 | John Playfair - 1806 - 320 σελίδες
...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 σελίδες
...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 - 1819 - 350 σελίδες
...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 - 1819 - 444 σελίδες
...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 - 442 σελίδες
...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 - 514 σελίδες
...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 - 1827 - 228 σελίδες
...; 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 - 1827 - 546 σελίδες
...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 - 1829 - 210 σελίδες
...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 - 1831 - 632 σελίδες
...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... | |
| |
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... 
