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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, the parts read in the University of Cambridge [book ... - Página 62
por Euclides - 1846
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Skeleton propositions &c. of Euclid, books i and ii, with ..., Volumen2

Euclides - 1858 - 136 páginas
...1. Conc. l ¡î.'1'ЯP. AIij. ,f AriIh. Hyp. Л l,l. РВОР. IX. PROP. IX. TUEUR. //' 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 - 672 páginas
...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 ...

1859 - 412 páginas
...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 two...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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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1860 - 334 páginas
...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...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 in the point D ; the...
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The examination papers as set for the preliminary literary examination of ...

Royal college of surgeons of England - 1860 - 336 páginas
...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, and also into two...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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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 páginas
...about the diagonal of a square are likewise squares. PROPOSITION V. THEOREM. -;I| If a straight line be divided into two equal parts, and also into two...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 - 472 páginas
...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 also into 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 - 380 páginas
...= <*'— m', to each of these equals add m' ; .'. (a + m) (a — m) + m' = a'. That is, if a number be divided into two equal parts, and also into two unequal parts, the product of the unequal parts together with the square 1 of half their difference, is equal to the square...
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Examination papers used at the examination of candidates for appointment to ...

War office - 1861 - 260 páginas
...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 páginas
...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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