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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. "
The first and second books of Euclid explained to beginners, by C.P. Mason - Page 152
by Euclid, Charles Peter Mason - 1872
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Plane Trigonometry for the Use of Colleges and Schools: With Numerous Examples

Isaac Todhunter - Plane trigonometry - 1874 - 360 pages
...x = a + Ъ, 4. If sin 30 = sin в cos 20 then & = -^ where и is zero or aa integer. 5. If an angle be divided into two equal and also into two unequal parts, the product of the sines of the unequal parts together with the square of the sine of the angle between...
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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 130 pages
...of AB and BC together. (AB+BC)3. Therefore, if a straight line, &c. QED Proposition 9. — Theorem. If a straight line be divided into two equal, and...the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section....
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The Pupil teacher, a monthly educational journal. H. Major, ed

Henry Major - 1876 - 784 pages
...described upon 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 lino between...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 pages
...made up of the whole and the first mentioned part. .. .. . . 145 9. If a straight line be divided īmo 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 line between the points of section....
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Examination Christmas,1875

Education Department,London - 1876 - 1010 pages
...is the nature 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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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry - 1876 - 446 pages
...added together in one straight line. Wherefore, if a straight line, &c, QED .1 PROPOSITION IX. THEOREM. If a straight line be divided into two equal, and also into two unequal parti; the squares on the two unequal parts are together double of the square on half the line, and...
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Examination Papers for Science Schools and Classes

Great Britain. Education Department. Department of Science and Art - 1877 - 562 pages
...Given that a : b '.'. b : c, show that :— a'+6'+c'=(a+6+c) (a-6+c) (20.) Section B.—Geometry. 27. If a straight line be divided into two equal and also into t\ro unequal parts, show that the rectangle contained by the unequal parts, together with the square...
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Civil Service of India: Open Competition for the Regulations, Examinations ...

Civil service - 1878 - 228 pages
...parallelogram with 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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Moffatt's scholarship answers, by T.J. Livesey (T. Page).

Moffatt and Paige - 1879 - 378 pages
...E. That is, 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...the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section....
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Euclid, books i. & ii., with notes, examples, and explanations, by a late ...

Euclides - 1879 - 146 pages
...Now BC contains a — x units, hence the analogous result is established.] PROPOSITION IX. THEOREM. If a straight line be divided into two equal, and...the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section....
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