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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. "
Elements of Geometry: Containing the First Six Books of Euclid with a ... - Page 51
by John Playfair - 1856 - 318 pages
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The British Annals of Education for ...: Being The Scholastic ..., Volumes 1-2

Education - 1844 - 688 pages
...shall be double of the triangle. 6. If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the...section, is equal to the square of half the line. 7. In obtuse angled-triangles, if a perpendicular be drawn from either of the acute angles to the opposite...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclides, James Thomson - Geometry - 1845 - 382 pages
...one of them. PROP. V. THEOR. — If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the...square of half the line. Let the straight line AB be bisected in C, and divided unequally in D : the rectangle AD.DB, together with the square of CD, is...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...double of the square of half the line, and of the square of the line between the points of section. Let the straight line AB be divided into two equal...the point C, and into two unequal parts in the point J). Then the squares of AD, DB together, shall be double of the squares of AC, CD. CD B From the point...
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845 - 444 pages
...be bisected in C, and divided unequally in D, 1 the rectangle AD-DB. together with the square on CD, the line between the points of section is equal to the square on (AC or CB) half the line. For AB2=AD-' + DB-+2AD-DB, (Prop. 37), but AB"=4AC2, (Prop. 37, Cor. 2),...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...likewise squares. PROP. V. THEOR. If a straight Kne be divided into two equal parts, and also into two unequal parts, the rectangle contained by the...the square of half the line. Let the straight line ATI be divided into two equal parts at the point C, and into two unequal parts at the point D : the...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 128 pages
...(a+by=a8+2ab+b8. PROP. XLIV. THEOR. 5. 2 Eu. If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the...points of section, is equal to the square of half the whole line. Let the str. line AB be divided into two equal parts at the pt. C, and into two unequal...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 128 pages
...b*. PROP. XLIV. THEOR. 5 . 2 EU. If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the...points of section, is equal to the square of half the whole line. Let the str. line AB be divided into two equal parts at the pt. C, and into two unequal...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 pages
...likewise squares. PROP. V. THEOREM. If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the...section, is equal to the square of half the line. EUCLID S ELEMENTS. PROP. VI. THEOREM. If a straight line be bisected, and produced to any point ; the...
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Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall, W. Hammond - 1848 - 390 pages
...the right angle. SECTION III. 1. If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the...of section is equal to the square of half the line. 2. In any triangle the square of the side subtending contained by either of these sides, and the straight...
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Minutes of the Committee of Council on Education: with Appendices, Volume 1

Great Britain. Committee on Education - Education - 1848 - 514 pages
...containing the right angle. Section 3. 1. If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the...line between the points of section is equal to the squares of half the line. 2. In any triangle the square of the side subtending any acute angle is less...
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