| Euclid, Thomas Tate - 1849 - 120 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...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 at the point D ; the... | |
| 1850 - 400 pages
...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 two...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 - Mathematics - 1851 - 196 pages
...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, and also into two...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... | |
| Education - 1851 - 502 pages
...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, and also into two...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 - 152 pages
...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, and also into two...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 at the point D ; the... | |
| Benjamin Greenleaf - Algebra - 1852 - 348 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 - 146 pages
...parallelograms about the diameter of a square are likewise squares. PROP. V. THEOREM. If a straight 'line be divided into two equal parts, and also into two...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 at the point D; the rectangle... | |
| Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...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,...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 at the point D ; the... | |
| Euclid, John Playfair - Geometry - 1853 - 336 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;...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 in the point D ; the... | |
| Euclides - Geometry - 1853 - 176 pages
...about the diameter of a square are likewise squares. PROPOSITION V. — THEOREM. If a straight line be divided into two equal parts, and also into two...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... | |
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