 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...triangle ADE ; and * The enunciation of this proposition, as given by Dr. Simson, is as follows : " If a straight line be drawn parallel to one of the...be parallel to the remaining side of the triangle." This enunciation is defective, and might lead to error in its application, as it does not point out... | |
 | William Whewell - 1837 - 226 pages
...i. Triangles and parallelograms of the same altitude are to one another as their bases. *PROP. ii. If a straight line be drawn parallel to one of the...; and if the sides, or the sides produced, be cut propertionally, the straight line which joins the points of section shall be parallel to the remaining... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...altitudes. PROPOSITION II. THEOREM. 133 a triangle, it shall cut the other sides, or the other sides produced, proportionally; and if the sides, or the...straight line which joins the points of section shall he parallel to the remaining side of the triangle. Let DE be drawn parallel to BC, one of the sides... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...same construction be made as in the proposition, the demonstration will be the same. PROP. II. THEOR. IF a straight line be drawn parallel to one of the...the straight line which joins the points of section shal 1 be parallel to the remaining side of the triangle.* Let DE be drawn parallel to BC, one of the... | |
 | Euclides - 1838 - 264 pages
...same construction be made as in the proposition, the demonstration will be the same. PROP. II. THEOR. If a straight line be drawn parallel to one of the sides of « triangle, it shall cut the other sides, or these produced, proportionally : and if the sides, or... | |
 | Thomas Keith - 1839 - 498 pages
...about the equal angles are proportional, viz. AB : BC : : A& : be, and AB '. BC '. ' AC ; AC, &c. (72) If a straight line be drawn parallel to one of the sides of a plane triangle, it will cut the other two sides proportionally. (73) An oblique-angled triangle is... | |
 | Euclides - 1840 - 82 pages
...triangles and parallelograms, having equal altitudes, are proportional to their bases. 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 - Geometry - 1841 - 378 pages
...same construction be made as in the proposition, the demonstration will be the same. PROP. II. THEOR. If a straight line be drawn parallel to one of the sides Q * 37. 1. . 1.6. of a triangle, it shall cut the other sides, or these produced, proportionally. And... | |
 | Euclides - 1842 - 316 pages
...are to one another in a ratio compounded of the ratios of their bases and altitudes. PROP. II. THEOR. 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... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...construction be made as in the proposition, the demonstration will be the same. PROP. II. THEOR. IJ 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... | |
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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... 
