I am concerned with details of the life and manuscripts including letters
of Peter Roth of whom very little is known. I can provide you with the
following informations: Roth worked in the German city Nuremberg as a
reckoningmaster until his death in 1617. Nothing is known about the place
and date of his birth.
He published in 1608 a book in Nuremberg the full title of which is:
Peter Roth, Arithmetica Philosophica, Oder sch"one newe wolgegru"ndte Vberauss
Kunstliche Rechnung der Coss oder Algebrae/ In drey vnterschiedliche Theil
getheilt.
Im I. Theil werden dess hochgelehrten/ fu"rtrefflichen vnd weitberu"hmbten
Herrn D. Hieronymi Cardani, Mathematici, Philosophi vnd Medici dreyzehn
Reguln (als der Schlu"ssel/ nach welchen alle ratio. vnd irrational/ wie
auch binomi vnd residui cubicossische Exempla vnd aequationes zu solviren
vnd auffzulo"sen) auffs trewlichst vnd fleissigst beschrieben vnd gesetzt.
Dessgleichen noch drey andere newerfundene nu"tzliche Reguln/ zu den ersten
drey cubiccossischen aequationib. (fu"rnemlich aber der andern vnd dritten
Regul Cardani/ wann der Cubus dess dritten theils der Zahlen Radicum
gro"sser/ als das Quadrat dess halben theils der ledigen Zahl) geho"rig.
Im II. Theil folget die allerku"nstlichste Resolution dess gantzen
Arithmetisch. Cubiccossischen Lustgartens/ welcher von dem Wolerfahrnen
Herrn Johann Faulhabern/ Burgern vnd Rechenmeistern zu Vlm/ mit 160.
Ba"umlein/ das ist/ ausserlesenen kunstlichen Quaestionen gepflantzt worden/
sampt deroselben nach notdurfft daran gehenckten erkla"rung/ Vnd einer noch
u"beraus scho"nen herrlichen incorporirten polygonalischen Regul/ vnd der
daraus componirten Taffeln/ dardurch auff beede Weg leichtlich die Summa
etlicher Polygonahlzahlen/ vnd herwiderumben derselben Radices mo"gen
gefunden werden.
Vnd dann endlich im III. Theil/ als zum Beschluss/ eine anzahl
wunderbarliche/ newerfundene/ ku"nstliche/ ja von vielen hochverstendigen
diser Kunst gelehrten/ fu"r vnmu"glich geachte Surdische/ Zensizensi.
Surdesoli. Zensicubi. Bsurdesoli. wie auch Longi. Plani. vnd
Stereometrische Cossische Quaestiones vnnd Exempla/ der gestalt vorhin in
keiner Sprach gesehen worden.
Calculirt/ solvirt/ auch auff das aller trewlichst den jenigen/ so was
mehrers in dieser edlen vnd sinnreichen Kunst zu erfahren begierig/
beschrieben vnd an tag geben. Nu"rnberg 1608
The title is selfexplaining at least for those who still understand 17th
century German. More important is that this book contains an early form of
the fundamental theorem of Algebra, namely, that an equation of degree n
cannot have more roots than n. This is the justification for the very few
authors, who did at all, to mention him in their histories of mathematics.
I could find as the only English history of mathematics which refers to
Roth that of David Eugene Smith which, of course, has fallen into oblivion.
D.E. Smith mentions in his Rara Arithmetica (Reprinted by Chelsea, NY, in
1970) on p. 493 a manuscript of a B. Roth with the date August 4, 1599
which deals with the problems contained in Stifel's edition of Rudolff's
Coss beginning with chapter 5. Gabriel Doppelmayr hints in his Historische
Nachricht von den Nu"rnbergischen Mathematicis und Ku"nstlern published in
Nuremberg in 1730 to a Nuremberg philomath who owned manuscripts from Peter
Roth, amongst them one whith the solutions of all the problems contained in
the Coss of Christoff Rudolff. So, it could well be that the Author of the
manuscript mentioned by D. E. Smith was not B. or Britenus but Peter or
Petrus Roth.
Since Smith does not give the location of this manuscript I have no
possibility to verify my claim.
I have checked with a great number of archives beginning in Nuremberg but
nowhere I could find any traces of Peter Roth's manuscripts. Nor could I
detect any correspondence.
However, in the correspondence between Sebastian Kurz and Johann Faulhaber
which is kept today in the Bibliothe\que Nationale in Paris, as I found out
some 15 years ago, Peter Roth is mentioned very often especially in the
years 1608 and 1609. It is clear from these letters that there existed a
correspondence between Faulhaber and Roth which seems to be lost. I have
described the relationship between especially Faulhaber and Roth in my
biography of Johannes Faulhaber (Birkha"user Basel 1993).
It is probable that Roth who enjoyed a reputation as the leading algebraist
in Germany of his time and who is mentioned in the juvenilia of Descartes
(see Oeuvres de Descartes X, p. 242) entertained more correspondences.
I have given here all these details in order to prevent those interested
and kind enough, to help me with further informations concerning Peter
Roth, to look into corners where I have tried already to turn every stone.
Thanks for every hint
Ivo Schneider
University of the Federal Armed Forces Munich.