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37.14 (a) Given four points on a line 1, and given a point 0 not on 1, let the angles at O subtended by AP, AQ, BP, BQ be OLP, aQ BP,B. Use the law of sines to show that Q sin B sin Bo sin ap (АВ, РQ) 11 sin ao A (b) If the four points A, B, P, Q on l are projected from O to four points A', B', P', Q' on another line m, then the cross-ratio is preserved: ( AB, PQ)- (A'Β', P'Q). A Conclude that cross-ratio is preserved by any projectivity, that is, a finite succession of projections from one line to another A'

37.14 (a) Given four points on a line 1, and given a point 0 not on 1, let the angles at O subtended by AP, AQ, BP, BQ be OLP, aQ BP,B. Use the law of sines to show that Q sin B sin Bo sin ap (АВ, РQ) 11 sin ao A (b) If the four points A, B, P, Q on l are projected from O to four points A', B', P', Q' on another line m, then the cross-ratio is preserved: ( AB, PQ)- (A'Β', P'Q). A Conclude that cross-ratio is preserved by any projectivity, that is, a finite succession of projections from one line to another A'

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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37.14 (a) Given four points on a line 1, and given a point 0 not on 1, let the angles at O subtended by AP, AQ, BP, BQ be OLP, aQ BP,B. Use the law of sines to show that Q sin B sin Bo sin ap (АВ, РQ) 11 sin ao A (b) If the four points A, B, P, Q on l are projected from O to four points A', B', P', Q' on another line m, then the cross-ratio is preserved: ( AB, PQ)- (A'Β', P'Q). A Conclude that cross-ratio is preserved by any projectivity, that is, a finite succession of projections from one line to another A'
Transcribed Image Text:37.14 (a) Given four points on a line 1, and given a point 0 not on 1, let the angles at O subtended by AP, AQ, BP, BQ be OLP, aQ BP,B. Use the law of sines to show that Q sin B sin Bo sin ap (АВ, РQ) 11 sin ao A (b) If the four points A, B, P, Q on l are projected from O to four points A', B', P', Q' on another line m, then the cross-ratio is preserved: ( AB, PQ)- (A'Β', P'Q). A Conclude that cross-ratio is preserved by any projectivity, that is, a finite succession of projections from one line to another A'
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