 | 1848
...Tate's Geometry," &c. page 39, where a new proof is given of this important theorem. SECTION 3. 1. If a straight line be divided into two equal parts,...parts, the rectangle contained by the unequal parts, togelher with the square of the line between the points of section, is equal to the square of half... | |
 | Euclides, Thomas Tate - 1849 - 108 sider
...manifest that the parallelograms about the diameter of a square are likewise squares. PROP. V. THEOR. If a straight line be divided into two equal parts,...section, is equal to the square of half the line. Let the straight line AB be divided into two equal parts in the point c, and into two unequal parts... | |
 | 1850
...produced, the exterior angle is greater than either of the interior opposite angles. 2. If a right line be divided into two equal parts, and also into...section, is equal to the square of half the line. 3. In every triangle, the square of the side subtending either of the acute angles, is less than the... | |
 | Harvey Goodwin - 1851 - 173 sider
...divided into four equal parts. In what case will the diameter bisect the angle of a parallelogram? 3. If a straight line be divided into two equal parts,...section, is equal to the square of half the line. 4. Equal straight lines in a circle are equally distant from the centre ; and conversely, those which... | |
 | 1851
...a given rectilineal angle. upon the same side together equal to two right angles. SECTION II.—1. If a straight line be divided into two equal parts,...section, is equal to the square of half the line. 3. The opposite angles of any quadrilateral figure inscribed in a circle are together equal to two... | |
 | Euclides - 1852
...same may be shown of any other division of 8, as into 6 and 2, or 7 and 1.] BOOK II. PROP. V. THEOR. If a straight line be divided into two equal parts,...section, is equal to the square of half the line. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts... | |
 | Benjamin Greenleaf - 1852 - 336 sider
...c=3. Then 12=9+3; And 4Xl2X9+3 2 =(3X2X9) 2 ; 441 = 441. THEOREM XIII. 17O. If any quantity or number be divided into two equal parts, and also into two unequal parts, the sum of the squares of the two unequal parts will be double the squares of half the quantity, plus twice... | |
 | Euclides - 1853
...manifest that the parallelograms about the diameter of a square are likewise squares. PROP. V. THEOREM. If a straight 'line be divided into two equal parts,...section, is equal to the square of half the line. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts... | |
 | Euclides - 1853 - 147 sider
...the parallelograms about the diameter of a square are likewise squares. PROPOSITION V. — THEOREM. If a straight line be divided into two equal parts,...points of section, is equal to the square of half the Une. LET the straight line ab be divided into two equal parts in the point С, and into two unequal... | |
 | Euclid, John Playfair - 1853 - 317 sider
...line is divided be denoted by a and b; then, (a+6)* PROP. V. THEOR. If a straight line bcdividedinto two equal parts, and also into two unequal parts;...section, is equal to the square of half the line. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts... | |
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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. 
