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Powers with fractional exponents by Archimedes

• Σταμάτης, Ευάγγελος Σ.

Powers with fractional exponents we meet for the first time in the history of Mathematics to the 8th problem of the second book of Archimedes work about sphere and cylinder. The ancient Greeks developed the algebra contemporarily to tbe arithmetic and geometry. This is concluded from the «bloom» of Thymaridas and fromthe books II, V, VIII, IX, X of Euclid's Elements. Powers with fractional exponents, but expressed indirectly and not visibly, we are finding in to the X book of Euclid's Elements......The use of powers with fractional exponents by Archimedes without any proof, means that the study of them has been done long time before of theArchimedes......"We believe very probable that the study of the powers with fractional exponents, has been done by the Pythagoreans during the 5th century b. C.

• Languages and Literature

• Classical philology

Καθηγητή ΙΩΣΗΦ Ε. ΧΟΦΜΑΝ Έπί τη 68η επετείω της γεννήσεως του (7.3.1900)For Prof. Dr. JOSEPH E. HOFMANN On his 68*k Birthday