 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...x D£-\- 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... | |
 | 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...of section is equal to the square of half the line. State and explain Euclid's corollary to this proposition. 3. The angles in the same segment of a circle... | |
 | 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.... | |
 | Euclides - 1862 - 172 pages
...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...section, is equal to the square of half the line. (References — Prop. i. 31, 34, 36, 43, 46; n. 4, Cor.) Let the straight line AB be divided into two... | |
 | Euclides - 1862 - 140 pages
...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 two unequal...contained by the unequal parts, together with the square on the line between the points of section, ^s equal to the square on half the line. (References—... | |
 | University of Oxford - Education, Higher - 1863 - 316 pages
...be equal, each to each, namely those to which the equal sides are opposite. 3. If a straight line be divided into two equal parts and also into two unequal...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. 4. Bisect a given... | |
 | Woolwich roy. military acad - 1864 - 588 pages
...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 two unequal...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. Hence show that... | |
 | Euclides - 1864 - 448 pages
...a' — 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 of half their difference, is equal to the square... | |
 | 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. 
