366 
EUCLID 
a journey to Spain, where he studied mathematics. In 970 he 
went to Rome with Bishop Hatto of Vich (in the province of 
Barcelona), and was there introduced by Pope John XIII 
to the German king Otto I. To Otto, who wished to find 
him a post as a teacher, he could say that ‘ he knew enough of 
mathematics for this, but wished to improve his knowledge 
of logic’. With Otto’s consent he went to Reims, where he 
became Scholasticus or teacher at the Cathedral School, 
remaining there for about ten years, 972 to 982. As the result 
of a mathematico-philosophic argument in public at Ravenna 
in 980, he was appointed by Otto II to the famous monastery 
at Bobbio in Lombardy, which, fortunately for him, was rich 
in valuable manuscripts of all sorts. Here he found the 
famous c Codex Arcerianus ’ containing fragments of the 
works of the Gromatici, Frontinus, Hyginus, Balbus, Nipsus, 
Epaphroditus and Vitruvius Rufus. Although these frag 
ments are not in themselves of great merit, there are things * 
in them which show that the authors drew upon Heron of 
Alexandria, and Gerbert made the most of them. They 
formed the basis of his own £ Geometry ’, which may have 
been written between the years 981 and 983. In Writing this 
book Gerbert evidently had before him Boetius’s Arithmetic, 
and in the course of it he mentions Pythagoras, Plato’s 
Timaeus, with Chalcidius’s commentary thereon, and Eratos 
thenes. The geometry in the book is mostly practical; the 
theoretical part is confined to necessary preliminary matter, 
definitions, &c., and a few proofs; the fact that the sum of the 
angles of a triangle is equal to two right angles is proved in 
Euclid’s manner. A great part is taken up with the solution 
of triangles, and with heights and distances. The Archimedean 
value of tv {Я?-) is used in stating the area of a circle; the 
surface of a sphere is given as D 3 . The plan of the book 
is quite different from that of Euclid, showing that Gerbert 
could neither have had Euclid’s Elements before him, nor, 
probably, Bodtius’s Geometry, if that work in its genuine 
form was a version of Euclid. When in a letter written 
probably from Bobbio in 983 to Adalbero, Archbishop of 
Reims, he speaks of his expectation of finding £ eight volumes 
of Bodtius on astronomy, also the most famous of figures 
(presumably propositions) in geometry and other things not