 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...will be the same. PROPOSITION 2. THEOREM. If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those...produced, be cut proportionally, the straight '.line which joint the points of section, shall be parallel to the remaining side of the triangle. Let DE... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...will be the same. PROPOSITION 2. THEOREM. If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those...produced, be cut proportionally, the straight line which joint the points of section, shall be parallel to the remaining tide of the triangle. Let DE... | |
 | Euclides - 1884 - 434 pages
...Triangles and [r8 are to one another in the ratio compounded of the ratios of their bases and altitudes. If a straight line be drawn parallel to one side of...shall cut the other sides, or those sides produced* proport ionally. Conversely : If the sides or the sides produced be cut proportionally, flie straight... | |
 | Woolwich roy. military acad - 1884 - 148 pages
...and the triangle A CD will be isosceles. 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. Prove the following construction for trisecting a line AB in G and H\ On AB as diagonal construct a... | |
 | Euclides - 1884 - 182 pages
...isosceles triangle cuts off equal lengths on the sides measured from the vertex of the triangle. 4. If a straight line be drawn parallel to one side of a parallelogram through an internal point, it divides the figure into two parallelograms. 5. Two rectilinear... | |
 | E. J. Brooksmith - Mathematics - 1889 - 356 pages
...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 from two angular points of a triangle to the middle points of the... | |
 | Dalhousie University - 1889 - 220 pages
...the greater circle has been shown to be a tangent to the leas, continue the proof to the end. • 6. If a straight line be drawn parallel to one side of a triangle cutting the other two, shew that it cuts them proportionately. (Draw only one figure). 7. Find a mean... | |
 | Royal Military College, Sandhurst - Mathematics - 1890 - 144 pages
...be proportionals, when taken inversely. 7. 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. In a triangle ABC, BC is bisected in D, AD is bisected in E, and BE produced to meet AC in F: show... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...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 of a triangle, or those sides produced, be cut proportionally, the... | |
 | Isaac Hammond Morris - Geometry, Plane - 1890 - 440 pages
...proportion, the product of the end terms, or extremes, equals the product of the middle terms, or means. ' If a straight line be drawn parallel to one side of a triangle, it cuts the other two sides, or those produced, proportionally.' (Eue. vi. 2.) PROBLEM 25. — To divide... | |
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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... 
