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" If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided... "
The Elements of Geometry, Symbolically Arranged - Page 63
by Great Britain. Admiralty - 1846
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Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1864 - 588 pages
...of n letters a, b, c, and their powers. Find the number of terms in the expansion of (a+b+c+d)\ 9. If a straight line be divided into any two parts,...twice the rectangle contained by the whole and that pan, together with the square of the other part. Prove that the area of any right-angled triangle is...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...CB, is equal to the square on CD. Wherefore, if a straight line, &c. QED PROPOSITION VII. THEOREM. If a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...AC is double of the squares of AD and DE. 24. Divide a given straight line into two parts, snch that the squares of the whole line and of one of the parts shall be equal to twice the square of the other part. 25. In any triangle, if a line be drawn from...
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Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - Education - 1866 - 336 pages
...proposition in the case of a triangle whose sides are 3, 4, and 5 units respectively. 5. Prove that if a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...VII. THEOREM. lf a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by tlie whole and that part, toaetlier with the square on the other part. Let the straight line AB be...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - Geometry - 1855 - 360 pages
...the equality, we shall have : b(2a+b)+a*=(a+b)z. PROP. VII. THEOR. If a straight line be divided into two parts, the squares of the whole line, and of one...together with the square of the other part. Let the straight line AB be divided into any two parts in the point 0 ; the squares of AB, BC, are equal to...
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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
...on CB, is equal to the square on CD. Wherefore, if a straight line &c. QED PUO POSITION 7. THEOREM. If a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole...
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The Edinburgh university calendar

Edinburgh univ - 1868 - 334 pages
...Parallelograms upon equal bases and between the same parallels are equal. 4. Prove Prop. 47, BI 5. If a straight line be divided into any two parts,...equal to twice the rectangle contained by the whole line and that part, together with the square of the other part. 6. If a straight line touch a circle,...
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Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1868 - 426 pages
...child go ? 11. If a straight line be divided into any two parts, the squares on the whole line and on one of the parts are equal to twice the rectangle...the whole and that part, together with the square on the other part. Where does Euclid afterwards use this proposition? 12. To inscribe a square in a...
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Report of the commissioners, Volume 6

Schools inquiry commission - Education - 1868 - 532 pages
...line be divided into any two parts : then the squares of the whole line and one of the parts shall be equal to twice the rectangle contained by the whole...that part together with the square of the other part. 4. The square of the difference of two numbers is equal to the sum of the squares of the two numbers...
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