Page:The sidereal messenger of Galileo Galilei.pdf/53

 Sun, that some summits within the portion of the Moon in shadow appeared illumined, although at some distance from the boundary of the light (the terminator), by comparing their distance with the complete diameter of the Moon, I learnt that it sometimes exceeded the one-twentieth (th) part of the diameter.

Suppose the distance to be exactly th part of the diameter, and let the diagram represent the Moon's orb, of which is a great circle,  its centre, and  a diameter, which consequently bears to the diameter of the Earth the ratio 2:7; and since the diameter of the Earth, according to the most exact observations, contains 7000 Italian miles,  will be 2000, and  1000, and the th part of the whole,, 100 miles. Also let be a diameter of the great circle which divides the bright part of the Moon from the dark part (for, owing to the very great distance of the Sun from the Moon this circle does not differ sensibly from a great one), and let the distance of  from the point  be th part of that diameter; let the radius  be drawn, and let it be produced to cut the tangent line