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" PROP. I. THEOR. If there oe two straight lines, one of which is divided into any number of parts; the rectangle contained by the two straight lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided line. "
The Elements of Euclid; viz. the first six books,together with the eleventh ... - Page 50
by Euclides - 1841 - 351 pages
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The papers set at the professional preliminary examination

College of preceptors - 1882
...rhombus ; prove that the lines which join opposite vertices of the triangles are equal. 4. If there be two straight lines, one of which is divided into any...number of parts, the rectangle contained by the two lines is equal to the sum of the rectangles contained by the undivided line and the several parts of...
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Guide to obtaining an army school certificate, 1st class, by an army ...

George Lund Dunnett - 1884
...yards of earth are taken out in forming 30 yards of its length ? PRACTICAL GEOMETRY. 1. If there be two straight lines, one of which is divided into any...undivided line and the several parts of the divided line. The sum of the perpendiculars let fall from any point within any equilateral figure upon its sides...
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Stewart's specific subjects. Euclid. [1st] (-3rd stage). [With 2 issues of ...

Stewart W. and co - 1884
...parallelogram HG, together with the complements AF, FC, is the gnomon AGK, or EHC. I. — If there be two straight lines, one of which is divided into any...lines, is equal to the rectangles contained by the tmdivided line, and the several parts of the divided line. Let A and BC be two straight lines ; of...
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The Elements of Plane Geometry ...

Association for the improvement of geometrical teaching - Geometry, Plane - 1884
...relation between Theor. 5 and Multiplication in Arithmetic. Ex. 1 2. If each of two straight lines is divided into any number of parts, the rectangle contained by the whole lines is equal to the sum of the rectangles contained by each part of the one taken together...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884
...either of them. 4. If two straight lines be each of them divided internally into any number of segments, the rectangle contained by the two straight lines is equal to the several rectangles contained by all the segments of the one taken separately with all the segments...
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The elements of plane geometry, Volume 1

Mathematical association - 1884
...relation between Theor. 5 and Multiplication in Arithmetic. Ex. 1 2. If each of two straight lines is divided into any number of parts, the rectangle contained by the whole lines is equal to the sum of the rectangles contained by each part of the one taken together...
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THE ELEMENTS OF GEOMETRY.

GEORGE BRUCE HALSTED - 1885
...get a(b + c -f- a)= ab + ac + ad. a We may state this in words as follows : ff there be any two sects one of which is divided into any number of parts, the rectangle contained by the two sects is equivalent to the rectangles contained by the undivided sect and the several parts of the...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1886 - 366 pages
...we get a(b + c + a)=a6 + at + ad. We may state this in words as follows : If there be any two sects one of which is divided into any number of parts, the rectangle contained by the two sects is equivalent to the rectangles contained by the undivided sect and the several parts of the...
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - Mathematics - 1889
...parallelogram equal to a given triangle and having an angle equal to a given rectilineal angle. 3. If there be two straight lines, one of which is divided into any...undivided line and the several parts of the divided line. If A, B, C, D are points in a straight line, taken in order, prove that the rectangle AC . BD = AB...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 pages
...inches and b inches respectively is equal & ' ab ' square inches. PROPOSITION 1. THEOREM. If there be two straight lines, one of which is divided into any...divided line. Let A and BC be two straight lines, of which BC is divided at D, E; then rect. A. BC=A. BD, A. DE, A. EC, Draw BF ir to BC, and cut off...
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