A New Analysis of Plane Geometry Finite And Differential With Numerous Example
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To quickly assess the difficulty of the text, read a short excerpt:
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) .
What to read after A New Analysis of Plane Geometry Finite And Differential With Numerous Example?
You can find similar books in the "Read Also" column, or choose other free books by A W H Ansle William Haughton Thompson to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
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) .
What to read after A New Analysis of Plane Geometry Finite And Differential With Numerous Example?
You can find similar books in the "Read Also" column, or choose other free books by A W H Ansle William Haughton Thompson to read onlineMoreLess
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