13 
ARISTARCHUS OF SAMOS 
(2) 0N:{diam, of sun) <1:9 
but > 22:225. 
(3) ON: YZ > 979 :10125. 
Prop. 14 (Fig. 3). 
Prop. 15 
BC:CS > 675 : 1. 
but 
(Diam. of sun) : (diam. of earth) >19:3 
<43:6. 
Prop. 17. 
(Diam. of earth) : (diam. of moon) > 108:43 
but < 60:19. 
It is worth while to show how these results are proved. 
Prop. 13. 
(1) In Fig. 2 it is clear that 
ON < 2LN and, a fortiori, < 2 LP. 
The triangles LON, GLN being similar, 
ON : NL = NL : LG; 
therefore ON : NL = NL : \ LP 
> 89: 45. 
(by Prop. 12) 
flf -7^ 
405 
obtain 1+ 
(2) 
But 
therefore 
Again 
and 
therefore, 
(3) Since 
the triang] 
similar, anc 
But 
therefore, a 
And 
But 
therefore, e