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EUCLIDE's Elements.
9
PROPOSITION I.
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UPon a finite right line given AB,to deſcribe an equilateral triangle ACB.
From the centers A and B, at the diſtance of AB, or BA, aa 3. poſt. deſcribe two circles cutting each other in the point C; from whence bb 1. poſt.
c 15. def.
d 1. ax.
e 23. def. draw two right lines CA, CB. Then is AC c = AB c = BC d = AC. e Wherefore the Triangle ACB is equilateral. Which was to be done.
Scholium.
After the ſame manner upon the line AB may be deſcribed an Iſoſceles triangle, if the diſtances of the equal circles be taken greater or leſs than the line AB.
PROP. II.
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At a point given A, to make a right line AG equal to a right line given BC.
From the center C at the diſtance of CB, aa 3. poſt.b 1. poſt.
c 1. 1.
d 2. poſt. deſcribe the circle CBE. b join AC; upon which c raiſe the equilateral triangle ADC. d Produce DC to E. From the center D, at the diſtance
