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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 on the line between the points of section, is equal to the square on half the line. "
Euclid's Elements [book 1-6] with corrections, by J.R. Young - Page 61
by Euclides - 1838
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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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...PROP. V. THEOR. If a straight line le dividedinto two equal parts, and also into two unequalparts ; the rectangle contained by the unequal parts, together...equal parts in the point C, and into two unequal parts in the point D ; the rectangle AD.DB, together with the square of CD, is equal to the square of CB,...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...square are 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 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...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
...(a+b)*—a*-\-2ab + 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...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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1847 - 340 pages
...denoted by a and b ; then, PROP. V. THEOR. If a straight linebe divided into two equal parts, andalsoinlo two unequal parts ; the rectangle contained by the...equal parts in the point C, and into two unequal parts in the point D ; the rectangle AD.DB, together with the square of CD, is equal to the square of CB,...
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Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall, W. Hammond - 1848 - 390 pages
...containing 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...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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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 pages
...are 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...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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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...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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Report of the Committee of Council on Education (England and Wales ..., Issue 1

Great Britain. Council on Education - Education - 1848 - 532 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...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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