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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... "
Elements of Plane Geometry According to Euclid - Σελίδα 44
των Andrew Bell - 1837 - 240 σελίδες
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Yale Examination Papers

F. B. Stevens - 1884 - 175 σελίδες
...line be divided into any two parts, the square 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 part. (LooMis AND LEGENDRE.) 1. If a straight line, meeting two other straight lines,...

Calendar of Dalhousie College and University

Dalhousie University - 1884
...parts, the squares of the whole line and one of the parts are together equal to twice the rectangle of the whole and that part, together with the square of the other part. Shew also that {a — t)2 — a" 4- *2 — 2 <*& i® the algebraic eqivalent of the proposition. 2....

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

Cambridge University Examination Papers.Michaelmas Term,1884 to Easter Term,1885.Volume XIV - 1885
...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 that part, together with the square on the other part. Enunciate any other proposition of the second book in which this theorem is used....

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...

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...

Calendar of Dalhousie College and University

Dalhousie University - 1887
...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 other part. 5. Hence give a Geometrical proof of the algebraic proposition, a2 + 'r>2ai, a and...

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

Richard Anthony Proctor - 1887 - 180 σελίδες
...BC = sq. on AC + 2 sq. on BC + 2 rect. AC, CB = sq.on AC + 2 rect. AB,BC (by III.). PROP. VIII. — Let the straight line AB be divided into any two parts in C, and produced to D, so that BD=BC : then shall the square on AD be equal to four times the rectangle...

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

E. J. Brooksmith - 1889
...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 that 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...

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

Eldred John Brooksmith, Robert Moir Milne - 1890 - 132 σελίδες
...divided into any two parts, prove that 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 part. Prove that the rectangle contained by the diagonals of the squares on the whole...

The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 σελίδες
...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 part. Let AB be divided at C. Then the sqs. on AB, BC = twice rect. AB, BC with sq. on...




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