 | Great Britain. Committee on Education - School buildings - 1853 - 1218 pages
...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 - Euclid's Elements - 1842 - 332 pages
...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 - 320 pages
...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 - Geometry - 1845 - 218 pages
...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 - Geometry - 1845 - 380 pages
...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 - 544 pages
...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... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 332 pages
...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 - 292 pages
...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... | |
 | Euclid - 1848 - 52 pages
...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 - 388 pages
...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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IF a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section. 
