Page:The sidereal messenger of Galileo Galilei.pdf/54

 , which represents the ray that illumines the summit, in the point. Then the arc or the straight line  will be 100 of such units, as  contains 1000. The sum of the squares of is therefore 1,010,000, and the square of  is equal to this; therefore the whole  will be more than 1004; and  will be more than 4 of such units, as  contained 1000. Therefore the height of in the Moon, which represents a summit reaching up to the Sun's ray,, and separated from the extremity  by the distance , is more than 4 Italian miles; but in the Earth there are no mountains which reach to the perpendicular height even of one mile. We are therefore left to conclude that it is clear that the prominences of the Moon are loftier than those of the Earth.

I wish in this place to assign the cause of another lunar phenomenon well worthy of notice, and although this phenomenon was observed by me not lately, but many years ago, and has been pointed out to some of my intimate friends and pupils, explained, and assigned to its true cause, yet as the observation of it is rendered easier and more vivid by the help of a telescope, I have considered that it would not be unsuitably introduced in this place, but I wish to introduce it chiefly in order that the connection and