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" IF a straight line be divided into two equal, and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section. "
The first and second books of Euclid explained to beginners, by C.P. Mason - Page 152
by Euclid, Charles Peter MASON - 1872
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Calendar of Dalhousie College and University

Dalhousie University - 1886 - 216 pages
...other and the angles included by the sides supplementary, the triangles shall be equal in area. 2. If a line be divided into two equal and also into two unequal parts, the rectangle contained by the two latter, together with the square of the line between the points of section,...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1886 - 394 pages
...2a*, ([ + ] + a)* + * = 2(a + b)* + W. Therefore If a sect be divided into two equal and also two unequal parts, the squares on the two unequal parts are together double the squares on half the sect and on the line between the points of section. 302. By 294, and...
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First Steps in Geometry: A Series of Hints for the Solution of Geometrical ...

Richard Anthony Proctor - Geometry - 1887 - 202 pages
...the rectangle ABCD is equal to twice the triangle AEF together with the rectangle BE, DF. 231. If a line be divided into two equal and also into two unequal parts, the squares of the two unequal parts are together equal to twice the rectangle contained by these parts together...
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Annual Report

Canada. Department of the Interior - 1888 - 756 pages
...respects. 2. Parallelograms on equal bases and between the same parallels are equal to one another. 3. If a straight line be divided into two equal, and...the squares on the two unequal parts are together doable of the square on half the line together with the square on the line between the points of section....
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Calendar

University College, Dundee - 1889 - 358 pages
...K respectively and making the parallelograms ALOK, CHOM equal. Prove that B, 0, C are colliuear. 4. If a straight line be divided into two equal and also into two unequal parts, the sum of the squares on the unequal parts is equal to twice the sum of the squares on half the line and...
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Calendar of Dalhousie College and University

Dalhousie University - 1889 - 220 pages
...of the same base are between the same parallels. 4. Prove, by means of a diagram or otherwise, that if a straight line be divided into two equal and also into two unequal parts, the rectangle of the two unequal parts together with the square of the line between the points of section...
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - Mathematics - 1889 - 356 pages
...the same base and between the same parallels, the parallelogram shall be double of the triangle. 4. If a straight line be divided into two equal and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of...
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 420 pages
...in 0: show that the square on OB is equal to the square on OA with twice the rectangle OA, AC. 48. If a straight line be divided into two equal and also into two unequal parts, the rectangle of the unequal parts with the square on the line between the points of section, is equal...
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Sandhurst Mathematical Papers for Admission Into the Royal Military College ...

Royal Military College, Sandhurst - Mathematics - 1890 - 144 pages
...but the methods of proof must be geometrical. Great importance will be attached to accuracy, ,] 1. If a straight line be divided into two equal and also into two unequal parts, prove that the rectangle contained by the two unequal parts, together with the square on the line between...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...congruent with the square. PROPOSITION 9. THEOREM. If a straight line be divided into two equal and into two unequal parts, the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section....
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