 | Benjamin Peirce - Geometry - 1847 - 204 pages
...To find the centre of an arc or circle (148, 149), ... 41 To draw a tangent to a circle (150, 151) 42 To inscribe a circle in a triangle (152, 153),...one side of a triangle into two parts proportional lo the other two sides (167), 48 To draw a line through a point in an angle so that it may be divided... | |
 | Sir Norman Lockyer - Electronic journals - 1902 - 688 pages
...propositions, Eue. VI., i and 33, already referred to, are proved, and also the proposition " that a straight line parallel to one side of a triangle divides the other two sides in the same ratio," Eue. VI., 2 (first part). Taking the proof furnished of this last theorem... | |
 | Sir Norman Lockyer - Electronic journals - 1902 - 1074 pages
...propositions, Euc. VI., I and 33, already referred to, are proved, and also the proposition "that a straight line parallel to one side of a triangle divides the other two sides in the same ratio,'1 Euc. VI., 2 (first part). Taking the proof furnished of this last theorem... | |
 | Simon Newcomb - Geometry - 1881 - 418 pages
...:: AB' : B'C?. CZ But BB' is parallel to the side (70" of the triangle. Therefore: 388. A straight line parallel to one side of a triangle divides the other two sides similarly. THEOREM IV. 182 Hypothesis. ABC, a triangle of which, the sides CA and CB are cut... | |
 | George Albert Wentworth - 1884 - 264 pages
...lines, third proportional, mean proportional, extreme and mean ratio, segments of a line. 139. Theorem. A line parallel to one side of a triangle divides the other two sides into proportional parts ; and these two sides have the same ratio as two corresponding segments.... | |
 | George Bruce Halsted - Geometry - 1885 - 389 pages
...—7 499. COROLLARY I. If the points A and A' coincide, the figure ACCr will be a triangle ; therefore a line parallel to one side of a triangle divides the other two sides proportionally. 500. COROLLARY II. If two lines are cut by four parallel lines, the intercepts... | |
 | George Bruce Halsted - Geometry - 1886 - 394 pages
...z 499. COROLLARY I. If the points A and A' coincide, the figure ACC' will be a triangle ; therefore a line parallel to one side of a triangle divides the other two sides proportionally. 500. COROLLARY II. If two lines are cut by four parallel lines, the intercepts... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...and CD are divided proportionally at E and F if i L i = CFD AE CF ' ' PROPOSITION XIV. THEOREM. 261. A line parallel to one side of a triangle divides the other two sides proportionally. Let DE be parallel to the side BC of the triangle ABC. To prove that — = —... | |
 | George Albert Wentworth - 1889 - 276 pages
...lines, third proportional, mean proportional, extreme and mean ratio, segments of a line. 139. Theorem. A line parallel to one side of a triangle divides the other two sides into proportional parts ; and these two sides have the same ratio as two corresponding segments.... | |
 | George Albert Wentworth - 1889 - 264 pages
...lines, third proportional, mean proportional, extreme and mean ratio, segments of a line. 139. Theorem. A line parallel to one side of a triangle divides the other two sides into proportional parts; and these two sides have the same ratio as two corresponding segments.... | |
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A line parallel to one side of a triangle divides the other two sides proportionally. 
