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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. "
Cambridge examination papers: a suppl. to the University calendar, 1856-59 - Page 181
by Cambridge univ, exam. papers - 1856
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Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - 672 pages
...income, and what the expenditure of each. Euclid. 1. If a straight line be divided into two equal, and also into two unequal parts, the rectangle contained...section, is equal to the square of half the line. 2. Describe a square equal to a given rectilineal figure. Give a construction for determining a square...
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Return to an Address of the Honourable the House of Commons, Dated 10 ...

Education - 1859 - 412 pages
...triangle. 8. Bisect a parallelogram by a line drawn through a given point within the figure. 9. If a line be divided into two equal parts and also into...unequal parts, the rectangle contained by the unequal paits, together with the square of the line between the points of section, is equal to the square of...
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The examination papers as set for the preliminary literary examination of ...

Royal college of surgeons of England - 1860 - 336 pages
...shall be equal to a 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,...section, is equal to the square of half the line. 9. Describe a square that shall be equal to a given rectilineal fignre. 10. What does Euclid mean by...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Geometry - 1860 - 334 pages
...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 - 288 pages
...the parallelograms about the diagonal of a square are likewise squares. PROPOSITION V. THEOREM. -;I| 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. Given the straight...
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - Geometry - 1860 - 468 pages
...equivalent to the equation AD x DŁ-\- CB*= CD , which i* the algehraic proof of the theorem. THEOREM XLV. If a straight line be divided into two equal parts,...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 - Geometry, Plane - 1860 - 380 pages
...the 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 - 260 pages
...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

Alexander Hadden Hutchinson - 1861 - 128 pages
...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 - 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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