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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 Geometry, Symbolically Arranged - Page 58
by Great Britain. Admiralty - 1846
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861 - 464 pages
...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 - 140 pages
...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 - 172 pages
...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 - Education, Higher - 1863 - 328 pages
...their other angles shall be equal, each to each, namely those to which the equal sides are opposite. 3. 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. 4. Bisect a given...
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Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1864 - 588 pages
...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 - 448 pages
...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 - 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
...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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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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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - Geometry - 1855 - 358 pages
...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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