 | John Playfair - Geometry - 1860 - 334 pages
...is divided be denoted by a and l; then, (a+6) 1 =o 2 +2a6+6 2 . PROP. V. THEOR. If a straight linele divided into two equal parts, and also into two unequal...contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line. Let the straight... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...equivalent to the equation AD x D£-\- CB*= CD , which i* the algehraic proof of the theorem. THEOREM XLV. If a straight line be divided into two equal parts,...two unequal parts, the rectangle contained by the two unequal parts together with the square of the line between the points of division, will be equivalent... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...the parallelograms about the diameter of a square, are 1 i ke wise squares. PROPOSITION V. THEOREM. If a straight line be divided into two equal parts, and also into tteo unequal parts ; the rectangle contained by the unequal parts, together with the square on the... | |
 | Alexander Hadden Hutchinson - 1861 - 128 pages
...described upon the sides which contain the right angle. 2. If a straight line be divided into two equal and also into two unequal parts, the rectangle contained by the unequal parts together with the square cf the line between the points of section is equal to the square of half the line. VOLUNTARY PORTION.... | |
 | War office - 1861 - 260 pages
...between the same parallels are equal to one another. 2. If a straight line be divided into two equal and also into two unequal parts, the rectangle contained by the unequal parts together with the square of the line between the points of section is equal to the square of half the line. State and explain... | |
 | Euclides - 1861 - 464 pages
...III. 47, I. Axs. 1, 2, 3, I. 36, 1. Parlms. upon eq. bases and between the same ||s are equal. 5, II. If a straight line be divided into two equal parts, and also into two uneq. parts, the rcct. contained by the nneq. parts, together with the square of the line between the... | |
 | Euclides - 1862 - 140 pages
...the parallelograms about the diagonal of a square are likewise squares. PROPOSITION 5.— THEOREM. If a straight line be divided into two equal parts,...square on the line between the points of section, ^s equal to the square on half the line. (References— Prop. I. 31, 34, 36, 43, 46; II. 4, cor.) Hypothesis.... | |
 | Euclides - 1862 - 172 pages
...that the parallelograms about the diameter of a square are likewise squares. PROP. V.— THEOREM. //' a straight line be divided into two equal parts, and also into two unequal parts ; then the rectangle contained by the unequal parts, together with the square of the line between the... | |
 | University of Oxford - Education, Higher - 1863 - 316 pages
...equal to the rectangles contained by the undivided line and the several parts of the divided line. 8 If a straight line be divided into two equal parts,...contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line. 9. Divide a given... | |
 | Euclides - 1864 - 262 pages
...— 2am + m'. Hence by adding these equals, .'. (a + m)' + (a - m)* = 2az + 2m*. That is, If a number be divided into two equal parts, and also into two unequal parts, the sum of the squares of the two unequal parts is equal to twice the square of half the number itself,... | |
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If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line. 
