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" IF a straight line be divided into two equal, and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section. "
First Steps in Geometry: A Series of Hints for the Solution of Geometrical ... - Page 175
by Richard Anthony Proctor - 1887 - 180 pages
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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 130 pages
...together. (AB+BC)3. Therefore, if a straight line, &c. QED Proposition 9. — Theorem. If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line, and of the square on the...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry - 1876 - 446 pages
...one-fourth from one of its sides, will also cut off a fourth part from the other side. 4. If a straight line be divided into two equal and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line, and of the square on.the...
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The Pupil teacher, a monthly educational journal. H. Major, ed

Henry Major - 1876 - 784 pages
...the other two sides of it ; the angle contained by these two sides is a right angle. 2. If a straight line be divided into two equal, and also into two unequal parts, the squares on the two nneqnal parts are together double of the square on half the line, and of the square on the...
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Examination Christmas,1875

Education Department,London - 1876 - 1010 pages
...of the triangle whose sides numerically represented are 112,147, 84? SECTION III. 1. If a straight line be divided into two equal and also into two unequal parts, the rectangle contained by the unequal parts together wit! the square on the line between the points...
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Civil Service of India: Open Competition for the Regulations, Examinations ...

Civil service - 1878 - 228 pages
...the middle points of either pair of opposite sides will trisect the other diagonal. 3. If a straight line be divided into two equal and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of...
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Euclid, books i. & ii., with notes, examples, and explanations, by a late ...

Euclides - 1879 - 146 pages
...contains a — x units, hence the analogous result is established.] PROPOSITION IX. THEOREM. If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line, and of the square on the...
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Moffatt's scholarship answers, by T.J. Livesey (T. Page).

Moffatt and Paige - 1879 - 378 pages
...square on semi-diameter is half of the whole square. SECTION IV. (Three Questions.) 1. If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line, and of the square on the...
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First Public Examination in Literis Graecis Et Latinis

University of Oxford - Greek language - 1879 - 412 pages
...shall be equal, each to each, namely those to which the equal sides are opposite. 3. If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the...
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Moffatt's pupil teachers' course (ed. by T. Page). Candidates, 2nd (-4th) year

Moffatt and Paige - 1879 - 506 pages
...in one straight line. Therefore, if a straight line, etc. QED Proposition IX. Theorem. If a straight line be divided into two equal and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the...
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Mathews' Euclid examination papers ... on Euc. i.-iv

Edward Harri Mathews - 1879 - 94 pages
...in order ; show that a, b, c, d, are the angular points of another parallelogram. 2. If a straight line be divided into two equal, and also into two unequal parts, the rectangle contained by the two unequal parts, together with the square of the line between the points...
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