| Euclides - 1842
...a square are likewise squares. PROP. V. THEOR. IF a straight line be divided into two equal parts, **and also into two unequal parts, the rectangle contained...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... | |
| 1844
...parallelogram shall 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...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... | |
| James Thomson - 1845 - 358 sider
...the square of one of them. PROP. V. THEOR. — If a straight line be divided into two equal parts, **and also into two unequal parts ; the rectangle contained...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... | |
| Robert Potts - 1845
...double of the square of half the line, and of the square of the line between the points of section. **Let the straight line AB be divided into two equal...the point C, and into two unequal parts in the point** J). Then the squares of AD, DB together, shall be double of the squares of AC, CD. CD B From the point... | |
| 1845
...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),... | |
| John Playfair - 1846 - 317 sider
...PROP. V. THEOR. If a straight line le dividedinto two equal parts, and also into two unequalparts ; **the rectangle contained by the unequal parts, together...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= _CB2. Upon CB describe... | |
| Euclides - 1846
...of a square are likewise squares. PROP. V. THEOR. If a straight Kne be divided into two equal parts, **and also into two unequal parts, the rectangle contained...the square of half the line. Let the straight line** ATI be divided into two equal parts at the point C, and into two unequal parts at the point D : the... | |
| 1846
...(a+b)*—a*-\-2ab + b*. PROP. XLIV. THEOR. 5 . 2 EU. If a straight line be divided into two equal parts, **and also into two unequal parts, the rectangle contained...points of section, is equal to the square of half the** whole line. Let the str. line AB be divided into two equal parts at the pt. C, and into two unequal... | |
| 1846
...is (a+by=a8+2ab+b8. PROP. XLIV. THEOR. 5. 2 Eu. If a straight line be divided into two equal parts, **and also into two unequal parts, the rectangle contained...points of section, is equal to the square of half the** whole line. Let the str. line AB be divided into two equal parts at the pt. C, and into two unequal... | |
| Euclides - 1848
...square are likewise squares. PROP. V. THEOREM. If a straight line be divided into two equal parts, **and also into two unequal parts ; the rectangle contained...section, is equal to the square of half the line.** EUCLID S ELEMENTS. PROP. VI. THEOREM. If a straight line be bisected, and produced to any point ; the... | |
| |