| Thomas Lund - Geometry - 1854 - 522 pages
...each, to which the equal sides are opposite, .-. / ACS = / BCD = a right angle. 44. PROP. XXII. If **a straight line be divided into any two parts, the square of the whole line is equal to the** sum of the squares of the two parts together with twice the rectangle* contained by the parts. QDEF.... | |
| Horatio Nelson Robinson - Conic sections - 1854 - 350 pages
...demonstration than an explanation of exactly what is meant by the words of the text. THEOREM 33. If **a straight line be divided into any two parts, the square of** th« whole line is equal to the sum of the squares of the two parts, and twice the rectangle contained... | |
| 1855 - 264 pages
...drawn through the middle points of two sides of a triangle will be parallel to the third side' 5. If **a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts.** 6. In every triangle, the square of the side suhtending either of the acute angles is less than the... | |
| Euclides - 1855 - 262 pages
...of the parts of the divided straight line, their rectangle becomes a square. PROP. IV. THEOREM. If **a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts.** Let the straig-ht line AB be divided into any two parts at С. square of AB is equal to the squares... | |
| Great Britain. Committee on Education - School buildings - 1855
...to a given triangle, and have one of its angles equal to a given rectilineal angle. Section 2. 1. If **a straight line be divided into any two parts, the...together with twice the rectangle contained by the** two parts. 2. If a straight line be divided into two equal and also into two unequal parts ; the squares... | |
| 1855 - 424 pages
...than in ordinary language. The proposition, (Euclid 4, 2,) that when a straight line is divided into **two parts, the square of the whole line is equal to...squares of the two parts, together with twice the** product of the parts, is demonstrated, by squaring a binomial. Let the side of a square be represented... | |
| John Playfair - Geometry - 1855 - 336 pages
...therefore, multiplying both members of this equality by c, we shall have oc^ic+c 2 . PROP. IV. THEOR. If **a straight line be divided into any two parts, the square of the whole line** ts equal to the squares of the two parts, together with twicetke rectangle contained by tin- parts.... | |
| Cambridge univ, exam. papers - 1856 - 252 pages
...Parallelograms on the same base and between the same parallels, are .equal to each other. 7. If a right **line be divided into any two parts, the square of...together with twice the rectangle contained by the parts.** 8. Describe a square that shall be equal to a given rectilineal figure. 9. Find the centre of a given... | |
| 1856 - 376 pages
...angles ; and the three interior angles of every triangle are together equal to two right angles. 5. If **a straight line be divided into any two parts, the...of the two parts, together with twice the rectangle** contamed by the parts. 6. In obtuse-angled triangles if a perpendicular be drawn from either of the... | |
| W. F. RICHARDS - Education, Primary - 1856 - 198 pages
...given triangle, and have one of its angles equal to a given rectilineal angle. Section II. — 1. If **a straight line be divided into any two parts, the square of the whole line** shall be equal to the sum of the squares of the parts, together with twice the rectangle contained... | |
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