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" IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. "
The Elements of Euclid; viz. the first six books, together with the eleventh ... - Page 45
by Euclides - 1814
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 88 pages
...showing that AB x BC = figures AD + CE, and that these are = AC x CB + CB*. PROPOSITION IV. Theorem. If a straight line be divided into any two parts,...together with twice the rectangle contained by the parts. * By the rectangle AX BC (the lines A and BC being separate) is' meant the rectangle which may be formed...
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Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - Geometry - 1837 - 215 pages
...the rectangle contained by ac and c b. M.- — Express this truth as a general proposition. P. — If a straight line be divided into any two parts,...together with twice the rectangle contained by the parts. The master will, here, have a suitable opportunity of directing the attention of his pupils to a numerical...
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Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - Geometry - 1837 - 215 pages
...twice the rectangle contained by ac and c b. M.—Express this truth as a general proposition. P.—If a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts. The master will, here, have a suitable opportunity of directing the attention of his pupils to a numerical...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 390 pages
...equal to the square of BC, together with the rectangle AC.CB. * If, therefore, &c. PROP. IV. THEOR. IF a straight line be divided into any two parts,...the squares of the two parts, together with twice their rectangle, t Let the straight line AB be divided into any two parts in C ; the square of AB is...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 pages
...twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BO, are equal to twice the rectangle AB-BC, together with the square...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...equal to the rectangle contained by the two parts, together with the square of the aforesaid part. Let the straight line AB be divided into any two parts in the point C : the rectangle AB-BC shall be equal to the rectangle AC-CB, together with the square of...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1839 - 332 pages
...than in ordinary language. The proposition, (Enc. 4. 2.) thai when a straight line is divided into two parts, the square of the whole line is equal to the squares of the iwo parts, together with twice the product of the parts, is demonstrated, by involving a binomial....
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Minutes of the Committee of Council on Education

Great Britain. Committee on Education - School buildings - 1853
...equal to a given triangle, and have one of its angles equal to a given rectilineal angle. Sec/ion 2. 1. If a straight line be divided into any two parts,...together with twice the rectangle contained by the parts. 2. If a straight line be divided into two equal and also into two unequal parts, the squares of the...
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A Treatise on Geometry and Its Application in the Arts

Dionysius Lardner - Curves, Plane - 1840 - 314 pages
...several rectangles under the line and each of its parts. (242.) If a line be divided into two or more parts, the square of the whole line is equal to the squares of the several parts together with twice the rectangles under every pair of parts. Let theline AB (fig.l 1...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...contained by the whole line and that part, together with the square of the other part. PROP. VIII. THEOR. If a straight line be divided into any two parts, the square of the sum of the whole line and one of its parts is equal to four times the rectangle contained by the whole...
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