| Euclides - 1855
...three interior angles oj every triangle are together equal to two right angles. Let ABC be a triangle, **and let one of its sides BC be produced to D. Then** the exterior angle ACD is equal to the two interior and opposite angles CAB, ABC. And the three interior... | |
| W. F. RICHARDS - Education, Primary - 1856 - 184 pages
...opposite to equal sides, show that these two triangles are not necessarily equal to one another. 4. **If a side of any triangle be produced, the exterior...every triangle are together equal to two right angles.** 5. If a straight line be divided into any two parts, the square of the whole line is equal to the squares... | |
| Cambridge univ, exam. papers - 1856
...into two equal angles. 2. Any two sides of a triangle are together greater than the third side. 4. **If a side of any triangle be produced, the exterior...and the three interior angles of every triangle are** equal to two right angles. If two sides of any triangle be produced, the two exterior angles are together... | |
| Euclides - 1856
...together equal to the two FBC, DBC, that is. to two right angles. XIV.— EUCLID I. 32. If one side of a **triangle be produced, the exterior angle is equal...the two interior and opposite angles; and the three** angles of every triangle are together equal to two right angles. Let ABC (Fig. 9) be a triangle, and... | |
| John Playfair - Euclid's Elements - 1856 - 318 pages
...given point A parallel to the given straight line BC. PROP. XXXII. THEOR. If a side of any triangle oe **produced, the exterior angle is equal to the two interior and opposite angles** ; andlthe three interior angles of every triangle are equal to two right i Let ABC be a triangle, and... | |
| Henry Latham - 1857 - 59 pages
...Construct a triangle of which the base, the sum of the other sides, and the vertical angle are given. 2. **If a side of any triangle be produced, the exterior...every triangle are together equal to two right angles.** At what angles are the sides of a regular duodecagon inclined to each other? 3. If a straight line... | |
| Education - 1857
...EUCLID. FIRST YEAR. SECTION I. — 1. The angles at the base of an isosceles triangle arc equal. 2. **The three interior angles of every triangle are together equal to two right angles.** 3. To a given straight line apply a rectangle equal to a given rectilineal figure. SECTION II. —... | |
| Great Britain. Parliament. House of Commons - Bills, Legislative - 1858
...less than the other two sides of the triangle, but shall contain a greater angle. 3. PKOP. XXXII.— **If a side of any triangle be produced, the exterior...every triangle are together equal to two right angles.** 4. Enunciate and prove the corollaries of the last proposition. 5. PROP. XLIV. — To a given straight... | |
| Euclides - 1858
...Def. 35, C. 6 Conel. 1 C.3&2, P.29 2 3 P. 4. Cor. P. 15. PROP. 32. — THEOR. — (Very Important.) **If a side of any triangle be produced, the exterior...every triangle are together equal to two right angles.** CONSTRUCTION. — P. 31. To draw a st. line, through a fjiven point, parallel to a given st. line.... | |
| 1858
...less than the other two sides of the triangle, but shall contain a greater angle. 3. PJSOP. XXXII.— **If a side of any triangle be produced, the exterior...every triangle are together equal to two right angles.** 4. Enunciate and prove the corollaries of the last proposition. 5. PUOP. XLIV. — To a given straight... | |
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