...act of affirming or denying are one and the same thing. When, for example, the mind affirms that the sum of the three angles of a triangle is equal to two right angles, that affirmation cannot exist or be thought without the idea of a triangle. Conversely, the...

...than Euclid's Elements. Among the most famous of the theorems in the Elements are the following. The sum of the three angles of a triangle is equal to two right angles. The area of the square on the hypotenuse of a right angled triangle is equal to the sum of...

...geometrical figures have different properties on the different surfaces. On the sheet of paper the sum of the three angles of a triangle is equal to two right angles, on the egg, or the sphere, it is larger, on the saddle it is smaller. On the flat paper —...

...could be replaced by the assertion that 'it is possible to divide space into equal cubes', or that 'the sum of the three angles of a triangle is equal to two right angles', or that 'a triangle exists similar to a given triangle but of arbitrary size '. Any one of...

...contains. GEOMETRY. Time: 2J hours. NOTE. — Seven questions only are to be attempted. Value— 100. 1 The sum of the three angles of a triangle is equal to two right angles. State the corresponding theorem for a polygon of n sides. 2. Finds the locus of a point which...

...physical theory. The simplest example of these structures is geometry. The theorem of geometry that the sum of the three angles of a triangle is equal to two right angles is not merely a concise description of a property of all triangles; it is a logical deduction...

...GEOMETRY.— i. What is Geometry? When are angles supplementary? When complementary? 2. Prove that the sum of the three angles of a triangle is equal to two right angles. 3. A straight line can not insersect the circumference of a circle in more than two places....