Practical engineering drawing and third angle projection, for students in scientific, technical and manual training schools and for ..draughtsmen .. . 1 To get the hypertolic logarithm of a number multiply Its common logarithm by In circular measure 3G0° = 2 IT r which for r = 1 becomes 6,28318; 180° = ; 90o = ; 60 = ; 1 ° = ; 45 o = ; 30 ° : TEE HYPERBOLIC SPIRAL.—THE L ITU US. 77 radius vector, a some nmiierical constant, and 0 is the angular rotation of /• (in circular measure)estimated from some initial line. The curve has an asymptote
Practical engineering drawing and third angle projection, for students in scientific, technical and manual training schools and for ..draughtsmen .. . 1 To get the hypertolic logarithm of a number multiply Its common logarithm by In circular measure 3G0° = 2 IT r which for r = 1 becomes 6,28318; 180° = ; 90o = ; 60 = ; 1 ° = ; 45 o = ; 30 ° : TEE HYPERBOLIC SPIRAL.—THE L ITU US. 77 radius vector, a some nmiierical constant, and 0 is the angular rotation of /• (in circular measure)estimated from some initial line. The curve has an asymptote parallel to the initial line and at a distance from it equal to - To construct the spiral fi-om its equation take 0 as the pole (Fig. 126): OQ as the initial line: a for convenience, some fi-action, as -: and as our unit some quantitv. say half an inch, that will 4 make - of convenient size. Then taking Q 0 as the initial line make 0 P = - = 2 and draw PRa a parallel to OQ for the asymptote. For 6=1. that is. for arc KH = radius OH we have?-=-=2. givintj H.— one point of the spiral. Writing the equation in the form r= and expressing various values of 9 in circular measure we get the following: — e = .30° = ; ;? = 0 J/ = + : 0= 45° = ; r=0 -Y = ;e = m° = ; r = 0 S = i:-l + : 6 = 180° = ; r = 0 T= .6366. tangent to the curve at any point makes with the radius vector an angle ^ which is found by analysis to sustain to the angle 6 the following trigonometrical relation, tan ^ 6; the circular measure of 0 xn&y therefore be found in a table of natural tangents and the corresponding value
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Keywords: ., bookcentury1800, bookdecade1890, booksubjec, booksubjectlettering
