 | John Playfair - Euclid's Elements - 1860 - 332 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 - 472 pages
...equation AD x DŁ-\- CB*= CD , which i* the algehraic proof of the theorem. THEOREM XLV. If a straight line be divided into two equal parts, and also into...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
...= <*'— m', to each of these equals add m' ; .'. (a + m) (a — m) + m' = a'. That is, if a number be divided into two equal parts, and also into two unequal parts, the product of the unequal parts together with the square 1 of half their difference, is equal to the square... | |
 | 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 - 1862 - 140 pages
...parallelograms about the diagonal of a square are likewise squares. PROPOSITION 5.— THEOREM. If a straight line be divided into two equal parts, and also into...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
...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 - 328 pages
...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, and also into...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... | |
 | Woolwich roy. military acad - 1864 - 588 pages
...arranged, under the restriction that the tvco vowels e shall never stand together 1 10. If a straight line be divided into two equal parts, and also into...of section is equal to the square on half the line. Hence show that a square is the greatest rectangle of given perimeter. 11. Describe a circle about... | |
 | Euclides - 1864 - 448 pages
...2am + at'. Hence by adding these equals, .-. (a + m)* + (o — m)' = 2aa + 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 on the line between the points of section, is equal to the square on half the line. 
