n – south — m compass — north

d c north — surface of the earth — centre of the earth

a – f – g –

If you wish to measure by a true method the size of the earth: having seen among the mathematical speculators the various opinions on the size of the earth's orbicular mass, I have judged that, since among so many disputants there are so many differing opinions, the certainty of the truth is very far from them; for if the truth had reached their minds, they would all be of one and the same opinion. And upon this great diversity of opinions I have taken courage to create, or rather to compose, an instrument which you shall use in this manner. Let there then be taken a board eight braccia high and one wide, in the form of the instrument a here at the side; and you shall set it on a sea-shore, and make in it two rings, as appears at f g, through which you may sight the north (pole star), and note where the thread that points to the centre meets the foot of the board. Then set a compass at the foot of the said board, which should be somewhat large, so that with it you may take a level upon a mountain that is as far off as you can see toward the south. But it would be best to have a light set on that mountain by night, and to measure it by night, as appears in the figure above at the point n; and when you know the miles exactly, go there with the same board and sight the north through the same rings, and note the plumb-line that points to the earth's centre; and you will see, from the lines made by the plumb-lines, a triangle composed; and as much as the base enters into the pyramid, so much do your miles enter as far as the earth's centre, as appears above in the figure d c.