| 1846
...str. line has been drawn through A || BC. EF || BC. Pt0ff ^ PROP. XXXI. THEOR. 32. 1 Eu. If a side **of any triangle be produced, the exterior angle is...and the three interior angles of every triangle are** together equal to two right angles. Let ABC be a ^, and the side BC be prod, to D. Then shall the ext.... | |
| 1846
.../. ADC, EF || BC. Prop.2H. PROP. XXXI. THEOR. 32. 1 Eu. If a side of any triangle be produced, t/ie **ex-terior angle is equal to the two interior and opposite...and the three interior angles of every triangle are** together equal to two riffht angles. Let ABC be a ^\, and the side BC be prod, to D. Then shall the... | |
| Dennis M'Curdy - 1846 - 138 sider
...of a triangle be produced, the exterior angle (ACD) is equal to the two interior angles (A and B) ; **and the three interior angles of every triangle are equal to two right angles.** Argument. Through C draw CE parallel to AB (a). Then because AC meets the parallels AB, CE, the alternate... | |
| John Playfair - 1846 - 317 sider
...angles are also equal. Now, this being demonstrated, it is easy to prove that the three angles of any **triangle are equal to two right angles. Let ABC be a triangle** right angled at A, draw AD perpendicular to BC. The triangles ABD, ABC have the angles BAC, BDA right... | |
| the london university calendar - 1846
...2. Prove that any two sides of a triangle are together greater than a third side. 3. If a side of a **triangle be produced, the exterior angle is equal to the two interior** opposite angles, and the three interior angles of every triangle are equal to two right angles. Prove... | |
| Anthony Nesbit - 1847 - 426 sider
...side, are together equal to H\ two right angles. (Euc. I. 29. Simp. I. 7. \ Em. I. 4.) c D THEOREM IV. **Let ABC be a triangle, and let one of its sides BC...be produced to D ; the exterior angle ACD is equal** A to the two interior and opposite angles CAB, ABC; also the three interior angles of every triangle... | |
| Euclides - 1847
...passes through D. Wherefore, of all triangles &c. — QED PROP. XXXII. THEOR. GEN. ENUN. — If a side **of any triangle be produced, the exterior angle is...the two interior and opposite angles ; and the three** inte. rior angles of every triangle are equal to two right angles. PART. ENUN. — Let ABC be a A,... | |
| Euclides - 1848
...straight line through a given point parallel to a given straight line. PROP. XXXII. THEOREM. If a side **of any triangle be produced, the exterior angle is...the two interior and opposite angles ; and the three** ulterior angles of every triangle are together equal to two right angles. COR. 1. All the interior... | |
| Elias Loomis - 1849 - 226 sider
...PROPOSITION XXVII. THEOREM. If one side of a triangle is produced, the exterior angle is equal to the sum of **the two interior and opposite, angles; and the three...angles of every triangle are equal to two right angles.** produced to D; then will the exterior angle ACD be equal to the sum of the two interior and opposite... | |
| University of Cambridge - 1849
...line an isosceles triangle, the sides of which shall be each equal to twice the base. 2. If a side **of any triangle be produced, the exterior angle is equal to the** sum of the two interior and opposite angles ; and the three interior angles of every triangle are together... | |
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