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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.
The first and second books of Euclid explained to beginners, by C.P. Mason - Page 144
by Euclid, Charles Peter MASON - 1872

Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 pages
...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, and also into...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. Let the straight...

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

Euclides - Euclid's Elements - 1837 - 112 pages
...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,...

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 unequal parts, together with the square of the line between the points of section, is equal to the square of half the line. Let the straight...

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

Robert Simson (master of Colebrooke house acad, Islington.) - 1838 - 206 pages
...triangle the 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...

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 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. Let the straight...

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 unequal parts, together with the square of the line between the points of section, is equal to the square of half the line. • Let the straight...

Ars Quatuor Coronatorum: Being the Transactions of the Quatuor ..., Volume 3

1840 - 288 pages
...fancies about numbers. All even numbers (except the duad — two — which is simply two unities) may be divided into two equal parts, and also into two unequal parts But the ODD number is only divisible into uneven parts, &c. The Antients also remarked the monad to...

The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...parallelograms about the diameter of a square are likewise squares. PROP. V. THEOR. If a straight fine be divided into two equal parts, and also into two...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. Let the straight...