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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 English Journal of Education - Page 272
1851
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 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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Papers for the schoolmaster, Volume 4

1868
...explain how 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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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 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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Elements of Geometry, Plane and Spherical: With Numerous Practical Problems

Horatio Nelson Robinson - 1868 - 262 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
...&c. 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...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
...Can a rectangle 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,...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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First Public Examination in Literis Graecis Et Latinis

University of Oxford - 1879
...their other angles 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 parts...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. 4. The diameter...
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Mathews' Euclid examination papers ... on Euc. i.-iv

Edward Harri Mathews - 1879
...right angle is equal to the square described on the sides which contain the right angle. Section IV. 1. If a straight line be divided into two equal parts...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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Queen's scholarship examination. Amner's eight years' scholarship questions ...

Joseph Wollman - 1879
...therefore they are between the same parallels (I. 39). Therefore DE is parallel to EC. QED SECTION IV. 1. If a straight line be divided into two equal parts,...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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Moffatt's scholarship answers, by T.J. Livesey (T. Page).

Moffatt and Paige - 1879
...the area of a triangle whose altitude is (a) units long, and whose base is (5) units long, is £ ab ? If a straight line be divided into two equal parts,...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. By the 41st proposition...
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