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" If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part. "
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Side 41
av Euclid, Robert Simson - 1838 - 416 sider
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1883
...the line, PROPOSITION III. THEOREM. // a straight line be divided into any two parts, the rectangk contained by the whole and one of the parts is equal to the netangle contained by the two parts together with the square on the aforesaid part. J) Let the st....
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Stewart's specific subjects. Euclid. [1st] (-3rd stage). [With 2 issues of ...

Stewart W. and co - 1884
...together with the rectangle AB, BC, is equal to the square of AB. III. — If a straight line be divided into any two parts, the rectangle contained by the...by the two parts, together with the square of the aforesaid part. Let AB be divided into any two parts in the point C; then the rectangle AB, BC, is...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884
...AB ; NOTE. — The enunciation of this proposition usually given is : If a straight line be divided into any two parts, the rectangle contained by the...contained by the two parts together with the square on the aforesaid part. That is, in reference to the figure, an expression which can be easily derived...
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Cambridge University Examination Papers

University of Cambridge - 1884
...respectively. Prove that the triangle DBG is double the triangle DEC. •i. If a straight line be divided into any two parts, the rectangle contained by the...contained by the two parts, together with the square on the aforesaid part. 5. Describe a square that shall be equal to a given rectilineal figure. On the...
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University of Oxford. Examination of women. Examination papers

Oxford univ, local exams - 1885
...right angles. Enunciate and prove the corollaries of this proposition. 3. If a straight line be divided into any two parts, the rectangle contained by the...contained by the two parts, together with the square on the aforesaid part. 4. The angles in the same segment of a circle are equal to one another. 5. About...
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Calendar of Dalhousie College and University

Dalhousie University - 1885
...lines towards the same parts, are themselves equal and parallel. 10. If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts is equal to the square of that part together with the rectangle of the two paits. GEOMETRY. (EXHIBITIONS AND BURSARIES.)...
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THE ELEMENTS OF GEOMETRY.

GEORGE BRUCE HALSTED - 1885
...Therefore 102 293. If c = a, then a(b + c) = a(b + a) = aa + a*. a*c Therefore If a sect be divided into any two parts, the rectangle contained by the whole and one of the parts is equivalent to the rectangle contained by the two parts, together with the square on the aforesaid part....
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The Elements of Geometry

George Bruce Halsted - 1886 - 366 sider
...IO2 293. If c = a, then a(b + e) = a(6 + a) = ab + aa = ab + of. ac Therefore If a sect be divided into any two parts, the rectangle contained by the whole and one of the parts is equivalent to the rectangle contained by the two parts, together with the square on the aforesaid part....
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Calendar of Dalhousie College and University

Dalhousie University - 1888
...parallel. 3. If a straight line be diyided into any two parts, the rectangle contained by the whole line and one of the parts, is equal to the rectangle contained...by the two parts, together with the square of the aforesaid part. 4. Prove, either by a diagram or in any other way, that if a straight line be bisected...
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - 1889
...parallel to the other diagonal, intersect in E. Prove that BE= CD. 3. If a straight line be divided into any two parts, the rectangle contained by the...contained by the two parts, together with the square on the aforesaid part. The diagonal AC of a square ABCD is produced to E, so that CE=BC. Prove that...
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