Plane and solid geometry . r figure just drawn,under the headings of Given and To prove. (4) The proof or demonstration, the argument by whichthe truth or falsity of a statement is established, with thereason for each step in the argument. 80. The student should be careful to quote the reason forevery step in the argument which he makes in proving atheorem. The only reasons admissible are of two kinds: 1. Sometliing assumed, , definitions, axioms, postulates,and the hypothesis. 2. Something previously proved, theorems, corollaries,and problems. BOOK I 21 81. The necessity for proof. So
Plane and solid geometry . r figure just drawn,under the headings of Given and To prove. (4) The proof or demonstration, the argument by whichthe truth or falsity of a statement is established, with thereason for each step in the argument. 80. The student should be careful to quote the reason forevery step in the argument which he makes in proving atheorem. The only reasons admissible are of two kinds: 1. Sometliing assumed, , definitions, axioms, postulates,and the hypothesis. 2. Something previously proved, theorems, corollaries,and problems. BOOK I 21 81. The necessity for proof. Some theorems seem evidentby merely looking at the figure, and the student will doubtlessthink a proof unnecessary. The eye, however, cannot alwaysdetect error, and reasoning enables us to be sure of our conclu-sions. The danger of trusting the eye is illustrated in thefollowing exercises.* Ex. 43. In the diagrams given below, tell which line of each pair isthe longer, a or 6, and verify your answer by careful measurement. a. Ex. 44. In the figures below, are the lines everywhere the same dis-tance apart ? Verify your answer by using a ruler or a slip of paper.
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