 | 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...parts shall be equal to the square of the other part. 4. The angle at the centre of a circle is double of the angle at the circumference, upon the same base,... | |
 | 1852 - 478 pàgines
...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... | |
 | Royal Military Academy, Woolwich - 1853 - 400 pàgines
...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 that the...parts, shall be equal to the square of the other part. Upon AB describe (46. i.) the square ABDC ; bisect (10. i.) AC in E, and join BE ; produce CA to F,... | |
 | Euclides - 1853 - 176 pàgines
...equal to the square of the other part. LET ab be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by...parts shall be equal to the square of the other part. Upon ab describe (i. 46) the square abdС; bisect (i. 10) a С in e, and join be, produce С a to f,... | |
 | Euclides - 1853 - 146 pàgines
...equal to the square of the other part. Let AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by...parts, shall be equal to the square of the other part. Upon AB describe (1. 46.) the square ABDC ; bisect (I. 10.) AC in E, and join BE; produce CA to F,... | |
 | Royal Military Academy, Woolwich - 1853 - 474 pàgines
...divide a line of 20 inches in length into two parts such that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Let x = the greater part ; then 20 — x = the less part, and hence by the question we have x8 = 20 (20... | |
 | Euclides - 1853 - 334 pàgines
...line. It is required to divide it into two such parts, that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. On AB describe (i. 46) the square ACDB ; and supposing A to be that extremity of AB adjacent to which... | |
 | Cambridge univ, exam. papers - 1854 - 284 pàgines
...therefore the difference of the parallelograms GF, EH is equal to twice the triangle KBD. 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
...therefore the difference of the parallelograms GF, EH is equal to twice the triangle KBD. 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 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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To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part. 
