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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 - Page 58
by Great Britain. Admiralty - 1846
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The Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New Text ..., Book 1

Euclides - Geometry - 1853 - 334 pages
...proved. PEOP. V. THEOE. If a straight line be bisected, and also divided into two unequal parts : then the rectangle contained by the unequal parts together with the square of the part of the line intercepted between the points of section, shall be equal to the square of half the...
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Orr's Circle of the Sciences: Organic nature, vols. 1-3 (1854-1856)

William Somerville Orr - Science - 1854 - 532 pages
...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 - Euclid's Elements - 1855 - 340 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...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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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 262 pages
...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 - 252 pages
...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,...points of 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...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856 - 168 pages
...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...points of 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...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856 - 200 pages
...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...points 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...
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National Society's Monthly Paper

1857 - 408 pages
...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 - 578 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,...points 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...
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Skeleton propositions &c. of Euclid, books i and ii, with ..., Volume 2

Euclides - 1858 - 134 pages
...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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