Galileo on the Height of the Mountains of the Moon

“I had often observed, in various situations of the moon with respect to the sun, that summits within the shadowy portion remained lighted, though lying some distance from the boundary of the light.  By comparing this separation to the whole diameter of the moon, I found that it sometimes exceeded
one-twentieth of the diameter.  Accordingly, let CAF be a great circle of the lunar body, E its center, and CF a diameter, which is to the diameter of the earth as two is to seven.

“Since according to very precise observations the diameter of the earth is seven thousand miles, CF will be two thousand, CE one thousand, and one-twentieth of CF will be one hundred miles.  Now let CF be the diameter of the great circle which divides the light part of the moon from the dark part and let A be distant from C by one-twentieth of this.  Draw the radius EA, which when produced, cuts the tangent line GCD (representing the illuminating ray) in the point D.  Then the arc CA, or rather the straight line CD will consist of one hundred units whereof CE contains one thousand, and the sum of the squares of DC and CE will be 1,010,000.  This is equal to the square of DE; hence ED will exceed 1,004, and AD will be more than four of those units of which CE contains one thousand.  Therefore the altitude AD on the moon, which represents a summit, exceeds four miles.”

–Galileo Galilei, Siderius Nuncius (The Starry Messenger) (1611)

Newton on the Visible Spectrum of Light

“I procured a triangular glass prism, to try therewith the celebrated phenomena of colors.  And for that purpose, having darkened my laboratory, and made a small hole in my window shade, to let in a convenient quantity of the sun’s light, I placed my prism at the entrance, that the light might thereby be refracted to the opposite wall.  It was at first a very pleasing diversion to view the vivid and pleasant colors produced thereby.”

–Sir Isaac Newton, The New Theory of Light and Colours (1672)