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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
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

Eldred John Brooksmith - Mathematics - 1901 - 368 pages
...the lengths of the perpendiculars from the other two angles on the opposite sides. 3. If a straight line be divided into two equal parts, 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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Calendar of the University of Sydney

University of Sydney - 1901 - 646 pages
...third side, then the two sides contain a right angle. 6. If a straight line is divided into two equal, and also into two unequal parts, the rectangle contained by the unequal parts, etc. Complete this examination and prove the theorem. 7. ABCD is a square, each side of which is eight...
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Annual Report of the Commissioners ..., Volume 68

1902 - 482 pages
...produced, the exterior angle is greater than either of the interior remote angles. 4. 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. 5. If a straight...
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Calendar of the University of Sydney

University of Sydney - 1902 - 640 pages
...drawing parallels to the sides, shall be a rhombus. 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 section is equal to the square on half the line. 5. Shew how to divide...
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Collectanea Hermetica, Volume 9

1902 - 130 pages
...between the parts. All even numbers also (except the dyad — two — which is simply two unities) may be divided into two equal parts, and also into two unequal parts, yet so that in neither division will either parity be mingled with imparity, nor imparity with parity....
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Elementary Geometry: Practical and Theoretical

Charles Godfrey, Arthur Warry Siddons - Geometry - 1903 - 384 pages
...(distant y from O), what are the lengths of the two unequal parts AP, PB? Prove algebraically that the rectangle contained by the unequal parts, together...the square on the line between the points of section (OP), is equal to the square on half the original line. Ex. 1O98. Show that in the above exercise AO...
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Elementary Geometry: Plane

James McMahon - Geometry, Plane - 1903 - 380 pages
...times their rectangle. Rectangles of equal parts and of unequal parts. 49. THEOREM 15. If a line is divided into two equal parts, and also into two unequal parts, the rectangle of the unequal parts, together with the square on the intermediate part, is equivalent to the square...
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A Text-book of Euclid's Elements for the Use of Schools, Book 1

Euclid - Euclid's Elements - 1904 - 488 pages
...EUCLID-S ELEMENTS. PROPOSITION 5. THEOREM. If a straight line is divided equally and also unequally, the rectangle contained by the unequal parts, together...section, is equal to the square on half the line. I. 46. I. 31. I. 43. Let the straight line AB be divided equally at P, and unequally at Q. Then the...
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Science Examinations ... Reports, Etc

1904 - 386 pages
...section. A. '21. A straight line is divided into two equal, and also into two unequal parts; show that the rectangle contained by the unequal parts, together...section, is equal to the square on half the line. A straight line is divided into two parts; show that the rectangle contained by the parts is greatest,...
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

Eldred John Brooksmith - 1904 - 376 pages
...into two unequal parts, prove that the rectangle contained by the two unequal parts, together witl1 the square on the line between the points of section, is equal to the square on half the line. Compare the lengths of the two unequal parts, if the rectangle contained by them is eight times the...
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