 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...or a' = m" + Imn + n'. That is, if a number be divided into any two parts, the square of the number is equal to the squares of the two parts together with twice the product of the two parts. From Euc. n. 4, may be deduced a proof of Eue. i. 47. In the fig. take DL... | |
 | Euclides - 1860 - 288 pages
...line be divided into any two parts, the square on the whole line is equal to the sum of the squares on the two parts, together with twice the rectangle contained by the parts. Given the straight line AB divided into any two parts in C ; to prove that the square on AB is equal... | |
 | William Grier - Mechanical engineering - 1861 - 316 pages
...AE, and AD and EF, and AD and FB : thus expressed, AD . AB=AD . AE -f-AD . EF+AD . FB.* If a right line be divided into any two parts, the square of the whole line, is equal to both the rectangles of the whole line and each of the parts. • Instead of the mark X > a point is... | |
 | War office - 1861 - 714 pages
...straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts together with twice the rectangle contained by the parts. 3. If in a circle straight lines cut one another which do not both pass through the centre, they do... | |
 | Euclides - 1862 - 172 pages
...line be divided, &c. QED PROP. IV. — THEOREM. If a straight line be divided into any two parts; then the square of the whole line is equal to the squares...together with twice the rectangle contained by the parts. (References — Prop. i. 5, 6, 29, 31, 34, 43, 46.) Let the straight line AB be divided into any two... | |
 | University of Oxford - Education, Higher - 1863 - 328 pages
...be equal to a given triangle, and have one of its angles equal to a given rectilineal angle. 7. If a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts. 8. If a straight line be divided into any two parts, the squares of the whole line and one of the parts... | |
 | Olinthus Gregory - 1863 - 482 pages
...line, are parallel to one another. G HI 6. If a right line A c be divided into two parts, AB, B c : the square of the whole line is equal to the squares of both the parts, and twice the rectangle of the parts, A c' = A B1 + B C' + 2 AB . B C. 7. The square... | |
 | Henry White - 1864 - 156 pages
...which it is proved that the three angles of a triangle are together equal to two right angles. 4. If a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts. 5. Divide a given straight line into two parts, so that the rectangle contained by the whole and one... | |
 | University of Calcutta - 1864 - 388 pages
...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. To what algebraical proposition... | |
 | Euclides - 1864 - 262 pages
...or a* = m' + 2mn + n'. That is, if a number be divided into any two parts, the square of the number is equal to the squares of the two parts together with twice the product of the two parts. From Euc. n. 4, may be deduced a proof of Euc. i. 47. In the fig. take DL... | |
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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. 
