 | 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 :—... | |
 | 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... | |
 | 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... | |
 | John Gibson - Civil service - 1903 - 288 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... | |
 | Walter Percy Workman - Geometry - 1908 - 228 pages
...line are proportional to the corresponding two segments on the other . 406 On Triangles.:;: T. 11. — If a straight line be drawn parallel' to one of the sides of a triangle, it shall divide the other sides (internally or externally) in the same ratio (Euc VI. 2)... | |
 | Euclid - Mathematics, Greek - 1908 - 456 pages
...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... | |
 | Trinity College (Dublin, Ireland) - 1911 - 614 pages
...describe a segment of a circle containing an angle equal to a given rectilineal angle. 8. Prove that if a straight line be drawn parallel to one of the sides of a triangle it cuts the other sides or those sides produced proportionally. State the converse. 9. Prove... | |
 | Saul Stahl - Geometry, Non-Euclidean - 1993 - 320 pages
...parallelograms which are under the same height are to one another as their bases. Proposition 2. // a straight line be drawn parallel to one of the sides of the triangle, it will cut the sides of the triangle proportionally; and, if the sides of the triangle... | |
 | W.S. Anglin - Mathematics - 1994 - 282 pages
...in the proof. Book VI concerns similar (equiangular) triangles. The key result is Proposition VI 2: if a straight line be drawn parallel to one of the sides of a triangle, it cuts the sides of the triangle proportionately — and vice versa. In other words, if... | |
 | Chris Pritchard - Mathematics - 2003 - 572 pages
...Triangles and parallelograms which are under the same height are to one another as their bases. Prop 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... | |
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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 sides produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight '.line which joint the points of... 
