Note 5 — MOONE. (continued 3)
Reading edition
Now the aggregate of the quadrate from A B a hundred, and B G a 1000 will bee 1010000, unto which the quadrate arising from A G must be equall according to the 47th proposition in the first booke of elements. Therefore the whole line A G is somewhat more than 104, and the distance betwixt H A must be above 4 miles, which was the thing to be proved.
That is: given that AB = 100 and BG = 1000, 100
2
+ 1000
2
= 1,010,000. By the Pythagorean Theorem (“the 47th proposition”), AG = √1010000. 104 is presumably an error for 1004; the actual figure is almost 1005.