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UPon a finite Right Line AB, to de∣scribe an Equilateral Triangle ACB.
From the Centers A and B, at the distance of AB, describe the Circles cutting each other in the Point C; from whence draw two Right Lines CA, CB; thence are AC, AB, BC, AC, equal; wherefore the Triangle ACB is equilateral, which was to be done.
EUclid has not applyed this Proposi∣tion to any other use, but to demon∣strate the two following Propositions, but we may apply it to the measuring of an in∣accessible Line.
* 1.1 As for Example, let AB be an in∣accessable Line, which is so by reason of a River or some other Impediment, make an Equaliteral Triangle, as BDE, on Wood, or Brass, or on some other convenient thing, which having placed Horizontally at a station at B, look to the Point A, along the Side BD, and to some other Point C, along the side BE; then carry your Triangle along the Line BC, so far, that is untill such time as you can see the Point B, your first station by the side CG, and the Point A by the Side CE: I say that then the Lines CB and CA are equal; wherefore, if you measure the Line BC, you will likewise know the length of the Line AB.
Use. 1.