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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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Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1864
...Chelsea be arranged, under the restriction that the tvco vowels e shall never stand together 1 10. 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. Hence show that...
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Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ...

Euclides - 1864
...— 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 school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...2am + at'. Hence by adding these equals, .-. (a + m)* + (o — m)' = 2aa + 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
...the parts. 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...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 of the squares of two...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1855 - 317 sider
...which this jine is divided be denoted by </ and b ; then, (u+4)1 PROP. V. THEOR. If a straight Itnelf divided into two equal parts, and also into two unequal...by the unequal parts, together with the square of tAt line between the points of section, is equal to the square of half the line. Let the straight line...
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Trigonometry ...

James McDowell - 1866
...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 - 1867 - 400 sider
...that parallellograms about the diameter of a square are likewise squares. PROPOSITION 5. THEOREM. If a straight line be divided into two equal parts and...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 ...

Euclid, Isaac Todhunter - 1867 - 400 sider
...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, Volum 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 sider
...= 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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