 | Euclides - 1874 - 120 pages
...equal to the difference of the squares on the lines." PROPOSITION 7. THEOREM. If a straight line l>e divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square on the... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...that square on BE = rect. (BC, DE) + square on CE. 9. Divide a straight line into two parts so that the squares on the whole line and on one of the parts shall be together equal to three times the square on the other part. 10. Prove that the squares on... | |
 | Euclides - 1874 - 342 pages
...square shall be equal to two given squares. 7. Divide a given straight line into two parts, such that the squares on the whole line and on one of the parts shall be equal to twice the square on the other part. 8. Show that the difference of the squares of... | |
 | Euclides, James Hamblin Smith - Geometry - 1876 - 376 pages
...V. and VI. might be deduced from thia Proposition! A. ri r, 7 1 âĒK i J7 PROPOSITION VII. THEOREM. If a straight line be divided into any two parts,...squares on the whole line and on one of the parts are equal to twice the rectangle contained by the whole and that part together with the square on the other... | |
 | Education Department,London - 1876 - 1010 pages
...intersection together with four right angles are equal to all the interior angles of the polygon. 3. If a straight line be divided into any two parts,...squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square on the... | |
 | Richard Wormell - 1876 - 268 pages
...line be divided into any two parts, the square on the whole line and one of the parts is equivalent to twice the rectangle contained by the whole and...part, together with the square on the other part. SECTION II. â The Theorem of Pythagoras. Enunciation. â " If squares are described on the sides... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...opposite angle, and acute angle. (Take the case where the perpendicular falls within the triangle.) 5. If a straight line be divided into any two parts, the squares on the whole line, and one of the parts, are equal to twice the rectangle contained by the whole and that part, together with... | |
 | Edward Atkins - 1876 - 130 pages
...to the square on CD. Therefore, if a straight line, &c. Q. K D. = 2AB'BC Proposition 7.â Theorem. If a straight line be divided into any two parts, the squares en the whole line and on one of ike parts are equal to twice the rectangle contained by the wJuile... | |
 | Henry Major - 1876 - 784 pages
...the triangle CNK equal to the triangle ARC, and the triangle BMF equal to the triangle ARB, &c.) 2. If a straight line be divided into any two parts, the squares ou the whole line and one of the parts are equal to twice the rectangle contained by the whole and... | |
 | 1877 - 678 pages
...straight line be divided into any two parte, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. What is the algebraical equivalent to this proposition? 5. To divide a given straight... | |
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If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided... 
