| Edward Brooks - Geometry, Modern - 1901 - 278 pages
...Find the area of a triangle whose base is 10 inches and altitude 6 inches. PROPOSITION X. — THEOREM. **The rectangle contained by the sum and difference of two lines is equivalent to the difference of** their squares. Given. — Let AB and BC be any two lines. To Prove. — Then we are to prove that (AB+BC)(AB-BC)... | |
| James McMahon - Geometry, Plane - 1903 - 380 pages
...difference is equivalent to the square on half their sum." Ex. Prove again that " the rectangle of **the sum and difference of two lines is equivalent to the difference of** their squares." Squares on equal parts and on unequal parts. 54. THEOREM 17. // a line is divided into... | |
| Joseph Claudel - Mathematics - 1906 - 758 pages
...(AB - BCf = Zfi2 + BC1 - 2 AB X BC. 729. The rectangle AC ED whose sides are respectively equal to **the sum and difference of two lines is equivalent to the difference of the squares** of the two lines (484) : (AB + BC) (AB - BC) =~AB* - BC* 730. The square constructed on the hypotenuse... | |
| Isaac Newton Failor - Geometry - 1906 - 440 pages
...BC. This theorem is expressed algebraically, thus : (a - 6)2 = a2 - 2 ab + 62. 817 The rectangle of **the sum and difference of two lines is equivalent to the difference of the squares** on the lines. Let AB and AC be two lines. Construct the squares ABDE and ACFG. Prolong GF to K, making... | |
| Isaac Newton Failor - Geometry - 1906 - 431 pages
...BC. This theorem is expressed algebraically, thus : (a - 6)2 = a2 - 2 ab + 62. 817 The rectangle of **the sum and difference of two lines is equivalent to the difference of the squares** on the lines. Let AB and AC be two lines. Construct the squares ABDE and A CFG. Prolong GF to K, making... | |
| |