may EUCLID. [FIRST YEAR.] POSTULATES. I. Let it be granted that a straight line be drawn from any one point to any other point. II. That a terminated straight line may be produced to any length in a straight line. III. That a circle may be described from any centre, distance from that centre. at any AXIOMS. I. Things equal to the same are equal to one another, II. If equals be added to equals, the wholes are equal. III. If equals be taken from equals, the remainders are equal. IV. If equals be added to unequals, the wholes are unequal. V. If equals be taken from unequals, the remainders are unequal. VI. Doubles of the same are equal to one another. VII. Halves or the same are equal to one another. VIII. Magnitudes which coincide with one another, or exactly fill the same space, are equal to one another. IX. The whole is greater than its part. X. Two straight lines cannot enclose a space. PROPOSITION 1.-To describe an equilateral triangle on a given finite straight line. Let AB be the given straight line; it is required to describe an equilateral triangle on it. |