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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... "
Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ... - Page 87
by Euclid - 1890 - 400 pages
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Elements of Plane and Solid Geometry: And of Plane and Spherical ...

Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...another problem of the same nature, in which it is required to p^gduce a straight line AB, such that the rectangle contained by the whole line thus produced and the part produced shall be equivalent to the square of the line AB itself. Bisect AB in C ; draw the perpendicular...
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A Book of Mathematical Problems on Subjects Included in the Cambridge Course

Joseph Wolstenholme - Mathematics - 1867 - 368 pages
...extreme and mean ratio and produced so that the part produced is equal to the smaller of the segments, the rectangle contained by the whole line thus produced and the part produced together with the square on the given line, will be equal to four times the square ou the...
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Annual Report

1868 - 876 pages
...equal to the squares described upon the sides which contain the right angle 20 4. If a straight line be bisected and produced to any point, the rectangle...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 made up of the half...
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Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1868 - 426 pages
...— as) in the expansion of - — — — , prove Cr=BJ.-B,._1. (1—3?)" 9. If a straight line be bisected and produced to any point ; the rectangle...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 made up of the half...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...rectangle contained by their sum AD and their difference DB. PROPOSITION VI. THEOREM. Tfaitraight line be bisected, and produced to any point; the rectangle contained by the whole line thus prodlwed, and the part of it produced, together with the square on half the line bisected, i3 equal...
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Civil service guide

Robert Johnston (F.R.G.S.) - Civil service - 1869 - 196 pages
...given triangle, and have one of its angles equal to a given rectilineal angle. 3. If a straight line be bisected, and produced to any point ; the rectangle...the part of it produced, together with the square of half the line bisected, is equal to the straight line which is made up of the half and the part...
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Elements of geometry, containing the first two (third and fourth ..., Part 1

Euclides - 1871 - 136 pages
...together with LG = sum of AL and CH and LG = sum of DF and CH and LG = sq. on CB. If a straight line be bisected and produced to any point, the rectangle...the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...parallelograms is equal to twice the triangle BKD. n. 11. Produce a given straight line to a point such that the rectangle contained by the whole line thus produced and the part produced shall be equal to the square on the given straight line. in. 22. If the opposite sides of...
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Elements of geometry, containing the first two (third and fourth ..., Part 2

Euclides - 1872 - 102 pages
...parallelograms is equal to twice the triangle BKD. II. 11. Produce a given straight line to a point such that the rectangle contained by the whole line thus produced and the part produced shall bo equal to the square on the given straight line. in. 22. If the opposite sides of...
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Civil service guide

Robert Johnston (F.R.G.S.) - 1873 - 208 pages
...given triangle, and have one of ita angles equal to a given rectilineal angle. 3. If a straight line be bisected, and produced to any point ; the rectangle...produced, and the part of it produced, together with the equare of half the line bisected, is eqiml to the straight line which is made up of the half and the...
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