A scalene triangle is that which has three unequal sides. XXVII. A right angled triangle is that which has a right angle. An obtuse angled triangle is that which has an obtuse angle. XXIX. An acute angled triangle is that which has three acute angles. Of four sided figures, a square is that which has all its sides XXXI. An oblong is that which has all its angles right angles, but has not all its sides equal. XXXII. A rhombus is that which has all its sides equal, but its angles are not right angles. ᄆᄆ XXXIII. A rhomboid is that which has its opposite sides equal to one another, but all its sides are not equal, nor its angles right angles. XXXIV. All other four sided figures, besides these, are called trapeziums. XXXV. Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways, do not meet. Book I. POSTULATES. I. LET it be granted that a straight line may 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. And that a circle may be described from any centre, at any distance from that centre. AXIOMS. THINGS which are 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. Things which are double of the same are equal to one another. Things which are halves of the same are equal to one another. Magnitudes which coincide with one another, that is, which "If a straight line meets two straight lines, so as to make the "two interior angles on the same side of it taken together "less than two right angles, these straight lines being con"tinually produced, shall at length meet upon that side on "which are the angles which are less than two right angles. "See the notes on prop. 29. of book I." |