8 HISTORY OF SCIENCE. 



particularly struck by his ascertaining the height of an obelisk or pyra- 

 mid by merely measuring the length of its shadow. This may have 

 been accomplished by Thales measuring the length of the shadow of 

 the obelisk, at that particular instant of the day when the length of 

 his own shadow was equal to his own height, and when, of course, 

 the like equally holds with regard to the shadows of all vertical objects 

 projected in a horizontal plane. Perhaps, however, he might make 

 the determination at any time of the day, knowing that the shadows 

 of different vertical objects have always the same proportions to the 

 objects themselves. Simple as this matter now seems to us, it is the 

 first suggestion we meet with of the problem of measuring inacces- 

 sible distances. Thales is also said to have been able to measure, by 

 a like application of the proportionality of similar triangles, the dis- 

 tances of vessels from the shore. It is indeed probable that Thales 

 would soon surpass his teachers, for the subsequent rapid progress of 

 geometry in the hands of the Greeks proved the special aptitude of 

 the Greek understanding for scientific de- 

 duction. When Thales returned to Ionia, 

 he imparted to his countrymen such know- 

 ledge as he had acquired by his journeys, 

 or had discovered by his own reflections, 

 and thus he laid the foundation of true geo- 

 metrical science. One of the most elegant 

 of his own geometrical discoveries is that 

 property of the circle by which two lines, 



one drawn from each extremity of the diameter, to meet at any point 

 whatever in the circumference, always form a right angle with each 

 other. (See Fig. 3.) 



As Thales taught his countrymen the true foundation of geometry, 

 so he appears also to have done them a like service in astronomy. 

 He introduced some reforms into the Greek calendar, then in great 

 confusion owing to very incorrect estimates of the length of the year. 

 He also determined the periods at which the equinoxes and solstices 

 occur. The equinoxes are, as everybody knows, the periods of the 

 year at which the day is the same length as the night over all the 

 world. The solstices are literally the periods at which the sun 

 appears to stand still, in the following sense : If the height of the 

 sun be observed at noon every day, as for instance by marking the 

 position on which the shadow of an obelisk's apex falls on a level 

 plain, it will be seen that from midwinter to midsummer he daily 

 attains a greater noon elevation. But about midsummer the increase 

 of noon elevation ceases, and for several successive days the shadow 

 will fall on the same place. This indicates the period of the summer 

 solstice. After this, the height obtained by the sun diminishes each 

 noon, until in midwinter another period occurs at which the noonday 

 height remains stationary, and this is the winter solstice. 



