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" If a straight line be bisected, and produced to any point; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line, which is... "
Euclid, books i. & ii., with notes, examples, and explanations, by a late ... - Page 109
by Euclides - 1879
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 pages
...unequal lines, AC, CD, is equal to the rectangle contained by theif sum and difference. PROP. VI. — THEOREM. If a. straight line be bisected, and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced, together with the...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...DB are double of the squares of AC, CD. If therefore a straight line, etc. QED PROPOSITION X. THEOR. If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 176 pages
...lines a С, С d, is equal to the rectangle contained by their sum and difference. PROPOSITION VI. — THEOREM. If a straight line be bisected, and produced to any point, the rectangle contained by the whqle line thus produced, and the part of it produced, together with the...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856 - 168 pages
...squares of two unequal lines AC, CD is equal to the rectangle contained by their sum and difference. LI. If a straight line be bisected, and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the...
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The English Journal of Education, Volumes 11-13

Education - 1857 - 1266 pages
...To a given straight line apply a rectangle equal to a given rectilineal figure. SECTION II. — 1. If a straight line be bisected and produced to any point, the squares of the whole une produced and the part of it produced arc together double of the squares of...
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1858 - 578 pages
...following equations (1) f+f_=l V ; a T3 4 2 (2) (#-5) (x-2) -(x-5) (2x-5) + (x+1) (sc-2) =0 Euclid. 1. If a straight line be bisected, and produced to any point, the rectangle contained by the whole line thus produced, together with the square of half the line bisected,...
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Parliamentary Papers, Volume 25

Great Britain. Parliament. House of Commons - Bills, Legislative - 1858 - 694 pages
...quadrilateral figure whose diameters bisect each other is a parallelogram. BOOK II. 7. PROP. VI. — If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced, together with the...
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Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - 672 pages
...arrangement.] 1. To bisect a given finite straight line, that is, to divide it into two equal parts. 3. If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 380 pages
...squares on AD, DB are double of the squares on AC, CD. If therefore a straight line be divided, &c. QED PROPOSITION X. THEOREM. If a straight line be bisected, and produced to any point, the square en the whole line thus produced, and the square on the part of it produced, are together double of...
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Guide to the Three Services: Civil, Naval, and Military

John Paxton Hall - 1860 - 186 pages
...The quadrilateral figure whose diameters bisect each other is a parallelogram. BOOK II. PROP. VI. — If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced, together with the...
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