Book I. XV. lines. XVI. XVII. XVIII. lines. XIX. has three equal sides. XX. AAN XXI. XXII. XXIII. Book I. XXIV. Xxv. equal, and all its angles right angles. XXVI. has not all its sides equal. XXVII. are not right angles. XXVIII. another, but all its sides are not equal, nor its angles right XXIX. ziums, 1 Book I. XXX., which, being produced ever so far both ways, do not meet. POSTULATES. I. any one point to any other point. II. in a straight line. III. distance from that centre. AXIOMS. I. another. II. III. IV. V. Book I. VI. another. VII. another. VIII. Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. IX. The whole is greater than its part. X. All right angles are equal to one another. “ Two straight lines, which intersect one another, cannot be “ both parallel to the same straight line.” equal to AB; but things which Book I. PROPOSITION I. PROBLEM. Let AB be the given straight line; it is required to des- From the centre A, at the distance AB, desa 3. Postu- scribea the circle BCD, late. and from the centre B, at D A В. E another, draw the straight b 1. Post. linesb CA, CB, to the points A, B: ABC shall Because the point A is the centre of the circle BCD, AC c 11. Defi. is equal to AB; and because the point B is the centre of the nition. circle ACE, BC is equal to BA: but it has been proved that CA is equal to AB; therefore CA, CB are each of them d 1. Axi- equal to one anotherd; therefore CA is equal to CB; where fore CA, AB, BC are equal to one another; and the triangle om. PROP. II. PROB. FROM a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line; it is required to draw from the point A a straight line equal to BC, |