 | 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 - 976 pages
...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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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. 
