| Great Britain. Committee on Education - 1853
...equal to the squares of the two parts, together with twice the rectangle contained by the parts. 2. If **a straight line be divided into two equal and also...square of the line between the points of section.** 3. If from any point without a circle two straight lines be drawn, one of which cuts the circle and... | |
| John Playfair - 1842 - 317 sider
...or 4ai+c2=(cr-26)2. PROP. IX. THEOR. If a straight line be divided into two equal, and also into twn **unequal parts ; the squares of the two unequal parts...points of section. Let the straight line AB be divided** at the point C into two equal, and at D into two unequal parts ; The squares of AD, DB are together... | |
| Euclides - 1842
...line. Wherefore, if a straight line, &c. QED PROP. IX. THEOR. equal parts are together equivalent to **double of the square of half the line, and of the...points of section. Let the straight line AB be divided** at the point c into two equal, and at D into two unequal parts : the squares of AD, DB are together... | |
| Euclid - 1845 - 199 sider
...together in one straight line. Wherefore, if a straight line, &c. QED PROPOSITION IX. THEOR. — If **a straight line be divided into two equal, and also...points of section. Let the straight line AB be divided** at the point C into two equal, and at D into two unequal parts : the squares of AD, DB are together... | |
| Euclid, James Thomson - 1845 - 352 sider
...BC added together in one straight line. Therefore, if a straight line, &c. PROP. IX. THEOR. — If **a straight line be divided into two equal, and also into two unequal parts ; the squares of the** unequal parts are together double of the square of half the line, and of the square of the line between... | |
| Euclides - 1845
...lines is never less than twice their rectangle. 8. If a straight line be divided into two equal and **into two unequal parts, the squares of the two unequal parts are** equal to twice the rectangle contained by the two unequal parts, together with four times the square... | |
| John Playfair - 1846 - 317 sider
...member of this equality, we shall have, 4aJ+c2=c2+4ic+4J2, or4ai+c2=(c4-26)2. PROP. IX. THEOR. • If **a straight line be divided into two equal, and also...points of section. Let the straight line AB be divided** at the point C into two- equal, and at D into two unequal parts ; The squares of AD, DB are together... | |
| Euclides - 1846
...the rectangle ABCD is equal to twice the triangle AEF together with the rectangle BE, DF. 21. If a **line be divided into two equal and also into, two...the squares of the two unequal parts are together** equal to twice the rectangle contained by these parts together with four times the square of the line... | |
| Euclides - 1848
...the square of the straight line, which is made up of the whole and that part. PROP. IX. THEOREM. If **a straight line be divided into two equal, and also...square of the line between the points of section.** PROP. X. THEOREM. If a straight line be bisected, and produced to any point, the square of the whole... | |
| J. Goodall, W. Hammond - 1848
...the square of the aforesaid part. 2. Prove that if a straight line be divided into two equal and also **two unequal parts, the squares of the two unequal...square of the line between the points of section.** 3. Prove that in obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles... | |
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