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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 on the line between the points of section, is equal to the square on half the line. "
The first and second books of Euclid explained to beginners, by C.P. Mason - Page 144
by Euclid, Charles Peter MASON - 1872
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Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ...

Euclides - 1864 - 262 pages
...— 2am + m'. Hence by adding these equals, .'. (a + m)' + (a - m)* = 2az + 2m*. That is, If a number be divided into two equal parts, and also into two unequal parts, the sum of the squares of the two unequal parts is equal to twice the square of half the number itself,...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...Cor. The parallelograms about the diameter of a square are likewise squares. Prop. 5. If a straight line be divided into two equal parts, and also into...contained by the unequal parts, together with the square of the line between the noinls of section, is equal to the square of half the line. Cor. The difference...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...1am + m*, Hence by adding these equals, .'. (a + m)t + (a — m) = 2o* + 2m. That is, If a number be divided into two equal parts, and also into two unequal parts, the sum of the squares of the two unequal parts, is equal to twice the square of half the number itself,...
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Trigonometry ...

James McDowell - 1866 - 124 pages
...f- = tan - - - 1. 1 + tan|a \4 2/ If a + ft + 7 = ^, prove that cos a + cos /3 + cos 7 If an angle be divided into two equal parts and also into two unequal parts, the rectangle of the sines of the unequal parts, together with the square of the sine of the angle between the dividing...
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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 ...

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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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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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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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1870 - 270 pages
...&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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Examination for women. Examination papers, with lists of syndics and examiners

Cambridge univ, exam. papers - 1870 - 272 pages
...half the line and of the square on the line between the points of section. The square on half the line together with the square on the line between the points of section and the rectangle contained by the parts is equal to half the square on the line. 3. In equal circles,...
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