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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. "
The synoptical Euclid; being the first four books of Euclid's Elements of ... - Página 53
por Euclides - 1853
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Papers Read at the Royal Institute of British Architects

1863
...9. Divide an equilateral trianglo into four equal triangles. Book 2. 10. Proposition 7, Theorem ; It a straight line be divided into any two parts the squares of the whole line, and one of the parts, are equal to twice the rectangle contained by the whole and that part, together with...
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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863
...the rectangle AD. DB. To each of these equals add LG, which is equal to the square of CB. Therefore the rectangle AD. DB, together with the square of CB, is equal to the gnomon CMG, and LG. But tho gnomon CMG and LG make up thesquare CF, which is the square of CD. Therefore...
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Responsions

University of Oxford - 1863
...with the square on the line between the points of section, is equal to the square on half the line. 9. 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 and...
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Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ...

Euclides - 1864 - 262 páginas
...the square on 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 tine, and on one of the parts, are equal to twice the rectangle contained by the whole...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 páginas
...BD, and by A, DE, and by A, EC. Wherefore, if there be two straight lines, &c. QED PROPOSITION II. THEOREM. If a straight line be divided into any two parts, the rectangles contain! 'I by the whole and each of the parts, are together equal to the square on I he...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 páginas
...LG; but the gnomon CMG and LG make up the whole figure CEFD, which is the square of CD ; therefore the rectangle AD, DB, together with the square of...the square of CD. Wherefore, if a straight line, &c. QE Du PROP. VII.— THEOREM. If a straight line be divided into any two parts ; then the squares of...
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Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - 1866
...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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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 426 páginas
...the square 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 Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 424 páginas
...the square on CB, is equal to the square on CD. Wherefore, if a straight line &c. QED PROPOSITION 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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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 páginas
...of which DA is equal to AB : and CE is contained by AB, BC, for BE is equal to AK : PROPOSITION III. THEOREM. If a straight line be divided into any two parts, the rectangle contained ky the whole and one of the parts, is equal to the rectangle contained by the twa...
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