 | 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... | |
 | Euclides - 1852 - 152 pages
...(squared or) multiplied by 7 is equal to 49. These added together make up 84.] BOOK n. PEOP. IV. THEOE. If a straight line be divided into any two parts,...whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts, Let the straight line AB be divided into... | |
 | 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 - 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,...whole line is 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... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...CB, together with the square of BC. If therefore a straight line, etc. QE n. PROPOSITION IV. THEOR. If a straight line be divided into any two parts,...whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. Let the straight line AB be divided into... | |
 | 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... | |
 | 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,...whole line is 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... | |
 | 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,...whole line is 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... | |
 | Thomas Lund - Geometry - 1854 - 520 pages
...to each, to which the equal sides are opposite, .-. / ACS = / BCD = a right angle. 44. PROP. XXII. If a straight line be divided into any two parts, the square of the whole line is equal to the sum of the squares of the two parts together with twice the rectangle* contained by the parts. QDEF.... | |
 | Horatio Nelson Robinson - Conic sections - 1854 - 350 pages
...other demonstration than an explanation of exactly what is meant by the words of the text. THEOREM 33. If a straight line be divided into any two parts, the square of th« whole line is equal to the sum of the squares of the two parts, and twice the rectangle contained... | |
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If a straight line be divided into any two 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. 
