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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

## 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...

## 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...

## The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 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...

## Practical Plane Geometry: Giving the Simplest Modes of Constructing Figures ...

John Fry Heather - Geometry, Modern - 1890 - 252 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...

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

Royal Military College, Sandhurst - Mathematics - 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...

## Competition for Situations as Assistant in the British Museum: And ...

Great Britain. Civil Service Commission - Civil service - 1896 - 112 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...

## 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...

## 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...