Of course, this information is open to all on the list.
With best regards
Ivo