 | Euclid - Geometry - 1838 - 478 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 unequal...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... | |
 | Euclides - 1840 - 194 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... | |
 | Euclides - 1840 - 82 pages
...square of the half. PROP. V. THEOR. If a straight line be bisected, and be also divided unequally, 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. P E_ AD PROP.... | |
 | Euclides - 1841 - 378 pages
...likewise squares. PROP. V. THEOR. If a straight fine be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal...equal parts in the point C, and into two unequal parts at the point D; the rectangle AD, DB, together with the square of CD, shall be equal to the square... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...then, (a-\-b)2 PROP. V. THEOR. If a straight line lie divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal...point C, and into two unequal parts in the point D ; the rectangle AD.DB, together with the square of CD, is equal to the square of CB, or AD.DB+CD2=... | |
 | Euclides - 1842 - 320 pages
...likewise squares. PROP. V. THEOR. IF a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal...square of the line between the points of section, is equivalent to the square of half the line. Let the straight line AB be divided into two equal parts... | |
 | Education - 1844 - 688 pages
...be double of the triangle. 6. If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal...section, is equal to the square of half the line. 7. In obtuse angled-triangles, if a perpendicular be drawn from either of the acute angles to the opposite... | |
 | John Playfair - Euclid's Elements - 1844 - 338 pages
...For, let the two parts into which this line is divided be denoted by a and 6 ; then, PROP. V. THEOR. Let the straight line AB be divided into two equal...point C, and into two unequal parts in the point D ; the rectangle AD.DB, together with the square of CD, is equal to the square of CB, or AD.DB+CD 2... | |
 | Euclid, James Thomson - Geometry - 1845 - 380 pages
...of them. PROP. V. THEOR. — If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal...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... | |
 | Scottish school-book assoc - 1845 - 434 pages
...be bisected in C, and divided unequally in D, 1 the rectangle AD-DB. together with the square on CD, the line between the points of section is equal to the square on (AC or CB) half the line. For AB2=AD-' + DB-+2AD-DB, (Prop. 37), but AB"=4AC2, (Prop. 37, Cor. 2),... | |
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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 of the line between the points of section, is equal to the square of half the line. 
