By Sir Thomas Heath
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Additional info for A History of Greek Mathematics, Vol. 1: From Thales to Euclid
When the colonizing spirit first arises in a nation and fresh fields for activity and development are sought, it is naturally the younger, more enterprising and more courageous spirits who volunteer to leave their homes and try their fortune in new countries; similarly, on the intellectual side, the colonists will be at least the equals of those who stay at home, and, being the least wedded to traditional and antiquated ideas, they will be the most capable of striking out new lines. So it was with the Greeks who founded settlements in Asia Minor.
Let us, confining ourselves to the main subject of pure geometry by way of example, anticipate so far as to mark certain definite stages in its development, with the intervals separating them. ) we find the first glimmerings of a theory of geometry, in the theorems that a circle is bisected by any diameter, that an isosceles triangle has the angles opposite to the equal sides equal, and (if Thales really discovered this) that the angle in a semicircle is a right angle. Rather more than half a century later Pythagoras was taking the first steps towards the theory of numbers and continuing the work of making geometry a theoretical science; he it was who first made geometry one of the subjects of a liberal education.
28); if the line joining the eye to the centre of a circle is perpendicular to the plane of the circle, all its diameters will look equal (Prop. 34), but if the joining line is neither perpendicular to the plane of the circle nor equal to its radius, diameters with which it makes unequal angles will appear unequal (Prop. 35); if a visible object remains stationary, there exists a locus such that, if the eye is placed at any point on it, the object appears to be of the same size for every position of the eye (Prop.
A History of Greek Mathematics, Vol. 1: From Thales to Euclid by Sir Thomas Heath