| John Playfair - 1819 - 317 sider
...drawn parallel to one of the sides of a triangle, it will tut the otlter sides, or the other sides **produced, proportionally : And if the sides, or the...sides produced, be cut proportionally, the straight** like which joins the points of section will be parallel to the remaining side of the triangle. Let... | |
| Miles Bland - 1819 - 377 sider
...drawn through P parallel to AB or DC, it may be shewn that APE, DPC together are half of ABCD. (8.) **If a straight line be drawn parallel to one of the sides of a** parallelogram, and one extremity of this line be joined to the opposite one of the parallel side, by... | |
| Miles Bland - 1819 - 377 sider
...parallelogram to the extremities of two opposite sides, are together half of the parallelogram. 8. **If a straight line be drawn parallel to one of the sides of a** parallelogram, and one extremity of this line be joined to the opposite one of the parallel side, by... | |
| Euclid, Robert Simson - 1821 - 516 sider
...construction be made as in the proposition, the demonstration will be the same. PROP. II. THEOR. x **IF a straight line be drawn parallel to one of the...be parallel to the remaining side of the triangle.*** Let DE be drawn parallel to BC, one of the sides of the triangle ABC; BD is to DA, as CE to EA. Join... | |
| George Lees - 1826
...parallel to one of the sides BC, of a triangle ABC, it will cut the other sides, or the other sides **produced proportionally ; and if the sides, or the...the straight line which joins the points of section,** will be parallel to the remaining side of the triangle. Join BE and CD ; then the triangle BDE is equivalent... | |
| Euclides - 1826
...parallelograms having equal bases, are to each other as their altitudes. PROPOSITION II. THEOREM. У a right **line be drawn parallel to one of the sides of a triangle, it shall cut the** sides of the triangle proportionally j and if the sides of a triangle be cut proportionally, the right... | |
| Euclid - 1826 - 180 sider
...lines be proportional, their squares shall also be proportional. PROPOSITION II. THEOREM. If a, right **line be drawn parallel to one of the sides of a triangle, it shall cut the** sides of the triangle proportionally ; and if the sides of a triangle be cut proportionally, the right... | |
| John Radford Young - 1827 - 208 sider
...; but by hypothesis, A2 : B" :': A : C, hence (Prop. IX. Cor. 3. BV), Q=C. PROPOSITION V. THEOREM. **If a straight line be drawn parallel to one of the...other sides, or those produced, proportionally ; and** conversely, if the sides or the sides produced, be cut proportionally, the cutting line will be parallel... | |
| Robert Simson - 1827 - 513 sider
...construction be made as in the pro, . - position, the demonstration will be the same. PROP. II. THEOR. 3ee N. **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 a1t proportionally, the... | |
| John Radford Young - 1827 - 208 sider
...triangle are respectively equal to those of another, the triangles are similar. Cor. 2. Therefore if a **line be drawn parallel to one of the sides of a triangle it** will cut off a triangle similar to the whole. PROPOSITION x. THEOREM. {Converse of Prop. IX.} The angles... | |
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