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. The English Journal of Education - Page 2721851Full view - About this book
| Euclid, Thomas Tate - 1849 - 108 pages
...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 squares... | |
| Harvey Goodwin - 1851 - 173 pages
...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... | |
| 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 pages
...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 pages
...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... | |
| Royal Military Academy, Woolwich - 1853
...diameter of a square are likewise squares. PROPOSITION V. THEOR. If a straight line be divided inio **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... | |
| Euclid, John Playfair - 1853 - 317 pages
...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... | |
| Euclides - 1853
...proved. PEOP. V. THEOE. If a straight line be bisected, and also divided into two unequal parts : then **the rectangle contained by the unequal parts together with the square of the** part of the line intercepted between the points of section, shall be equal to the square of half the... | |
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