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" PROP. I. THEOR. If there oe 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. "
The Elements of Euclid; viz. the first six books,together with the eleventh ... - Page 50
by Euclides - 1841 - 351 pages
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Pure mathematics, Volume 1

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...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 pages
...a 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...undivided line, and the several parts of the divided line. . . ,. . . . . . . . . . . 145 3. If a straight line be divided into any two parts, the rectangles...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1876 - 376 pages
...EFGH 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...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...
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The Pupil teacher, a monthly educational journal. H. Major, ed

Henry Major - 1876 - 784 pages
...altitude 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...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...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1876 - 382 pages
...EFGH 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...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...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

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...
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Examination Papers for Science Schools and Classes

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...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...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1878 - 398 pages
...rect. EFGH coincides with and is therefore equal to rect. ABCD. QED PROPOSITION I. THEOREM. If there be two straight lines, one of which is divided into any...line and the several parts of the divided line. Let AB and CD be two given st. lines, and let CD be divided into any parts in E, F. Then must rect. AB,...
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The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

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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Elements of Plane Geometry, Part 1

Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...of AB is equal to the sum of the squares of AC and CB. PKOPOSITION XIV.—THEOREM. • If there be two straight lines, one of which is divided into any...number of parts, the rectangle contained by the two lines is equal to the sum of the rectangles contained by the undivided line and the several parts of...
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