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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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The school Euclid: comprising the first four books, by A.K. Isbister

Euclides - 1862
...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 - Education, Higher - 1863
...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 into any...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
...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
...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
...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 into any...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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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - Conic sections - 1865 - 444 pages
...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 - Geometry - 1855 - 317 pages
...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...contained by the undivided line, and the several parts nj the divided line. Let A and BC be two straight lines ; and let BC be divided into any parts in the...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...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 into 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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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 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...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, Plane and Spherical: With Numerous Practical Problems

Horatio Nelson Robinson - Geometry - 1868 - 262 pages
...to (AB+CD)xEF. Hence the theorem; the area of a trapezoid, etc. THEOREM XXXV. If one of two lines is divided 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...
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