If a line parallel to one side of a triangle intersects the other two sides, either side is to one of its segments as the other side is to its corresponding segment. For AD:DB = AE : EC. Plane and Solid Geometry - Page 123by Arthur Schultze - 1901Full view - About this book
| William James Milne - Geometry, Modern - 1899 - 258 pages
...to one side of a triangle and meets the other two sides divides them so that one side is to either **of its segments as the other side is to its corresponding segment.** Proposition II 291. Draw a line dividing each of two sides of a triangle into halves, or into other... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...EC as a limit. AD AE The variables j-^ and yr/», being always equals, must have equal limits. ™ **AD AE 281. SCHOLIUM. If the transversal intersects...the other side is to its corresponding segment. For** AD:DB = AE : EC. By composition AD + DB : DB = AE + EC: EC, or AB : DB = AC : EC. Ex. 531. In the diagram... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...limit. The variables ^-=., and -=^, being always equals, must have equal limits. Whence AD DB AE EC QED **281. SCHOLIUM. If the transversal intersects two sides...the other side is to its corresponding segment. For** AD:DB = AE : EC. By composition AD + DB : DB = AE + EC : EC, or AB : DB = AC : EC. Ex. 531. In the... | |
| Arthur Schultze - 1901 - 260 pages
...limit. AD AE The variables .=.=.. and .=7=, being always equals, must have equal limits. DJ3 111 L, **281. SCHOLIUM. If the transversal intersects two sides...the other side is to its corresponding segment. For** AD:DB = AE: EC. By composition AD + DB:DB = AE + EC: EC, or AB:DB = AC:EC. Ex. 531. In the diagram... | |
| George Clinton Shutts - 1905 - 260 pages
...§ 215. 291. COROLLARY. // a line be drawn parallel to the base of a triangle, one side is to either **of its segments as the other side is to its corresponding segment.** AB AC AB AC To prove = or = . 1 AD AE DB EC tion in the conclusion of the proposition, and see by what... | |
| Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...and — will approach — as a limit (243). MS 3/C Consequently, = (?) (242). QED LB MC 303. THEOREM. **If a line parallel to one side of a triangle intersects the other** sides, these sides and their corresponding segments are proportional. A Given : A ABC ; LM \\ to BC.... | |
| Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...LB and - will approach — — as a limit MS MC (243). Consequently, = (?) (242). QED 303. THEOREM. **If a line parallel to one side of a triangle intersects the other** sides, these sides and their corresponding segments are proportional. Given : A ABC; LM || to BC. To... | |
| William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 286 pages
...limit, their limits are equal) . QBD 341. COR. 1. If a line parallel to one side of a triangle cuts **the other two sides, either side is to one of its...as the other side is to its corresponding segment.** AB For CD:DA=CE: EB. § 340 .'. CD + DA : CD= CE + EB: CE, § 332 or CA:CD=CB:CE. Similarly CA : DA... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry, Modern - 1911 - 266 pages
...internally, if it meets their prolongations, the sides are divided externally in the same ratio. 282. COK. **If a line parallel to one side of a triangle intersects...the other side is to its corresponding segment. For** AD:DB = AE-.EC. By composition AD + DB: DB = AE + EC: EC, or AB: DB = AC: EC. Ex. 531. In the diagram... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...internally; if it meets their prolongations, the sides are divided externally in the same ratio. 295. COR. 1. **If a line parallel to one side of a triangle intersects...AD + DB : DB = AE + EC : EC, \ or AB : DB = AC: EC.** 296. COR. 2. Three parallel lines cut off proportional segments on any two transversals. HINT. Draw... | |
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