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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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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...added together in one straight line. Wherefore, if a straight line, &c. QED PROP. IX. — THEOREM. If a, straight line be divided into two equal and also into two unequal parts; then the squares of the two unequal parts are together double of the •quare of half the line, and...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...the diameters of the squares on its two sides. 17. 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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Mathematical Questions and Solutions, from the "Educational Times.", Volume 3

1865 - 128 pages
...geometrically, in the following form, which is analogous to that of Euclid II. 5. If a circular arc be divided into two equal and also into two unequal parts, the rectangle contained by the chords of the two unequal arcs, together with the square on the chord of...
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Mathematical Questions and Solutions, Volume 3

Mathematics - 1865 - 132 pages
...geometrically, in the following form, which is analogous to that of Euclid II. 5. If a circular arc be divided into two equal and also into two unequal parts, the rectangle contained by the chords of the two unequal arcs, together with the square on the chord of...
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Examination papers collected by A. Clark as a student and as an examiner

1867 - 224 pages
...equal to three given straight lines, but any two whatever of these must be greater than the third. 5. If a straight line be divided into two equal, and...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 Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...the line made of AB and BC together. Wherefore, if a straight line &c. QED PROPOSITION 9. THEOREM. If a straight line be divided into two equal, and...unequal parts, the squares on the two unequal parts are t 'gather double of the square on half the line and of the square on the line between the points of...
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Elementary Geometry, Volume 1

James Maurice Wilson - Geometry - 1868 - 132 pages
...three theorems 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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Elementary geometry

James Maurice Wilson - 1869 - 260 pages
...lines is equivalent to the difference of the squares tin those lines 6l One Corollary. THEOREM 28. If a straight line be divided into two equal and also into two unequal segments, the squares of the two unequal segments are together double of the square of half the line...
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Examination for women. Examination papers, with lists of syndics and examiners

Cambridge univ, exam. papers - 1870 - 272 pages
...two equal 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...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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