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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: Viz. the First Six Books, Together with the Eleventh ... - Side 53
av Euclid, Robert Simson - 1821 - 516 sider
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Elements of Geometry, Plane and Spherical: With Numerous Practical Problems

Horatio Nelson Robinson - 1868 - 262 sider
...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
...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, and...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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The Edinburgh university calendar

Edinburgh univ - 1871
...of the other. A complete demonstration is required. 4. If a straight line be divided into two equal, and also into two unequal parts, the rectangle contained...section, is equal to the square of half the line. Prove this also algebraically. 3. Prove Prop. 47, introducing in addition a variation in which one...
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Elements of geometry, containing the first two (third and fourth ..., Del 1

Euclides - 1871
...rectangle, contained by the segments of the base, is equal to the square on the perpendicular. SE 6 If a straight line be divided into two equal parts and...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. JD K. S. Let the...
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The National Schoolmaster, Volumer 7-8

1877
...line into two parts, so that the square on one part shall be double of the square on the other. 2. If a straight line be divided into two equal parts, and...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. Algebra. a'ly'z...
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Moffatt's scholarship answers, by T.J. Livesey (T. Page).

Moffatt and Paige - 1879
...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, and...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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Mathews' Euclid examination papers ... on Euc. i.-iv

Edward Harri Mathews - 1879
...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 and...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 - 1879
...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 and...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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Euclid, books i. & ii., with notes, examples, and explanations, by a late ...

Euclides - 1879
...the line intercepted between the other equal angle and the perpendicular. PROPOSITION V. THEOREM. If a straight line be divided into two equal parts, and...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 lint. Let AB be divided...
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