| 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 sides of a triangle, it** shall cut the other sides, or those produced, proportionally ; and if the sides, or the sides produced,... | |
| Robert Simson - Geometry - 1838 - 434 pages
...: then, if the 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 a triangle, it** shall cut the other sides, or those produced, proportionally ; and if the sides, or the sides produced,... | |
| Euclides - 1838 - 264 pages
...another. Then, if the 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 - 194 pages
...PROP. II. THEOR. If a straight (DE) be drawn parallel to one of the sides (BC) of a triangle (BAC), **it will cut the other sides, or the other sides produced, proportionally : and if the sides** (AC, AB), or the sides produced, be cut proportionally, the straight line (DE) which joins the points... | |
| Euclides - 1841 - 378 pages
...23.1 Then, if the 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 - 320 pages
...them) they, also, 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,... | |
| Janet Taylor - Nautical astronomy - 1842 - 588 pages
...equal angles are proportional, viz : CA : AB : : CD : DE AC : CB : : DC : CE CB : BA : : CE : ED Henee, **if a straight line be drawn parallel to one of the sides of a** plane triangle, it will cut the other two sides proportionally. Any two sides of a triangle added together,... | |
| Nicholas Tillinghast - Geometry, Plane - 1844 - 96 pages
...(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 ABC; then we have... | |
| Euclid - Geometry - 1845 - 218 pages
...construction t 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 sides of a triangle, it** shall cut the other sides, or these produced, proportionally : and if the sides, or the sides produced,... | |
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