| 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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