 | John Playfair - Euclid's Elements - 1832 - 358 pages
...AB'. Therefore AB.AC+AB.BC=AB'. Therefore, if a straight line, &c.QED G F K. LH A PROP. III. THEOR. If a straight line be divided into any two parts, the...the rectangle contained by the two parts, together ivith the square of the aforesaid part. Let the straight line AB be divided into two parts in the point... | |
 | 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... | |
 | Education - 1833 - 412 pages
...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...parts together with the square of the aforesaid part. 5. If a straight line be divided into any two parts, the square of the whole line is equal to the squares... | |
 | Euclides - 1834 - 518 pages
...straight line, &c. QED BOOK II. PROP. 111. IV. AC 46. 1. • 31. 1. D PROPOSITION III. TDEOR. — If a straight line be divided into any two parts, the...aforesaid part. Let the straight line AB be divided into any two parts in the point C : the rectangle AB, BC shall be equal to the rectangle AC, CB, together... | |
 | 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, the...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... | |
 | Robert Simson - Trigonometry - 1835 - 544 pages
...BC, is equal to the square of AB. " If, therefore, a straight line," &c. QED PROP. III. THEOR. . If a straight line be divided into any two parts, the rectangle contained by the whole and one of tJie parts, is equal to the rectangle contained by the two parts, together with the square of the foresaid... | |
 | 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, the...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
...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, the...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... | |
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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. 
