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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. "
Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ... - Page 117
by Charles Reiner - 1837 - 215 pages
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 112 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, the...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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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 pages
...BC is equal to the rectangle AC • CB, together with the square of BC. PROPOSITION TV. THEOREM. If a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts. Let the straight line AB be divided into any two parts in C ; the square of AB is equal to the squares...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Geometry - 1837 - 410 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...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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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 pages
...IV. THEOR. If a straight line be divided into any two parts, the sqtmre of the whole line is equal in the squares of the two parts, together with twice the rectangle contained by the parts. Let the straight line AB be divided into any two parts in C ; the square of AB shall be equal to the...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1839 - 354 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 - 1218 pages
...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, the...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 - 386 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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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 194 pages
...by the parts. F T PROP. IV. THEOR. If a straight line (AB) be divided into any two parts (AF, FB), the square of the whole line is equal to the squares of the parts, together with twice the rectangle contained by the parts. Upon AB describe the square ACDB ;...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840 - 82 pages
...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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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 378 pages
...rectangle AC, CB, together with the square of BC. If therefore a straight, &c. QED PROP. IV. THEOR. If a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts. Let the straight line AB be divided into any two parts in C; the square of AB is equal to the squares...
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