| 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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