 | Edinburgh univ - 1871 - 392 pages
...straight line. Show that your construction has given you exactly what your definition required. 2. If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles. Modify your demonstration so as to bring out distinctly the property of straightness... | |
 | Euclides - 1871 - 136 pages
...hereafter how this definition may be extended, so as to embrace angles greater than two right angles. If one side of -a triangle be produced, the exterior angle is greater than either of the interior opposite angles. I> Let the side BC of A ABC be produced to D. Then must L ACD be greater than either... | |
 | Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...equal sums, and the remainders will be equal, ie, the /. AE C is equal to the ^ DE B. PEOPOBITION XVI. If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite* angles. For the construction employed in this proposition we must be able, — * That is,... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...may be extended, so as to embrace angles greater than tico right angles. PBOPOSITION XVI. THEOREM. If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles. Let the side BC of A ABC be produced to D. Then must L ACD be greater than either... | |
 | Lewis Sergeant - 1873 - 182 pages
...A draw the angle DAE = ADC. Then EA is parallel to g BC, by Prop. 25. Proposition 30. — Theorem. If one side of a triangle be produced, the exterior angle is equal to the two interior and opposite angles. If BC be produced to D, the a angle ACD = the two angles... | |
 | Braithwaite Arnett - 1874 - 130 pages
...EXAMINATION FOR FIRST APPOINTMENTS TO THE CAVALRY AND INFANTRY. May, 1873. EUCLID. (BooK I.) l^hr. 1. If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles. 2. If two triangles have two angles of the one equal to two angles of the other, each... | |
 | Charles Astor Bristed - 1874 - 632 pages
...EXAMINATION. WEDNESDAY, Jan. 1, 1845. 9. . .11J. [NB The Differential Calculus is not to be employed.] 1. IF one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles. a. In equal circles equal circumferences are subtended by equal straight lines. 3.... | |
 | Euclides - 1874 - 342 pages
...meeting in one point, are together equal to four right angles. PROPOSITION 16. — Theorem. If one lide of a triangle be produced, the exterior angle is greater than either of the interior opposite angles. Let ABC be a triangle, and let the side BC be produced to D. Then the exterior angle... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...BOK, (Const. ) therefore MN is parallel to AB. (I. 20.) QE jr. PUOP. XXIII.— THEOREM. (Euc. I. 32.) If one side of a triangle be produced, the exterior angle is eqiml to the two interior and remote angles ; and the three interior angles of every triangle are together... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...respects, (i. i) Hence ^4 C is = DB. Also iACBis = L DBC, and .-. AC is \\ to BD. (i. 20) PROPOSITION XXIV. If one side of a triangle be produced, the exterior angle is equal to the two interior and opposite angles; also the three interior angles of every triangle are... | |
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If one side of a triangle be produced, the exterior angle is greater than either of the interior, and opposite angles. 
