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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 123
by Arthur Schultze - 1901

## Plane Geometry

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...

## Plane and Solid Geometry

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...

## Plane and Solid Geometry

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...

## Plane Geometry

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...

## Plane Geometry Suggestive Method

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...

## Plane Geometry

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....

## Plane and Solid Geometry

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...

## Elements of Plane Geometry

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...