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" If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line. "
The Elements of Euclid, the parts read in the University of Cambridge [book ... - Page 62
by Euclides - 1846
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...parallellograms about the diameter of a square are likewise squares. PROPOSITION 5. THEOREM. If a straight line be divided into two equal parts and also into two unequal parts, the rectangle contained by iht unequal parts, together with the square on the line between the points of section, is equal to...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...about the diameter of a square are likewise squares. PROPOSITION 5. THEOREM. If a straight line 1ie divided into two equal parts and also into two unequal parts, the rectangle contained l)y the unequal parts, together with the square on the line between the points of section, is equal...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...= a' — m*, to each of these equals add m* ; .'. (a + m) (a — m) + m' = a*. That is, if a number be divided into two equal parts, and also into two unequal parts, the product of the unequal parts together with the square of half their difference, is equal to the square...
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Papers for the schoolmaster, Volume 4

1868 - 344 pages
...rectangular areas are represented by the product of two numerical symbols. SECTION VI. 1. If a straight line be divided into two equal parts, and also into two unequal parts, the rectal gle contained by the unequal parts, together with the square of the line between the points...
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Elements of Geometry, Plane and Spherical: With Numerous Practical Problems

Horatio Nelson Robinson - Geometry - 1868 - 276 pages
...be divided into two equal parts, and aha into two unequal parts, the rectangle contained by the two unequal parts together with the square of the line between the points of division, will be equivalent to the square on one half the line. Let AB be a line bisected in (7, and...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1870 - 270 pages
...Psts. 2 and 3 ; 3. I. 10. I. To bisect a given finite st. line. Pst. 1. DEM. — 5. II. If a st. line be divided into two equal parts, and also into two...rectangle contained by the unequal parts together with the squai e of the line between the points of section, equals the square of half the line. Def. 15 and...
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Handbook to government situations: or, The queen's Civil service considered ...

Civil service - 1871 - 258 pages
...always be described on a given straight line equal to a given rectilineal figure ? 4. If a straight line be divided into two equal parts, and also into two...section, is equal to the square of half the line. 5. Draw a straight line to touch a given circle from a given point without it. Algebra. 1. Show, by...
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Mathews' Euclid examination papers ... on Euc. i.-iv

Edward Harri Mathews - 1879 - 94 pages
...the square described on the sides which contain the right angle. Section IV. 1. If a straight line be divided into two equal parts and also into two...contained by the unequal parts together with the square on the line between the points of section, is equal to the square on half the line. Construct a rectangle...
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First Public Examination in Literis Graecis Et Latinis

University of Oxford - Greek language - 1879 - 412 pages
...exterior angle shall be greater than either of the interior opposite angles. 6. If a straight line be divided into two equal parts and also into two...contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line. 7. In a circle...
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Moffatt's scholarship answers, by T.J. Livesey (T. Page).

Moffatt and Paige - 1879 - 378 pages
...AC and BC. .-. Angle ACB is an obtuse angle. SECTION IV. (Three questions.)—1. If a straight line be divided into two equal parts, and also into two...contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line. At what point must...
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