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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 - Pagina 58
di Great Britain. Admiralty - 1846
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858
...to various operations connected with the extraction of the Square root. PROP. 9. — THEOR. If a st. line be divided into two equal parts, and also into two unequal parts, the squares of the two unequal parts are together double of the square of the half line and of the square...
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Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - 1869 pagine
...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...points of 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...
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Return to an Address of the Honourable the House of Commons, Dated 10 ...

1859
...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
...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,...points of 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...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1860 - 317 pagine
...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...points of 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...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...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 - 1860 - 453 pagine
...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 - 1860 - 361 pagine
...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
...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...points 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...
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Guide to the Army Competitive Examinations: being a Compendium of practical ...

Alexander Hadden Hutchinson - 1861 - 100 pagine
...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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