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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 examination papers as set for the preliminary literary examination of ... - Side 3
av Royal college of surgeons of England - 1860
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861
...III. 47, I. Axs. 1, 2, 3, I. 36, 1. Parlms. upon eq. bases and between the same ||s are equal. 5, II. If a straight line be divided into two equal parts, and also into two uneq. parts, the rcct. contained by the nneq. parts, together with the square of the line between the...
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Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862
...the parallelograms about the diagonal of a square are likewise squares. PROPOSITION 5.— THEOREM. If a straight line be divided into two equal parts,...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
...that the 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
...one another, and the diameter bisects the parallelogram, that is, divides it into two equal parts. 7. Describe a parallelogram that shall be equal to...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
...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,...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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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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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 College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865
...by 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,...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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