 | Alfred Wrigley - 1845 - 222 pages
...points of contact, and the diameter drawn from one of these points. (Euclid, iii. 18. Cape, ii. 38.) 59. 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 a given line, which... | |
 | Scottish school-book assoc - 1845 - 444 pages
...AB, CD, cut one another in a point E, within a circle A CD, the rectangle contained by the segments of the one shall be equal to the rectangle contained by the segments of the other. That is, the rectangle AE-EB=CE-ED. Join CA and BD, then the Z.CAE is = the... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...(2a+i)2+J2=2o2+2(a+4)2, and the proposition is evident from this algebraical equality. PROP. XI. PROB. 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.... | |
 | Euclides - 1848 - 52 pages
...bisected, and of the square of the line made up of the half and the part produced. PROP. XI. PROBLEM. To divide a given straight 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.... | |
 | Euclid, Thomas Tate - 1849 - 120 pages
...squares of AC, CD: Wherefore, if a straight line, &c. QED Again, because EG F is EF PROP. XI. PROB. To divide a given straight line into two parts, so that the -rectangle contained by the whole, and one of the parts, shall Tie equal to the square of the other... | |
 | Bengal council of educ - 1852 - 348 pages
...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 by the whole and one of the parts, shall be equal to the square of the other part.... | |
 | Education - 1852 - 478 pages
...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.... | |
 | Euclides - 1852 - 152 pages
...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 that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.... | |
 | Euclides - 1853 - 146 pages
...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 that the rectangle contained by the whole and one of the parts, shall be equal to the square of the other part.... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...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 that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.... | |
| |
AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part. 
