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" IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally ; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section... "
The figures of Euclid with the enunciations, as printed in Euclid's Elements ... - Page 54
by Euclides - 1840
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First Steps in Geometry: A Series of Hints for the Solution of Geometrical ...

Richard Anthony Proctor - Geometry - 1887 - 202 pages
...triangle, it will form with the other sides, produced if necessary, another equilateral triangle. 80. If a straight line be drawn parallel to one of the sides of a triangle, it will form with the other sides, produced if necessary, a triangle equiangular to the first. 81. Two straight...
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - Mathematics - 1889 - 354 pages
...given circle. Shew that - any equilateral figure inscribed in a circle must also be equiangular. 10. If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those sides produced, proportionally. Shew that two straight lines drawn...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 pages
...or without a given AABC, such that AAOB : ABOC : ACOA :: AB : BC : CA. PROPOSITION 2. THEOREM. (1) If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those sides produced proportionally. (2) Conversely :— If two sides...
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Practical Plane Geometry: Giving the Simplest Modes of Constructing Figures ...

John Fry Heather - Geometry, Plane - 1890 - 172 pages
...CHAPTER III. ON THE DIVISION OF LINES AND THE CONSTRUCTION OF SCALES. THEOREMS. 103. THEOB. 15. — If a straight line be drawn parallel to one of the sides of a triangle it shall cut the other sides, or these produced, proportionally. (Eu. VI. 2.) dicular be drawn from the...
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Mathematical Papers for Admission Into the Royal Military College for the ...

Eldred John Brooksmith, Robert Moir Milne - 1890 - 144 pages
...circle are a, /3, and y, what are the angles of the triangle formed by joining the points of contact? 5. If a straight line be drawn parallel to one of the sides of a triangle, prove that it will cut the other sides, or the sides produced, proportionally. Straight lines are drawn...
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Competition for Situations as Assistant in the British Museum: And ...

Great Britain. Civil Service Commission - Civil service - 1896 - 96 pages
...contained by the segments of one of them is equal to the rectangle contained by those of the other. 8. If a straight line be drawn parallel to one of the sides of a triangle, prove that it will cut the other sides, or those sides produced proportionally. AC, BD are parallel...
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Report of the Committee of Council on Education in Scotland...[without Appendix]

Education - 1900 - 898 pages
...three times the square on the radius. U_ ii. If a straight lino be drawn parallel to one side of я triangle, it will cut the other sides (or the other sides produced) proportionately. 7. Similar triangles are to one another in the duplicate ratio of their homologous...
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First Stage Practical Plane and Solid Geometry

G. F. Burn - Geometry - 1903 - 272 pages
...= v/36 = 6 ; that is, a mean proportional between two numbers is the square root of their product. If a straight line be drawn parallel to one of the sides of a triangle, it cuts the other sides, or these produced, proportionally (Euc. VI. 2). It will now be shown how the...
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Guide to the Civil Service

John Gibson - Civil service - 1903 - 268 pages
...Prove that BC is equal to the side of a regular pentagon inscribed in the circle ADC. 6. Prove that if a straight line be drawn parallel to one of the sides of a triangle, it cuts the other sides or those produced proportionately. In the side BC of a triangle ABC take a point...
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Books 3-9

Euclid - Mathematics, Greek - 1908
...German text-books adopt the less rigorous method of appealing to the theory of limits. PROPOSITION 2. If a straight line be drawn parallel to one of the sides of a triangle, it will cut the sides of the triangle proportionally ; and, if the sides of the triangle be cut proportionally, the...
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