| 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... | |
| |