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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 first and second books of Euclid explained to beginners, by C.P. Mason - Σελίδα 149
των Euclid, Charles Peter MASON - 1872
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Stewart's specific subjects. Euclid. [1st] (-3rd stage). [With 2 issues of ...

Stewart W. and co - 1884
...therefore the rectangle AD, DB, together with the square of CB, is equal to the square of CD. VII. — 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...

THE ELEMENTS OF GEOMETRY.

GEORGE BRUCE HALSTED - 1885
...zab + b2 = 2a(a + &) + &*. By the commutative law, 2a(a + K) + <52 = 2(0 + £)a + &*, Therefore 105 rectangle contained by the whole and that part, together with the square on the other part. a> 300. By the commutative and distributive laws, and 294, 4(a + b)a -fb* = 4#2 + 40^ + b* = (2 a +...

Cambridge University Examination Papers.Michaelmas Term,1884 to Easter Term ...

Cambridge University Examination Papers.Michaelmas Term,1884 to Easter Term,1885.Volume XIV - 1885
...sides of a triangle is greater than the square on the third side, the triangle is acute-angled. 5. If a straight line be divided into any two parts, the squares on the whole Une, and on one of the parts, are equal to twice the rectangle contained by the whole and that part,...

The Elements of Geometry

George Bruce Halsted - 1886 - 366 σελίδες
...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)*....

Examination Papers for Science Schools and Classes

Great Britain. Education Department. Department of Science and Art - 1886
...number of linear feet in the perimeter; find the sides of the rectangle. (20.) Section B. 27. Show that if a straight line be divided into any two parts, the squares on the ivhole line and on one of the parts are equal to twice the rectangle contained by the whole line and...

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 of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square on the...

First Steps in Geometry: A Series of Hints for the Solution of Geometrical ...

Richard Anthony Proctor - 1887 - 180 σελίδες
...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...

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

E. J. Brooksmith - 1889
...to AB to meet AD in H 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,...squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square on the...

The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 σελίδες
...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 of the parts are equal to twice the rectangle contained by the whole and that part together with the square on the other...

Mathematical Papers for Admission Into the Royal Military College for the ...

Eldred John Brooksmith, Robert Moir Milne - 1890 - 132 σελίδες
...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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