 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...side of the transversal are supplementary, the lines are parallel. PROPOSITION XIX. THEOREM 107. The sum of the three angles of a triangle is equal to two right angles. c 7 A Given the triangle ABC. To prove that ZA + Z JB+ZC = 2 rt. A. Proof. Suppose BY drawn... | |
 | Boris Sidis - Consciousness - 1914 - 436 pages
...uniformity. Under similar conditions like results follow. Suppose a geometrician should prove to you that the sum of the three angles of a triangle is equal to two right angles, suppose that some sceptic should come in and say, "Yes, that is all right in relation to the... | |
 | Charles Ernest Chadsey, James Hamblin Smith - Arithmetic - 1917 - 326 pages
...parts so that you can arrange the angles about a point on one side of a straight line. Show that the sum of the three angles of a triangle is equal to two right angles (or 180°). Draw other shaped triangles to show that this principle holds true for any shaped... | |
 | Michael Joseph Mahony - Logic - 1918 - 112 pages
...JUDGMENTS are arrived at by the process of deductive reasoning, as when it is demonstrated that "The sum of the three angles of a triangle is equal to two right angles". Pure mathematical conclusions are the outcome of mediate analytical judgments. IMMEDIATE SYNTHETIC... | |
 | Sir Thomas Little Heath - Mathematics - 1921 - 474 pages
...through a given point of a parallel to a given straight line) ; and then, in 32, Euclid proves that the sum of the three angles of a triangle is equal to two right angles by means of a parallel to one side drawn from the opposite vertex (cf. the slightly different... | |
 | Charles Austin Hobbs - Geometry, Solid - 1921 - 216 pages
...respectively perpendicular to two intersecting lines cannot be parallel, and hence intersect. Prop. 43. The sum of the three angles of a triangle is equal to two right mngles. Prop. 43, Cor. III. // an acute angle of a right triangle is equal to an acute angle of another... | |
 | Laura A. Knott - Jews - 1922 - 424 pages
...nearest analogy to this to-day is our attitude toward mathematical truth. In stating the fact that the sum of the three angles of a triangle is equal to two right angles we do not think of giving credit to the person who first discovered and announced that truth,... | |
 | Henry Eastman Bennett - Psychology - 1923 - 324 pages
...statements are said to be true by definition. By logical necessity. But it is also inevitably true that the sum of the three angles of a triangle is equal to two right angles. Why? Well (not to go through the familiar details of the proof), it is because certain vertical... | |
 | David Eugene Smith - Mathematics - 1923 - 200 pages
...theorems to which he refers, and which are conjecturally ascribed to Thales, are as follows : (1) "The sum of the three angles of a triangle is equal to two right angles ; (2) "The sides of equiangular triangles are proportional." The second passage from Dr. Allman's... | |
 | Walter Burton Ford, Charles Ammermann - Geometry, Modern - 1923 - 406 pages
...it flat against the board. What is the locus of the point A ? 3. Prove by means of § 132 that the sum of the three angles of a triangle is equal to two right angles. 4. If a circumference be divided into four equal arcs (quadrants), show that the chords which... | |
| |
After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles... 
