Full text: Vitruvius: The architecture of Marcus Vitruvius Pollio in ten books

204 
to those contained in the square, whose side is five feet. 
When Pythagoras discovered this property, convinced 
that the Muses had assisted him in the discovery, he 
evinced his gratitude to them by sacrifice. This propo¬ 
sition is serviceable on many occasions, particularly in 
measuring, no less than in setting out the staircases of 
buildings, so that each step may have its proper height. 
For if the height from the pavement to the floor above 
be divided into three parts, five of those parts will be the 
exact length of the inclined line which regulates the 
blocks of which the steps are formed. Four parts, each 
equal to one of the three into which the height from the 
pavement to the floor was divided, are set off from the 
perpendicular, for the position of the first or lower step. 
Thus the arrangement and ease of the flight of stairs 
will be obtained, as the figure will show. 
CHAPTER III. 
OF THE METHOD OF DETECTING SILVER WHEN 
MIXED WITH GOLD. 
THOUGH Archimedes discovered many curious matters 
which evince great intelligence, that which I am about 
to mention is the most extraordinary. Hiero, when he 
obtained the regal power in Syracuse, having, on the 
fortunate turn of his affairs, decreed a votive crown of gold 
to be placed in a certain temple to the immortal gods, 
commanded it to be made of great value, and assigned 
an appropriate weight of gold to the manufacturer. He, 
in due time, presented the work to the king, beautifully 
wrought, and the weight appeared to correspond with 
that of the gold which had been assigned for it. But a 
report having been circulated, that some of the gold had
	        
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