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" If a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square on the other part. Let the straight line AB be divided... "
Examination Papers for Science Schools and Classes - Page 30
by Great Britain. Education Department. Department of Science and Art - 1886
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 186 pages
...divided into any two parts AC, CB, the squares of the whole line and of one of the parts are together equal to twice the rectangle contained by the whole line and that part together with the square of the other part. That is, ABa + BO 2 AB . BC + AC3, by adding 2AB . BC to the two equals in the...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 pages
...VII. THEOR. If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to 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...
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The Element of Geometry

John Playfair - Geometry - 1836 - 114 pages
...XXV. THEOR. If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts are equal to 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...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 472 pages
...produced. VII. If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Сон. Hence the sum of the squares of...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 88 pages
...VII. Theorem. If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle...whole line and that part, together with the square of the other part. i> K Proved by showing that AB* + uc* = figs. AG + GE + 2 CH + KF, and that these...
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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
...square CF. IF a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to 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...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...VII. THEOR. If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to 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...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...VII. THEOR. If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle...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...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...square of the sum of the whole line AB and one of its parts CB, is equal to 4 AB'CB, or four times the rectangle contained by the whole line and that part, together with AC2 or the square of the other part. PROP. IX. THEOR. If a straight line (AB) be divided equally (in...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 351 pages
...a * 43. 1. If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the otherpart. Let the straight line AB be divided into...
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