CHAPTER VII 



ARISTARCHUS AND THE DISTANCE AND 

 GRANDEUR OF THE SUN 



UPON some far crag of the Matterhorn, fancy, if you will, that 

 a man was born and brought up with no other knowledge of 

 the world than what he there might gain. Conceive that this 

 crag is surrounded on every side by precipices, shelving down 

 thousands of feet to depths hidden by the clouds, so that, by no 

 construction he may devise, can he escape. He looks out over 

 an Alpine waste, and sees in the distance other vast crags lifting 

 their lion heads from out the mist. In intervals of guarding 

 his flock of goats," I picture him gazing across the grey expanse 

 with a vague longing to form some estimate of how far these 

 far-off peaks may be. What idea can he gain ? 



He has no instruments save such as he may carve with' a 

 belt knife ; but in his cabin there is a volume of Euclid. 

 Stimulated by the attentive study of that Open Sesame to the 

 mysteries of space and form, he seeks to learn what he may. 



One day I see him note that, as he holds up his hands to 

 scan the mountain-side in search of his flock, he seems to have 

 two hands ; he shuts one eye, one of the hands disappears ; 

 at once he has begun to work out the theory of vision. He 

 next observes that if he holds up his finger at arm's length, 

 and with one eye open, sights across it to some object on the 

 further wall of his hut, or against the mountains, the position 

 of his finger seems to shift as he shuts the one eye and opens 

 the other. Try, and you observe the same thing. 



Just the same thing happens when he takes a long walk 

 from his habitation and sees two peaks shift in their position 

 to each other, as he changes his point of view. Aided by a 

 theorem of Euclid, can he combine these new experiences to 

 make a measure ? He sits down, and on a smooth chip of 

 wood traces this figure. (See Fig. 6.) 



Seen from the door of his cabin, the two peaks, P and Q, 



