 | Euclid, Robert Simson - Geometry - 1821 - 514 pages
...parallelograms about the diameter of a square are likewise squares. PROP. V. THEOR. IP a straight line be divided into two equal parts, and also into two...section, is equal to the square of half the line. i H M Let the straight line AB be divided into two equal parts in the point C, and into two unequal... | |
 | Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...parallelograms about the diameter of a square are likewise squares. •f PROP. V. THEOR. If a straight line be divided into two equal parts, and also into two unequal parts ; the reetangle eontained by the unequal parts, together with the square of the line between the points of... | |
 | John Playfair - Euclid's Elements - 1836 - 488 pages
...parallelograms about the diameter of a square are likewise squares. PROP. V. THEOR. If a straight line be divided into two equal parts, and also into two...square of half the line. Let the straight line AB he .divided into two equal parts in the point C, and into two unequal parts in the point D ; the rectangle... | |
 | Mathematics - 1836 - 488 pages
...that the parallelograms about the diameter of a square are likewise squares. V. If a straight line be divided into two equal parts, and also into two...section, is equal to the square of half the line. COR. From this proposition it is manifest, that the difference of the squares of two unequal lines... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...the rectangle of the parts is equal to the square of one of them. PROP. V. THEOR. IF a straight line be divided into two equal parts, and also into two...square of half the line. Let the straight line AB be bisected in C, and divided unequally in D : the rectangle AD.DB, together with the square of CD, is... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...the squares of AC, CB, and twice the rectangle AC-CB. PROPOSITION V. THEOREM. . If a straight line be divided into two equal parts, and also into two...square of half the line. Let the straight line AB he divided into two equal parts in the point C, and into two unequal parts at the point D ; the rectangle... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...+ GE, and that these are = AC* + CB8 + 2 AC x CB. D H M PROPOSITION V. Theorem. If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle A contained by the unequal parts, I together with the square of the line between the points of section,... | |
 | Euclid - Geometry - 1838 - 470 pages
...demonstration it is manifest, that the parallelograms about the diameter of a square are likewise squares. two unequal parts: the rectangle contained by the...square of half the line. • Let the straight line AH be divided into two equal parts in the point C, and into two unequal parts at the point D ; the... | |
 | Robert Simson (master of Colebrooke house acad, Islington.) - 1838 - 206 pages
...square of the hypotenuse is equal to the sum of the squares of the other two sides. 14. If a right line be divided into two equal parts, and also into two unequal parts, what equations will result? 15. The base of a right-angled triangle is 300 feet, and the sum of the... | |
 | Euclides - 1840 - 192 pages
...half. PROP. V. THEOR. If a straight line (AB) be bisected (in c), and be also divided unequally (in D), the rectangle contained by the unequal parts, together with the square of the part intermediate between the points of section, is equal to the square of half the line. Upon AC describe... | |
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If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line. 
