A New Analysis of Plane Geometry Finite And Differential With Numerous Example
The book A New Analysis of Plane Geometry Finite And Differential With Numerous Example was written by author A W H Ansle William Haughton Thompson Here you can read free online of A New Analysis of Plane Geometry Finite And Differential With Numerous Example book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is A New Analysis of Plane Geometry Finite And Differential With Numerous Example a good or bad book?
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T. G. 34 MEASURES CONTAINING EQUATIONAL ELEMENTS [ill §35. Ill the case in which 2^, = the foregoing results break down. We shall consider this case. From the equation 2^, (K)+25. Cos(^y3, ) = 0, subtract '$A, . {^c), where c is an arbitrary point. We get %A, \{a, c)\ sin (a^c^) + SB, cos (/3, ^) = 0. Let 7 be any line, and let (^7) = 6. Then tA, \(a, c) \ sin {(a, C7) - 6] + ^B, cos {{/3, . Y) - 0] = 0. Hence l. A;. [(a, . C7) cos 6 - sin {a, . C'y„)\ + S5, {cos (/3, 7) cos + sin (^, y) sin 0\... = 0. Hence {XA, {a, ry) + IB, cos (/3, 7)} cos = {lA, {a, y. ) - 25, sin (0, y)} sin 0, giving independent of the particular line chosen. Hence the equation represents a direction. § 36. To reduce {■^AX^a, ) + tB, cos{ll3, ) = 0y), tvhen 2^, = 0. We have from § 35 tan {tA, (^a, ) + 25, cos (^5, ) = 07) ^ 2^, (a, 7)+25, cos(/3, 7) tA, {a, ry„) - tB, sin (/3, 7) ' § 37. Examples. 1. Shew that SSOj-^gSin (a, /3j) 2a, sin Oa, ) Now sm (Sa^ (^o?-) + a = /3) = -7 - -^^, V 2''/, ^ + 22a, ag cos (a, ag) .
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