| University of Durham - Education, Higher - 1851 - 222 pages
...Equal triangles upon the same base and upon the same side of it are between the same parallels. 4. If a straight line be divided into any two parts, the square of the whole line is equal to the square of the parts together with twice the rectangle contained by the parts. 5. To divide a given... | |
| 1867 - 336 pages
...undivided line, and tho several parts of the divided line. 2. If a straight line be divided into any t»o parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. Prove geometrically that the sum of the squares of two... | |
| 1851 - 382 pages
...by those two sides is a right angle, . . 3. If a straight line be divided into any two parts, _ 20 2 the square of the whole line is equal to the squares of the two parts, together with twice their rectangle, 4. In any plane triangle the sides are to each 21 other as what ? Demonstrate... | |
| Education - 1863 - 830 pages
...intercepted between the first and second shall be equal to that intercepted between the second and third. 5. If a straight line be divided into any two parts,...the square of the whole line is equal to the squares on the two parts, together with twice the rectangle contained by the parts. Entrance Examination. 6.... | |
| Euclides - 1852 - 152 pages
...is equal to the two numbers multiplied together.] 90 BOOK II. • xlvi. 1. THE ELEMENTS PROP. III. THEOR. If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts is equal to the rectangle contained by the two... | |
| Euclides - 1853 - 146 pages
...AC, CB, together with the square of BC. If, therefore, a straight line, &c. QED PROP. IV. THEOREM. If a straight line be divided into any two parts,...equal to the squares of the two parts, together with twice the rectangle contained by the parts. 3 Let the straight line AB be divided into any two parts... | |
| Euclides - Geometry - 1853 - 176 pages
...straight lines ab, ас is sometimes simply called the rectangle ab, ac. Я PROPOSITION IV. — THEOREM. If a straight line be divided into any two parts,...the square of the whole line is equal to the squares oftíie two parts, togetlwr with twice the rectangle contained by the parts. LET the straight line... | |
| Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...rectangle AB, BC, is equal to the square of AB. If therefore a straight line, etc. QED PROPOSITION III. THEOR. If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two... | |
| Allan Menzies - 1854 - 520 pages
...Euclid's general reasoning, and point out the part of your demonstration in which it is evaded. 3. If a straight line be divided into any two parts,...equal to the squares of the two parts, together with twice the rectangle contained by the parts. A modification of what you have here proved constitutes... | |
| Upper Canada. Chief Superintendent of Schools - Education - 1854 - 196 pages
...required in the demonstrations of the 7th, 27th, 32nd and 48th prop, of the 1st book of Euclid. . 3. If a straight line be divided into any two parts,...equal to the squares of the two parts, together with twice their rectangle. 4. If a straight line be divided into two equal and also into two unequal parts... | |
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