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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, the parts read in the University of Cambridge [book ... - Página 62
por Euclides - 1846
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## Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862 - 140 páginas
...about the diagonal of a square are likewise squares. PROPOSITION 5.— THEOREM. If a straight line be divided into two equal parts, and also into two...contained by the unequal parts, together with the square on the line between the points of section, ^s equal to the square on half the line. (References—...
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## The school Euclid: comprising the first four books, by A.K. Isbister

Euclides - 1862 - 172 páginas
...parallelograms about the diameter of a square are likewise squares. PROP. V.— THEOREM. //' a straight line be divided into two equal parts, and also into two unequal parts ; then the rectangle contained by the unequal parts, together with the square of the line between the...
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## Responsions

University of Oxford - 1863 - 316 páginas
...given triangle and have one of its angles equal to a given rectilineal angle. 8. If a straight line be divided into two equal parts, and also into two...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. 9. If a straight...
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## Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1864 - 588 páginas
...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 also into two...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 - 262 páginas
...— 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 - 448 páginas
...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 - 402 páginas
...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 two...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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## Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 páginas
...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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## Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1855 - 350 páginas
...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 M'Dowell - 1866 - 124 páginas
...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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