 | Euclid, Robert Simson - 1821 - 514 pàgines
...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, be cut proportionally, the... | |
 | Euclid - 1826 - 234 pàgines
...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... | |
 | Euclides - 1826 - 226 pàgines
...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... | |
 | Robert Simson - 1827 - 546 pàgines
...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...other sides, or these produced, proportionally : and if the sides, or the sides produced, be a1t proportionally, the straight line which joins the points... | |
 | John Radford Young - 1827 - 228 pàgines
...; 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 sides produced, be cut proportionally,... | |
 | John Radford Young - 1827 - 246 pàgines
...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... | |
 | John Playfair - 1829 - 210 pàgines
...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... | |
 | Euclides - 1834 - 518 pàgines
...made aq in the proposition, the demonstration will be the same. PROPOSITION II. ^ See N. THEOR. — If a straight line be drawn parallel to one of the...other sides, or these produced, proportionally : and if the tides, or the sides produced, be cut proportionally, the straight line which joins the points... | |
 | John Playfair - 1836 - 148 pàgines
...altitude, therefore triangles of equal altitude are to one another as their bases. PROP. III. THEOR. \ If a straight line be drawn parallel to one of the...other sides, or these produced, proportionally ; and if the sides, or the sides produced be cut proportionally, the straight line which joins the points... | |
 | 1836 - 488 pàgines
...that triangles and parallelograms that have equal al. titudes, are to one another as their bases. II. 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... | |
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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 these produced, proportionally : and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section... 
