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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. Let... "
The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ... - Page 40
by Robert Simson - 1827 - 513 pages
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The Elements of Euclid

Euclid - Geometry - 1838 - 416 pages
...to the rectangles contained by the undivided line, and the several parts of the divided line. Let-A and BC be two straight lines; and let BC be divided...the rectangle contained by the straight lines A, BC is equal to the rectangle B DEC contained by A, BD, together with that contained by A, DE, and that...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...and AB), of which one (AB) is divided into any number of parts (AF, FH, HB), is equal to the sum of the rectangles contained by the undivided line and the several parts of the divided line. From A draw AC perpendicular to AB, make it equal to L, and complete the parallelogram AD (that is...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...contained by two straight lines, of which one is divided into any number of parts, is equal to the sum of the rectangles contained by the undivided line and the several parts of the divided line. PROP. II. THEOR. If a straight line be divided into any two parts, the square of the whole line is...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 317 pages
...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...into any parts in the points D, E ; the rectangle A.BC is equal to the several rectangles A.BD, A.DE, A.EC. From the point B draw (Prop. 11.1.) BF at...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...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...undivided line, and the several parts of the divided line. by A, BD, together with that contained by A, DE, and that contained by A, EC. From the point в draw...
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The British Annals of Education for ...: Being The Scholastic ..., Volumes 1-2

Education - 1844
...straight lines, one of which is divided into any number ot parts, the rectangle contained by the two straight lines is equal to the rectangles contained...undivided line and the several parts of the divided line. 7. If a straight line be divided into any two parts, the squares of the whole line, and of one of the...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 199 pages
...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...the rectangle contained by the straight lines A, BC is equal to the rectangle contained by A, BD, together with that contained by A, DE, and that contained...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...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...let BC be divided into any parts in the points D, E. Then the rectangle contained by the straight lines A and BC, shall be equal to the rectangle contained...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 352 pages
...straight lines, one of which is divided into any number of parts ; the rectangle contained by the two lines, is equal to the rectangles contained by the...and BC be two straight lines ; and let BC be divided * Thia book treats of right-angled parallelograms, and in particular of squares. t That iť. by any...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845
...PROPOSITION V. THEOREM. If there be two right lines, of which one is divided into parts, the sum of the rectangles contained by the undivided line and the several parts of the other, will be equal to the rectangle contained by the two whole lines. Let the lines be AB, AC, of...
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