17. If a triangle be equicrurall, the angles at the base are equall: and contrariwise, 5. and 6. p. j.
The antecedent is apparent by the [7. e iij]. The converse is apparent by an impossibilitie, which otherwise must needs follow. For if any one shanke be greater than the other, as ae: Then by the [7. e v]. let oe, be cut off equall to it: and let oi, be drawne: then by [7. e iij]. the base oi, must
be equal to the base ae; but the base oi, is lesser than ae. For by the [9. e], ia; and ao, (to which ae, is equall, seeing that oe, is supposed to be equall to the same ai: and ao, is common to both) are greater than the said oi; therefore the same, oi, must be equall to the same ae, and lesser than the same, which is impossible. This was first found out by Thales Milesius.
Therefore
18. If the equall shankes of a triangle be continued or drawne out, the angles under the base shall be equall betweene themselves.
For the angles aei, and ieo: Item aie, and eiu, are equall to two right angles, by the [14. e v]. Therefore they are equall betweene themselves: wherefore if you shall take away the inner angles, equall betweene themselves, you shall leave the outter equall one to another.
And
19. If a triangle be an equilater, it is also an equiangle: And contrariwise.