Amyntas I, king of Macedonia (c. 540-498 B.C.), was a
tributary vassal of Darius Hystaspes[?] of Persia. With him the history of Macedonia may be said to begin. He was the first of its rulers to have relations with other countries; he entered into an alliance with the Peisistratidae[?] of Athens, and when Hippias was driven out of Athens he offered him the territory of Anthemus[?] on the Thermaic Gulf[?], with the object of turning the Greek party feuds to his own advantage
... to both sides, getting
<math>x^2+\frac{b}{a}x+\frac{b^2}{4a^2}=-\frac{c}{a}+\frac{b^2}{4a^2}.</math>
The left side is now a perfect square; it is the ...