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Prove that the following two statements (axioms) are equivalent: (i) If e is a line and P is a point not on , then there exists exactly one line k through P and parallel to e. (ii) If k, l and t are lines such that k || and t intersects k (so tnk|= 1) then t intersects (so |tn= 1).

Prove that the following two statements (axioms) are equivalent: (i) If e is a line and P is a point not on , then there exists exactly one line k through P and parallel to e. (ii) If k, l and t are lines such that k || and t intersects k (so tnk|= 1) then t intersects (so |tn= 1).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Prove that the following two statements (axioms) are equivalent: (i) If e is a line and P is a point not on (, then there exists exactly one line k through P and parallel to t. (ii) If k, and t are lines such that k || and t intersects k (so tnk| = 1) then t intersects (so tn=1).
Transcribed Image Text:Prove that the following two statements (axioms) are equivalent: (i) If e is a line and P is a point not on (, then there exists exactly one line k through P and parallel to t. (ii) If k, and t are lines such that k || and t intersects k (so tnk| = 1) then t intersects (so tn=1).
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