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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. "
The Elements of Euclid, the parts read in the University of Cambridge [book ... - Página 58
por Euclides - 1846
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Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862 - 140 páginas
...of which is dicided into any number of parts, the rectangle contained by the tiro straight lin<!,< is equal to the rectangles contained by the undivided line, and the several parts of the divided line. , (References— Prop. I. 3, 11, 31, 34.) Hypothesis. — Let A and BC be two straight lines ; and...
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The school Euclid: comprising the first four books, by A.K. Isbister

Euclides - 1862 - 172 páginas
...which are at the opposite angles of the parallelograms which make the Gnomon.' PROP. I.— THEOREM. If there be two straight lines, one of which is divided into any number of parts ; then the rectangle contained by the two straight lines, is equal to the rectangles contained by the...
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Responsions

University of Oxford - 1863 - 316 páginas
...subtending the right angle is equal to the squares described on the sides which contain the right angle. 11. If there be two straight lines, one of which is divided...contained by the two straight lines is equal to the rectangle contained by the undivided line, and the several parts of the divided line. 12. Describe...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 páginas
...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...lines, is equal to, the rectangles contained by the several parts of one line and the several parts of the other respectively. The method of reasoning...
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Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ...

Euclides - 1864 - 262 páginas
...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...lines, is equal to the rectangles contained by the several parts of one line and the several parts ol the other respectively. The method of reasoning...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 páginas
...Define a rectangle. By what is it contained? 2. Define a gnomon. PROPOSITIONS AND COROLLARIES. Prop. 1. If there be two straight lines, one of which is divided...undivided line, and the several parts of the divided line. Prop. 2. If a straight line be divided into any two parts, the rectangles contained by the whole and...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 páginas
...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...lines, is equal to the rectangles contained by the several parts of one line and the several parts of the other respectively. The method of reasoning...
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - 1865 - 474 páginas
...into any number of parts, the rectangle contained by the two lines is equal to the sum of the several rectangles contained by the undivided line and the several parts of the divided line. Let AB and AD be two lines, and suppose AB divided into any number of parts at the points E, F, G, etc....
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1855 - 350 páginas
...may also, for the sake of 4 brevity, be called the gnomon AGK •or EHC." JJ DEC PROP. I. THEOR. I/ there be two straight lines, one of which is divided into any number ej parts ; the rectangle contained by the two straight lines is equal to the rectangles contained by...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Isaac Todhunter - 1867 - 426 páginas
...at the opposite angles of the parallelograms which make the gnomon. AE K DE PROPOSITION 1. THEOREM. If there be two straight lines, one of which is divided...any number of parts, the rectangle contained by the tiro sir-tight lines is equal to the rectangles contained by the undleided line, and the several parts...
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