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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... "
Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ... - Página 53
por Euclides - 1860
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 12 páginas
...to it. 2. Triangles upon the same base, and between the same parallels, are equal to one another. 3. If a straight line be divided into any two parts,...that part together with the square on the other part. 4. When are circles said to touch one another ? One circle cannot touch another in more points than...
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Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1861
...expect to find the " differences " largest at the early part of the table and gradually decreasing. 14. If a straight line be divided into any two parts,...by the whole and that part together with the square of the other part. Enunciate any subsequent proposition of Euclid in which this result is employed....
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Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862
...to the square on CD. Conclusion. — Therefore, if a straight line, &c. QED PROPOSITION 7. -THEOREM. If a straight line be divided into any two parts, the squares on the wlutle line) and on one of the parts, are equal to twice the rectangle contained by the whole and that...
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Papers Read at the Royal Institute of British Architects

1863
...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...the whole and that part, together with the square of the other part : Prove this by Euclid's demonstration, and also (if there be time) algebraically....
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Responsions

University of Oxford - 1863
...equal to the squares of the two parts, together with twice the rectangle contained by the parts. 8. If 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...
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Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ...

Euclides - 1864
...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 and that part,...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...squares shall be equal to a given square. 13. Divide a given straight line into two parts, such that the squares on the whole line and on one of the parts shall be equal to twice the square on the other part. 14. Any rectangle is the half of the rectangle...
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Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1864
...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, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and...
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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,...part, together with the square on the other part. Give Euclid's demonstration of this proposition ; also, prove it algebraically. 6. Describe a square...
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The college Euclid: comprising the first six and the parts of the eleventh ...

Euclides - 1865
...equal to the square of the straight line which is made up of the half and the part prodnced. Prop. 7 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...
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