 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...rectangle BP, PQ + rectangle BP, QC. Hence, if a straight line be divided into any number of parts, the rectangle contained by the whole line and one of the parts is equal to the square on that part together with the rectangles contained by that part and the other... | |
 | Edward Atkins - 1876 - 130 pages
...square on AC. Therefore, if a straight line, &c. Q. E, D. Proposition 8. — Theorem. If a straight line be divided into any two parts, four times the...line and one of the parts, together with the square on the other part, is equal to the square on the straight line which is made up of the whole line and... | |
 | Euclides, James Hamblin Smith - Geometry - 1876 - 376 pages
...to B and from (f to D, shew that BO D ia a straight line. PROPOSITION VIII. THEOREM. If a straight line be divided into any two parts, four times the rectangle contained by ike whole line and one of the parts, together with the square on the other part, is equal to the square... | |
 | Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...several parts into which the other is divided. COR. T. If a straight line is divided into two parts, the rectangle contained by the whole line and one of the parts is equal to the sum of the square on that part and the rectangle contained by the two parts. COR. 2.... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...other part. Let AB\vt the given straight line. It is required to divide 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 FO CK 1) Upon AB describe the square A CDB ; (I. 46.)... | |
 | Richard Wormell - 1876 - 268 pages
...AB:BC = AD:DE. PROBLEM XX. To divide a straight line in extreme mean ratio — that is to say, so that the rectangle contained by the whole line and one of the parts shall be equal to the square on the other part. Let AB be the straight line. Construct the square ABDE... | |
 | Euclides - 1878 - 398 pages
...to B and from. (? to D, shew that BGD is a straight line. PROPOSITION VIII. THEOREM. If a straight line be divided into any two parts, four times the...contained by the whole line and one of the parts, together vrith the square on the other part, is equal to the square on the straight line which is made up of... | |
 | W J. Dickinson - Geometry - 1879 - 44 pages
...that the sum of the squares on two lines is never less than twice their rectangle. 8. If a straight line be divided into any two parts, four times the...square of the other part, is equal to the square of the straight line, which is made up of the whole and that part. . . 9. If a straight line be divided into... | |
 | Euclides - 1879 - 146 pages
...shall be equal to a given square. Is this always possible ? PROPOSITION VIII. THEOREM. If a straight line be divided into any two parts, four times the...line and one of the parts, together with the square on the other part, is equal to the square on the straight line which is made up of the whole and that... | |
 | Moffatt and Paige - 1879 - 506 pages
...the square on A C. Therefore, if a straight line, etc. QED Proposition VIII. Theorem. If a straight line be divided into any two parts, four times the...line and one of the parts, together with the square on the other part, is equal to the square on the straight line which is made up of the whole and that... | |
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If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that... 
