t
of the pulse and its metrical movement. But if there is a wound to be
healed or a sick man to be saved from danger, the musician will not
call, for the business will be appropriate to the physician. So in the
case of a musical instrument, not the physician but the musician will be
the man to tune it so that the ears may find their due pleasure in its
strains.

16. Astronomers likewise have a common ground for discussion with
musicians in the harmony of the stars and musical concords in tetrads
and triads of the fourth and the fifth, and with geometricians in the
subject of vision (in Greek [Greek: logos optikos]); and in all other
sciences many points, perhaps all, are common so far as the discussion
of them is concerned. But the actual undertaking of works which are
brought to perfection by the hand and its manipulation is the function
of those who have been specially trained to deal with a single art. It
appears, therefore, that he has done enough and to spare who in each
subject possesses a fairly good knowledge of those parts, with their
principles, which are indispensable for architecture, so that if he is
required to pass judgement and to express approval in the case of those
things or arts, he may not be found wanting. As for men upon whom nature
has bestowed so much ingenuity, acuteness, and memory that they are able
to have a thorough knowledge of geometry, astronomy, music, and the
other arts, they go beyond the functions of architects and become pure
mathematicians. Hence they can readily take up positions against those
arts because many are the artistic weapons with which they are armed.
Such men, however, are rarely found, but there have been such at times;
for example, Aristarchus of Samos, Philolaus and Archytas of Tarentum,
Apollonius of Perga, Eratosthenes of Cyrene, and among Syracusans
Archimedes and Scopinas, who through mathematics and natural philosophy
discovered, expounded, and left to posterity many things in connexion
with mechanics and with sundials.

17. Since, therefore, the possession of such talents due to natural
capacity is not vouchsafed at random to entire nations, but only to a
few great men; since, moreover, the function of the architect requires a
training in all the departments of learning; and finally, since reason,
on account of the wide extent of the subject, concedes that he may
possess not the highest but not even necessarily a moderate knowledge of
the subjects of study,