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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. "
A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ... - Página 90
por Euclides - 1874
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The Elements of Geometry

George Bruce Halsted - 1886 - 366 páginas
...the commutative law, 2a(a + 6) + P = a(a + b)a + P, .-. (a + i>Y + a* = 2(0 + 6)a + 6*. Therefore 105 rectangle contained by the whole and that part, together with the square on the other part. 300. By the commutative and distributive laws, and 294, 4(a + t)a + 6* = 4** + yib + P = (20 + 6)*....
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Calendar of Dalhousie College and University

Dalhousie University - 1887
...inequality, in which the four small triangles stand to one another. \ 4. If a straight line be divided into two parts, the squares on the whole line, and on one...part, together with the square on the other part. 5. Hence give a Geometrical proof of the algebraic proposition, a2 + 'r>2ai, a and b being unequal...
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First Steps in Geometry: A Series of Hints for the Solution of Geometrical ...

Richard Anthony Proctor - 1887 - 180 páginas
...important one. It may be enunciated also thus : — To divide a given straight line into two parts so that the squares on the whole line and on one of the parts may be together equal to three times the square on the other part. That this enunciation is equivalent...
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - 1889
...and BC in G; the triangles AGF, AEH&ce. together equal to the triangle ABC. 4. If a straight line be divided into any two parts, the squares on the whole...part, together with the square on the other part. If AB be divided in C so that the square on AC is double the square on CB, the sum of AB and CB will...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 páginas
...of the same magnitude however the line be drawn F PROPOSITION 7. If a straight line is divided into two parts, the squares on the whole line and on one...part together with the square on the other part. Let AB be divided at C. Then the sqs. on AB, BC = twice rect. AB, BC with sq. on AC. On AB describe the...
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Mathematical Papers for Admission Into the Royal Military College for the ...

Eldred John Brooksmith, Robert Moir Milne - 1890 - 132 páginas
...together with the square on the other part. Prove that the rectangle contained by the diagonals of the squares on the whole line and on one of the parts is equal to twice the rectangle contained by the whole line and that part. 2. Enunciate and prove a...
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The Educational Record of the Province of Quebec: The Medium ..., Volumen11

1891
...rectilineal figure, and having an angle equal to a given rectilineal angle. 3. If a straight line be divided into any two parts, the squares on the whole...part, together with the square on the other part. 4. What proposition of the second book would be formed from Euclid II. 12, by bringing the vertex A...
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Educational Review

Nicholas Murray Butler, Frank Pierrepont Graves, William McAndrew - 1906
...equal to b, prove that each equation has its two roots equal to one another. 9. If a straight line be divided into any two parts, the squares on the whole...part, together with the square on the other part. 10. From a given point O external to a given circle draw a straight line OPQ to cut the circle at two...
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Rider Papers on Euclid: Books i and Ii, Graduated and Arranged in Order of ...

Rupert Deakin - 1891 - 79 páginas
...square on the straight line which is made up of the half and the part produced. 7. If a straight line be divided into any two parts, the squares on the whole...part, together with the square on the other part. 8. If a straight line be divided into any two parta, four times the rectangle contained by the whole...
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Annual Report of the Chief Superintendent of Education

1891
...contained by 5. If a straight line be divided into any two parts, the squares on the whole line andón one of the parts are equal to twice the rectangle...that part together with the square on the other part. NOTE. — Female candidates for Class I. will omit the 2nd and 4th of the foregoing questions and work...
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