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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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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1860 - 317 sider
...is divided be denoted by a and l; then, (a+6) 1 =o 2 +2a6+6 2 . PROP. V. THEOR. If a straight linele divided into two equal parts, and also into two unequal...section, is equal to the square of half the line. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...parallelograms about the diagonal of a square are likewise squares. PROPOSITION V. THEOREM. -;I| 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. Given the straight...
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - 1860 - 453 sider
...to the equation AD x D£-\- CB*= CD , which i* the algehraic proof of the theorem. THEOREM XLV. If a straight line be divided into two equal parts, and...two unequal parts, the rectangle contained by the two unequal parts together with the square of the line between the points of division, will be equivalent...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 361 sider
...parallelograms about the diameter of a square, are 1 i ke wise squares. PROPOSITION V. THEOREM. If a straight line be divided into two equal parts, and also into tteo unequal parts ; the rectangle contained by the unequal parts, together with the square on the...
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Examination papers used at the examination of candidates for appointment to ...

War office - 1861
...between the same parallels are equal to one another. 2. If a straight line be divided into two equal and also into two unequal parts, the rectangle contained...of section is equal to the square of half the line. State and explain Euclid's corollary to this proposition. 3. The angles in the same segment of a circle...
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Guide to the Army Competitive Examinations: being a Compendium of practical ...

Alexander Hadden Hutchinson - 1861 - 100 sider
...described upon the sides which contain the right angle. 2. If a straight line be divided into two equal and also into two unequal parts, the rectangle contained by the unequal parts together with the square cf the line between the points of section is equal to the square of half the line. VOLUNTARY PORTION....
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861
...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, and...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
...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 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. 4. Bisect a given...
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