 | Euclides - 1852 - 152 pàgines
...and part produced (25). These two Propositions may be omitted at the first reading.] PEOP. XL PROB. To divide a given straight line into two parts, so...rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part. Let AB be the given straight line ; it is required... | |
 | 1852 - 478 pàgines
...two sides which contain the right angle. Is this proposition included in any more general one ? 2. To divide a given straight line into two parts, so that the rectangle contained hy the whole and one of the parts, shall be equal to the square of the other part. Can this be solved... | |
 | Charles Astor Bristed - 1852 - 470 pàgines
...every triangle are equal to two right angles. 3. Divide a given straight line into two such parts, that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. 4. The angle at the centre of a circle is double of... | |
 | Royal Military Academy, Woolwich - 1853 - 400 pàgines
...are double of the squares of AC, CD. Wherefore, if a straight line, etc. QED PROPOSITION XI. PROB. To divide a given straight line into two parts, so...rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part. Upon AB describe (46. i.) the square ABDC ; bisect... | |
 | Euclides - 1853 - 146 pàgines
...are double of the squares of AC, CD. Wherefore, if a straight line, &c. QED PROP. XI. — PROBLEM. To divide a given straight line into two parts, so...rectangle contained by the whole and one of the parts, shall be equal to the square of the other part. Let AB be the given straight line ; it is required... | |
 | Euclides - 1853 - 176 pàgines
...С d. Wherefore, if a straight line, &c. QED PROPOSITION XI. — PROBLEM. To divide a given straigM line into two parts, so that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. LET ab be the given straight line ; it is required... | |
 | Cambridge univ, exam. papers - 1854 - 284 pàgines
...BD the other diameter, the difference of the parallelograms is equal to twice the triangle BKD. 2. Divide a given straight line into two parts so that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Produce a given straight... | |
 | William Walton, Charles Frederick Mackenzie - 1854 - 266 pàgines
...BD the other diameter, the difference of the parallelograms is equal to twice the triangle BSD. 2. Divide a given straight line into two parts so that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Produce a given straight... | |
 | G. Ainsworth - 1854 - 216 pàgines
...— - = -- (-4, and solving, x=lo. 3. Divide the number 20 into two such parts, that the product of the whole and one of the parts may be equal to the square of the other part. Let 2ж=; the difference of the two parts. Now, 20 being the sum, 10 + ж= the greater... | |
 | William Somerville Orr - 1854 - 534 pàgines
...the remarks at the end of this book. PROPOSITION XI.— PROBLEM. To divide a given straight line (AB) into two parts, so that the rectangle contained by the whole, and от of the parts, shall be equal to the square of the other part. From A draw AC perpendicular and... | |
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AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part. 
