 | John Playfair - Euclid's Elements - 1833 - 346 pages
...AB.AC+AB.BC=AB2. Therefore, if a straight line, &c. QED D IT E: 14 i A. PROP. III. THEOR. If a straight line he divided into any two parts, the rectangle contained...aforesaid part. Let the straight line AB be divided into two parts in the point C ; the rectangle AB.BC is equal to the rectangle, AC.BC, together with BC2.... | |
 | Education - 1833 - 412 pages
...subtending the right angle is equal to the squares described upon the sides containing the right angle. 4. If a straight line be divided into any two parts, the rectangle contained OCT. 1832— JAN. 1833. B by the whole and one of the parts is equal to the rectangle contained by... | |
 | Euclid - 1835 - 540 pages
...AB, BC, is equal to the square of AB. " If, therefore, a straight line," &c. QED PROP. III. THEOH. If a straight line be divided into any two parts,...by the two parts, together with the square of the foresaid part. AC Let the straight line AB be divided into any two parts in the point C; the rectangle... | |
 | Mathematics - 1835 - 684 pages
...each of the parts, shall be together equal to the square of the whole une. PROP. 31. (Eue. ii. 3.) If a straight line be divided into any two parts, the rectangle contained by the whole line and one of the parts, shall be equal to the rectangle contained by the two parts, together with... | |
 | John Playfair - Euclid's Elements - 1835 - 336 pages
...therefore, multiplying both members of this equality by a, we shall have a'=ab+ad. PROP. III. THEOR. If a straight line be divided into any two parts, the rectangle contained by Ike whole and one of the parts, is equal to the rectangle contained by the two parts, together with... | |
 | Mathematics - 1836 - 488 pages
...contained by the whole and each of the parts, are together equal to the square of the whole line. III. If a straight line be divided into any two parts,...by the two parts, together with the square of the foresaid part. IV. If a straight line be divided into any two parts, the square of the whole line is... | |
 | John Playfair - Euclid's Elements - 1836 - 488 pages
...and AE = AB2. Therefore AB.AC + AB.BC = AB2. Therefore, if a straight line, &c. QED PROP. III. THEOR. If a straight line be divided into any two parts,...contained by the two parts, together with the square ofthefbresaid part. Let the straight line AB be divided into two parts in the point C ; the rectangle... | |
 | John Playfair - Geometry - 1836 - 148 pages
...to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC. Upon AB... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...both members of this equality by a, we shall have azs=ab+ad FE, 6 • F K J. H A PROP. III. THEOR. If a straight line be divided into any two parts,...aforesaid part. Let the straight line AB be divided into two parts, in the point C ; the B E rectangle AB.BC is equal to the rectangle AC.BC, together with... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...showing that AB* = figures AF + CE ; and that these are = AB x AC + AB x BC. PROPOSITION III. Theorem. If a straight line be divided into any two parts,...parts, together with the square of the aforesaid part. Proved by showing that AB x BC = figures AD + CE, and that these are = AC x CB + CB*. PROPOSITION IV.... | |
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If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part. 
