 | Edward Rutledge Robbins - Geometry, Plane - 1915 - 280 pages
...geometry was the perfection of a rigorous theory of ratio and proportion. BOOK III. PLANE GEOMETRY PROPOSITION XIII. THEOREM 293. A line parallel to one side of a triangle divides the other sides into proportional segments. Given : A ABC and line LM II to BC. To Prove : AL : LB = AM : MC.... | |
 | Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry, Plane - 1915 - 320 pages
...applications. They are stated as a theorem and proved in the following article. 192 411. Theorem. A straight line parallel to one side of a triangle divides the other two sides in the same ratio. Given AABC, having DE II AC. in j* To prove — = -, where m=AD, ns n=DB, r=CE,... | |
 | Webster Wells, Walter Wilson Hart - Geometry, Plane - 1915 - 330 pages
...— ~ - are variables which are always Z AOB arc AB equal. 8. ZAOB PROPOSITION XVII. THEOREM 424. A parallel to one side of a triangle divides the other two sides proportionally, when the segments of one side are incommensurable. A. Hypothesis. In A ABC, segments AD and BD are... | |
 | John Charles Stone, James Franklin Millis - Geometry - 1916 - 306 pages
...sawing lengthwise through these points. Prove that the strips are of equal width. 8 122. Theorem. — A line parallel to one side of a triangle divides the other two sides proportionally. Hypothesis. In A ABC, DE II AB and DE meets AC at D and BCsA. E. Conclusion. Proof. 1. Suppose that... | |
 | Ernst Rudolph Breslich - Mathematics - 1916 - 392 pages
...equal; the interior angles on the same side are supplementary. (196) Proportional Line-Segments 48. A line parallel to one side of a triangle divides the other two sides into corresponding parts having equal ratios. (244) 49. A line bisecting an angle of a triangle divides... | |
 | Webster Wells, Walter Wilson Hart - Geometry - 1916 - 490 pages
...variables which are always Z AOB arc AB equal. , , Z BOC are BC • PROPOSITION XVII. THEOREM 424. A parallel to one side of a triangle divides the other two sides proportionally, when the segments of one side are incommensurable. A Hypothesis. In A ABC, segments AD and BD are incommensurable... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...A'B' externally. The segments of AB are AC and A~ SC. The segments of A'B' are A' C' ^ and B'C'. A.' PROPORTIONAL LINES PROPOSITION XIII. THEOREM* 293....parallel to one side of a triangle divides the other tioo sides proportionally. Given in A ABC, DE parallel to BC. To prove AD : DB = AE : EC. Proof, t... | |
 | Claude Irwin Palmer - Geometry, Solid - 1918 - 192 pages
...difference as the sum of the last two is to their difference. PROPORTIONAL LINES § 411. Theorem. A straight line parallel to one side of a triangle divides the other two sides in the same ratio. § 412. Theorem. If two straight lines are cut by a series of parallel straight... | |
 | Edson Homer Taylor, Fiske Allen - Mathematics - 1919 - 272 pages
...sides into four segments which are proportional. This is briefly stated in the following Principle. A line parallel to one side of a triangle divides the other two sides proportionally. When a line is drawn parallel to one side of a triangle, this principle may be used to find any one... | |
 | John Charles Stone - Mathematics - 1919 - 248 pages
...accurately drawn, measured, and computed, you will find the ratios to be the same. And in general, D /; held A line parallel to one side of a triangle divides the other two sides proportionally. 13. Wishing to measure the distance across a pond from A to B, some boys made use of the principle... | |
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A line parallel to one side of a triangle divides the other two sides proportionally. 
