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" If a straight line be divided into two equal, and also 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. "
Elements of Euclid Adapted to Modern Methods in Geometry - Page 87
by Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 216 pages
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Elementary Geometry, Volume 1

James Maurice Wilson - Geometry - 1868 - 132 pages
...may be used to demonstrate other properties of divided lines. For example, THEOREM 28. 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 bisected, and the square...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...the diameters of the squares on its two sides. 15. If a straight line be divided into two equal and into two unequal parts, the squares on the two unequal parts are equal to twice the rectangle contained by the two unequal parts, together with four times the square...
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Examination for women. Examination papers, with lists of syndics and examiners

Cambridge univ, exam. papers - 1870 - 272 pages
...parts. If the diagonals of a quadrilateral bisect one another, it is a parallelogram. 2. If a straight line be divided into two equal, and also into two...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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Elements of geometry, containing the first two (third and fourth ..., Part 1

Euclides - 1871 - 136 pages
...AC =sum of the eight rectangles and XH =AEFD = sq. on AD. X X 0 K Tf -U -XZ~ F p -R 0 If a straight line be divided into two equal, and also into two...the squares on the two unequal parts are together double of the square an half the line and of the square on the line between the points of section....
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The Edinburgh university calendar

Edinburgh univ - 1871 - 392 pages
...angle is greater than the base of the other. A complete demonstration is required. 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 of the line between the points of...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...rectangles and XH =AEFD — sq. on AD. QED JC G ^ V 0 JT j> it PROPOSITION IX. THEOREM. If a straight line be divided into two equal, and also into two...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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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...on the hypotenuse is equal to the sum of the squares on the other two sides. (I. 47.) 2. That if a 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 part between the points of...
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - Student teachers - 1873 - 580 pages
...The parallelograms about the diameter of it square, are likewise squares. ,7\ V. — 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 of the line between the points of...
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Recent Military, Naval, and Civil Service Examination Papers in Mathematics ...

Braithwaite Arnett - 1874 - 130 pages
...equal to the two interior and opposite angles. Trisect a given finite straight line. 3. If a straight line be divided into two equal and also into two unequal...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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A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ...

Euclides - 1874 - 120 pages
...on the sum of the two lines by the square on their difference. PROPOSITION 9. THEOREM. If a straight line be divided into two equal, and also into two...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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