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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 student's guide to the University of Durham, with information respecting ... - Página 136
1880 - 144 páginas
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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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The Practical Teacher, Volumen3

1884
...whole дАЕО, Wherefore дАЕХ^дАСВ, and it has the iA which is common to both. — QEF 2. If a straight line be divided into any two parts,...parts, together with the square on the aforesaid part. Prop. 3, Bk. II. 3. To divide a given straight line into two parts, so that the rectangle contained...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884
...CB. But DA and EB are each = AB ; NOTE. — The enunciation of this proposition usually given is : If a straight line be divided into any two parts,...parts together with the square on the aforesaid part. That is, in reference to the figure, an expression which can be easily derived from that in the text...
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Cambridge University Examination Papers

University of Cambridge - 1884
...ABC are bisected in D, E respectively. Prove that the triangle DBG is double the triangle DEC. •i. If a straight line be divided into any two parts,...parts, together with the square on the aforesaid part. 5. Describe a square that shall be equal to a given rectilineal figure. On the diagonal of a parallelogram...
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Stewart's specific subjects. Euclid. [1st] (-3rd stage). [With 2 issues of ...

Stewart W. and co - 1884
...rectangle contained by AB, AC, together with the rectangle AB, BC, is equal to the square of AB. III. — If a straight line be divided into any two parts,...contained 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,...
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University of Oxford. Examination of women. Examination papers

Oxford univ, local exams - 1885
...equal to three given straight lines, but any two whatever of these must be greater than the third. 5. If a straight line be divided into any two parts,...parts, together with the square on the aforesaid part. 6. If a straight line be divided into two equal parts and also into two unequal parts, the rectangle...
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Calendar of Dalhousie College and University

Dalhousie University - 1885
...extremities of equal and parallel lines towards the same parts, are themselves equal and parallel. 10. If a straight line be divided into any two parts,...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
...= a2. Cif 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 páginas
...a*. Therefore 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...
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