 | John Playfair - 1844 - 338 pàgines
...and parallelograms that have equal altitudes, are to one another as their bases. PROP. II. THEOR. lj a straight line be drawn parallel to one of the sides of a triangle, it will cut the other sides, or the other sides produced, proportionally: And if the sides, or the sides... | |
 | Nicholas Tillinghast - 1844 - 108 pàgines
...(Prop. 4, Cor.), and 4DP is the square of DB ; hence AD2-|-DC2+AB2+BC2=AC2+DB2. PROP. XII. THEOREM. If a line be drawn parallel to one of the sides of a triangle, it will cut the other sides proportionally. Fi«- 69- Let DE be drawn parallel to the side AB of the triangle... | |
 | Euclides - 1845 - 546 pàgines
...construction be made as in the proposition, the demonstration will be the same. PROPOSITION II. THEOREM. If a straight line be drawn parallel to one of the...produced, proportionally : and conversely, if the sides, or the sides produced, be cut proportionally, the straight line nhich joins the points of section shall... | |
 | Euclid - 1845 - 218 pàgines
...2s. i. be made as in the proposition, the demonstration will be the same. PROPOSITION II. THEOR. — If a straight line be drawn parallel to one of the...other sides, or these produced, proportionally : and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points... | |
 | Great Britain. Admiralty - 1846 - 128 pàgines
...CD:: ^\ ABC : I d7 m ABCE : /—7 Prop. TO. :: ( ACDF. Therefore triangles, &c. PROP. LXXII. THEOR. If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides proportionally: and if the sides be cut proportionally, the straight line which joins the points of... | |
 | Great Britain. Admiralty - 1846 - 128 pàgines
...^± ABC : I £Z7 m ABCE : i — 7 Prop. 70. : : ( ACDF. Therefore triangles, &c. PROP. LXXII. THEOR. If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides proportionally: and if the sides be cut proportionally, the straight line which joins the points of... | |
 | Euclid, John Playfair - 1846 - 334 pàgines
...and parallelograms that have equal altitudes, are to one another as their bases. 123 PROP. II. THEOR. If a straight line be drawn parallel to one of the sides of a triangle, it will cut the other sides, or the other sides produced, proportionally : And if the sides, or the sides... | |
 | Euclides - 1848 - 52 pàgines
...and parallelograms that have equal altitudes, are one to another as their bases. PROP. II. THEOREM* If a straight line be drawn parallel to one of the...produced, proportionally: and conversely, if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall... | |
 | Great Britain. Committee on Education - 1850 - 790 pàgines
...contained by the segments of the other. Section 3. 1. To describe a circle about a given triangle. 2. If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other two sides of the triangle proportionally ; and conversely if two sides of a triangle be cut proportionally,... | |
 | Janet Taylor - 1851 - 674 pàgines
...proportional, viz : [Eu. vi. 4.] CA : AD : : CD : DE AC : CB : : DC : CB CB : BA : : CE : ED Hence if a straight line be drawn parallel to one of the sides of a plane triangle, it will cut the other two sides proportionally, [Eu. vi. 2.] or Theorem D, page 26.... | |
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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 these produced, proportionally : and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section... 
