 | Benjamin Peirce - Geometry - 1841 - 186 pages
....... 45 Lines divided into equal parts (158), 45 To divide a line into equal parts (159), ..... 45 A line parallel to one side of a triangle divides the other two proportionally (K;0 - 162) ; and the converse (163), . . 46 To divide a line into parts proportional... | |
 | Benjamin Peirce - Geometry - 1847 - 204 pages
...LINES, .... 45 Lines divided into equal parts (158), 45 To divide a line into equal parts (159) 45 A line parallel to one side of a triangle divides the other two proportionally (160 - 162) ; and the converse (163), . . 46 To divide a line into parts proportional... | |
 | Charles Knight - Encyclopedias and dictionaries - 1866 - 532 pages
...found that the equation (3.) is true, and a necessary consequence of the proposition, that a line drawn parallel to one side of a triangle divides the other sides into proportional segments. The synthetical form of the preceding process differs from it much less on the paper than would be... | |
 | Encyclopedias and dictionaries - 1866 - 520 pages
...found that the equation (3.) is true, and a necessary consequence of the proposition, that a line drawn parallel to one side of a triangle divides the other sides into proportional segment?. The synthetical form of the preceding process differs from it much less on the paper than... | |
 | 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
...Proportional 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
...Proportional 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, George Anthony Hill - Geometry - 1894 - 150 pages
...sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. 219. Theorem. A line parallel to one side of a triangle divides the other sides proportionally. 220. Theorem. A line which divides two sides of a triangle proportionally is parallel... | |
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A line parallel to one side of a triangle divides the other two sides proportionally. 
