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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

## The Element of Geometry

John Playfair - Geometry - 1836 - 114 pages
...about the diagonal of a square are likewise squares. / G H / CPROP. XXI. THEOR. If a straight line lie divided into two equal parts, and also into two unequal...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...

## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Geometry - 1837 - 410 pages
...line being bisected, the rectangle of the parts is equal to the square of one of them. PROP. V. THEOR. IF a straight line be divided into two equal parts,...points of section, is equal to the square of half the line. Let the straight line AB be bisected in C, and divided unequally in D : the rectangle AD.DB,...

## Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 pages
...square of AB is equal to the squares of AC, CB, and twice the rectangle AC-CB. PROPOSITION V. THEOREM. . If a straight line be divided into two equal parts,...points of section, is equal to the square of half the line. Let the straight line AB he divided into two equal parts in the point C, and into two unequal...

## Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Geometry - 1837 - 332 pages
...(a+i)2 =a*+2a6+62. PROP. V. THEOR. If a straight line le divided into two equal parts, andalsointo two unequal parts; the rectangle contained by the...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...

## A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 112 pages
...AC2 + CB2 + figs. AG + GE, and that these are = AC* + CB8 + 2 AC x CB. D H M PROPOSITION V. Theorem. If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle A contained by the unequal parts, I together with the square of the line between the points of section,...

## Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 pages
...square on half the line. PROP. V THEOR. If a straight line be divided into two equal parts, and aim into two unequal 'parts ; the rectangle contained...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...

## The Elements of Euclid

Euclid - Geometry - 1838 - 478 pages
...demonstration it is manifest, that the parallelograms about the diameter of a square are likewise squares. two unequal parts: the rectangle contained by the...points of section, is equal to the square of half the line. • Let the straight line AH be divided into two equal parts in the point C, and into two unequal...

## The parent's guide to a liberal ... education; containing a selection of ...

Robert Simson (master of Colebrooke house acad, Islington.) - 1838 - 206 pages
...square of the hypotenuse is equal to the sum of the squares of the other two sides. 14. If a right line be divided into two equal parts, and also into two unequal parts, what equations will result? 15. The base of a right-angled triangle is 300 feet, and the sum of the...