 | 1855 - 264 pages
...line 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,...whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. 6. In every triangle, the square of the side... | |
 | Euclides - 1855 - 270 pages
...one 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,...whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. Let the straig-ht line AB be divided into... | |
 | 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 the squares of the two parts, together with twice the product of the parts, is demonstrated, by squaring a binomial. Let the side... | |
 | John Playfair - Geometry - 1855 - 334 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...whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. 8. Describe a square that shall be equal... | |
 | W F. Richards - Elementary school teaching - 1856 - 198 pages
...a 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... | |
 | Euclides - 1856 - 168 pages
...Cor. 1. — By making A equal to the whole line considered as divided into two parts, it appears that if a straight line be divided into any two parts, the square of the whole liriiHs equal to the sum of the rectangles contained by the whole line and each of the parts. Cor.... | |
 | 1858 - 398 pages
...the sides is bisected in that point, and also bisects the parallelogram. BOOK II. 5. PROP. IV. — If a straight line be divided into any two parts,...whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. 6. PROP. IX. — If a straight line be divided... | |
 | Great Britain. Parliament. House of Commons - Bills, Legislative - 1858 - 694 pages
...the sides is bisected in that point, and also bisects the parallelogram. BOOK II. 5. PROP. IV. — If a straight line be divided into any two parts,...whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. 6. PROP. IX. — If a straight line be divided... | |
 | War office - 1858 - 578 pages
...the vertical angle of the triangle and the point of intersection will bisect the vertical angle. 4. If a straight line be divided into any two parts,...square of the whole line is equal to the squares of the parts and to twice the rectangle contained by the parts. Explain how a rectangle is represented arithmetically,... | |
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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. 
