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... First Stage Practical Plane and Solid Geometry - Page 23by G. F. Burn - 1903 - 255 pagesFull view - About this book
| John Playfair - Mathematics - 1806 - 320 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 a triangle, it will cut the other sides, or the other sides produced proportionally ; and if the sides, or the sides... | |
| John Mason Good - 1813 - 714 pages
...Triangles and parallelograms of the same altitude are one to another as their, basesProp. II. Theor. If a straight line be drawn parallel to one of the sides of a triangle, it shall cat the other sides, or those produced, proportionally: and if the sides, or the sides produced,... | |
| John Playfair - Circle-squaring - 1819 - 350 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 a triangle, it ' will cut the other sides, or the other sides produced, proportionally : And if the sides, or the... | |
| Miles Bland - Euclid's Elements - 1819 - 444 pages
...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 - Euclid's Elements - 1819 - 442 pages
...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 - Geometry - 1821 - 514 pages
...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 sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced,... | |
| John Radford Young - Euclid's Elements - 1827 - 228 pages
...; 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 sides of a triangle, it shall cut the other sides, or those produced, proportionally ; and conversely, if the sides or the... | |
| Robert Simson - Trigonometry - 1827 - 546 pages
...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,... | |
| John Playfair - Geometry - 1829 - 210 pages
...1), 2ACH : 2ADL : : HC : DL (Proper. 30). Therefore, triangles &c. QED ED. PROPOSITION II. THEOREM. If a straight line be drawn parallel to one of the sides of a triangle it will cut the other sides proportionally. Let DK be drawn parallel to BC1, one of the sides of the triangle... | |
| Charles Hutton - Mathematics - 1831 - 632 pages
...means are equal, as in the terms 3, в, 6, 12, their product becomes a square. Hence THEOREM in. The mean proportional between two numbers is the square root of their product. We may, without destroying the accuracy of a proportion, give to its various terms all the changes... | |
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