 | Euclides - 1874 - 342 pages
...opposite angles of the parallelograms which make the gnomon." PROPOSITION 1.. — Theorem. If there be two straight lines, one of which is divided into any number...the rectangle contained by the two straight lines ^s equal to the rectangles contained by the undivided line, and the several parts of the divided line.... | |
 | Edward Atkins - 1874 - 428 pages
...opposite angles of the parallelograms which make the gnomon. Proposition 1. — Theorem. If t/iere be two straight lines, one of which is divided into any number of parts, t/ie rectangle contained by the two straight lines is equal to t/ie rectangles contained by the undivided... | |
 | Richard Wormell - 1876 - 268 pages
...square upon a given straight line. . . . . . . . . 132 EUCLID.-BOOK II. Prop. Page i. If there be two straight lines, one of which is divided into any number...undivided line, and the several parts of the divided line. . . ,. . . . . . . . . . . 145 3. If a straight line be divided into any two parts, the rectangles... | |
 | Euclides, James Hamblin Smith - Geometry - 1876 - 376 pages
...coincides with and is therefore equal to rect. ABCD. q. ED 77 PROPOSITION I. THEOREM. If there be two straight lines, one of which is divided into any number...undivided line and the several parts of the divided line. (f .-:/: Let AB and CD be two given st. lines, and let CD be divided into any parts in E, F. Then must... | |
 | Henry Major - 1876 - 784 pages
...be l> units, the area of the triangle will be algebraically represented by ia b. 2. If there be two straight lines, one of which is divided into any number...undivided line and the several parts of the divided line. 3. If a straight line bo divided into two equal, and also into two unequal parts ; the squares on the... | |
 | Edward Atkins - 1876 - 130 pages
...as AB and BC, Is concisely expressed thus ; — AB, BO. Proposition 1. — Theorem. If there be two straight lines, one of which is divided into any number...undivided line, and the several parts of the divided line. Let A and BC be two straight lines; and let BC be divided into any parts in the points D, E ; The rectangle... | |
 | Euclides, James Hamblin SMITH - 1876 - 382 pages
...coincides with and is therefore equal to reet. ABCD. QED PROPOSITION I. THEOREM. . If there be two straight lines, one of which is divided into any number...equal to the rectangles contained by the undivided lint and the several parts of the divided line. Let AB and CD be two given st. lines, and let CD be... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...sometimes " the rectangle ABC." To this proposition may be added the corollary : If two straight lines be divided into any number of parts, the rectangle contained by the two straight lines, IB equal to the rectangles contained by the several parts of one line and the severe! parts of the... | |
 | Great Britain. Education Department. Department of Science and Art - 1877 - 562 pages
...(25). + *•• — x+y + z '.'.x -y + s :x + y — z. (25). Section B.—Geometry. 27. If there be two straight lines, one of which is divided into any number...equal to the rectangles contained by the undivided lirfe and the several parts of the divided line. The sum of the perpendiculars let fall from any point... | |
 | Āryabhaṭa - 1878 - 100 pages
...PKOP. A, THEOREM. (E. 2. I). If there be two straight lines, one of whieh is divided in I •any two parts, the rectangle contained by the two straight...rectangles contained by the undivided line and the parts of the divided line. In the above figure, let BC and BL be two straight 'mes. Let BC be devided... | |
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If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. 
