| Aaron Schuyler - Geometry - 1876 - 384 pages
...adjacent angle of ACD ; A and B are the opposite interior angles. 52. Proposition XVI.— Theorem. The sum of the three angles of any triangle is equal to tiro right angles. Let ABC be a triangle. Then the B sum of its angles is equal to two right /\ angles.... | |
| Benedictus de Spinoza - Ethics - 1876 - 394 pages
...eternal decrees of God with the same necessity as it follows from the essence of the triangle that the sum of its three angles is equal to two right angles. 3rd. Our doctrine is also useful in promoting the amenities of social life, inasmuch as it teaches... | |
| Humanities - 1877 - 626 pages
...Further, since any triangle can be resolved into two right-angled triangles, it follows immediately that the sum of the three angles of any triangle is equal to two right angles. If, then, we accept the evidence of Pamphila as satisfactory, we are forced to the conclusion that... | |
| William Chauvenet - Geometry - 1879 - 380 pages
...+ AC •we subtract AB, we shall have BC — AB<AC, otAC> BC—AB. PROPOSITION XVIII—THEOREM. 68. The sum of the three angles of any triangle is equal to two righl angles. Let ABC be any triangle; then, the sum of its three angles, A, B and C, is equal to two... | |
| Alfred Hix Welsh - Geometry - 1883 - 326 pages
...and lying in the same or in opposite directions, are equal. THEOREM XII. The sum of the angles of a triangle is equal to two right angles. Let ABC be any triangle; then will the sum of its angles, a, b and e, be equal to two B right angles. For, produce the base AC to... | |
| Connecticut. Board of Education - 1885 - 306 pages
...sphere is measured by the circumference of one of its great circles multiplied by its diameter. IL 1. The sum of the three angles of any triangle is equal to two right angles. 2. If a straight line is divided into any two parts, the square described on the whole line is equivalent... | |
| Joseph Baldwin - Educational psychology - 1887 - 334 pages
...three angles of this triangle is equal to two right angles ; But this is a typical triangle ; .•. The sum of the three angles of any triangle is equal to two right angles. (Give two examples, and show that a single typical case justifies a general conclusion.) 2. Deductive... | |
| William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...interior angles on the same side of the secant line is equal to two right angles. PROPOSITION XXVI. The sum of the three angles of any triangle is equal to two right angles. Corollary. If one side of a triangle is extended, the exterior angle is equal to the sum of the two... | |
| George Johnston Allman - Geometry - 1889 - 266 pages
...Further, since any triangle can be resolved into two right-angled triangles, it follows immediately that the sum of the three angles of any triangle is equal to two right angles. If, then, we accept the evidence of Pamphila as satisfactory, we are forced to the conclusion that... | |
| Edward Albert Bowser - Geometry - 1890 - 418 pages
...BC, (Ax. 10) Taking AC from each, AB - AC < BC, or BC > AB - AC. QED A Proposition 2O. Theorem. 97. The sum of the three angles of any triangle is equal to two right angles. Hyp. Let ABC be any A . To prove Proof. Produce AB to D, and draw BE || to AC. AB ° Then since BE... | |
| |