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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 English Journal of Education - Page 272
1851
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Orr's Circle of the Sciences: The mathematical sciences

William Somerville Orr - 1854
...л straight line (AB) be divided into two equal parts (inC), and also info two unequal parts (in D), the rectangle contained by the unequal parts, together with the square of (CD), the line between the points of section, is equal to the square of hilf the line : that is, DB...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1855 - 318 pages
...T) B PROP. V. THEOR. If a straight linele divided into two equal parts, andalsointo twounequalparts; the rectangle contained by the unequal parts, together...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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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...into turn equal parts, and also into two unequal part'; the rectangle contained by the unequal parta, together with the square of the line between the points of section (or division), is equal to the square of half the line. Let the straight line AB be divided into two...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...triangle, and have one of its angles equal to a given rectilineal angle. Is this a determinate problem? 6. If a straight line be divided into two equal parts,...section, is equal to the square of half the line. Prove this proposition algebraically. 6. Find the centre of a given circle. Shew that if in a circle...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856
...of a square are likewise squares. L. EUCLID II. 5. 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. Let the straight line AB (Fig. 40) be divided into two equal parts at the point C, and into two unequal...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...times that on one of the sides; compare the two sides. 4. 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 this result algebraically. 5. Draw a straight line from a given point, either without or in the...
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National Society's Monthly Paper

1857
...described upon the other two sides of it, the angle contained by these two sides is a right angle. 5. If a straight line be divided into two equal parts, and also into two unequal parts, the reptangle contained by the unequal parts, together with the square of the line between the points of...
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1858 - 12 pages
...24Z. 12s., and loses 18 per cent, on what the horse cost him ; what was the original cost? Euclid. 1. If a straight line be divided into two equal parts,...of section is equal to the square of half the line. 2. Equal straight lines in a circle are equally distant from the centre ; and those which are equally...
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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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Skeleton propositions &c. of Euclid, books i and ii, with ..., Volume 2

Euclides - 1858
...Лx. 1. Conc. l ¡.'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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