. The railroad and engineering journal . Fig. 84. From A as a center and A B &s a. radius draw the arc / i? as a center and with /> C as a radius draw an arc I I,cutting / C at /. Through A and /draw the line A I J, and itwill be the required tangent. Problem 39 (fig. 83). To draw a tangent to an arc of a circlefrom a given point without the arc, the cetiter not being accessible. Let A B C be the arc and B the given point. From P drawthe line P B E touching the arc. To ascertain the true tangentpoint at any convenient distance from P B, P E, drawE D G parallel to P B /■, and cutt
. The railroad and engineering journal . Fig. 84. From A as a center and A B &s a. radius draw the arc / i? as a center and with /> C as a radius draw an arc I I,cutting / C at /. Through A and /draw the line A I J, and itwill be the required tangent. Problem 39 (fig. 83). To draw a tangent to an arc of a circlefrom a given point without the arc, the cetiter not being accessible. Let A B C be the arc and B the given point. From P drawthe line P B E touching the arc. To ascertain the true tangentpoint at any convenient distance from P B, P E, drawE D G parallel to P B /■, and cutting the arc at C and the chord .■/ D C at />, and from / erect a perpendicular/? B, cutting the arc at B; then will B be the true tangentpoint o( E B / to the arc. Problem 40 (fig. 84). To draw a tans^ent to two given circles. Let A and B be the two circles. Draw the line C Z> so as totouch both of them. To ascertain the true tangent points,. Fig. 85. from the centers A and B of the two circles draw A E andB (7 perpendicular to C D. E and G will then be the pointsrequired. The same method may be adopted if the tangent should berequired to pass between the two circles, as represented by thedotted line <: (/. Lines ^/and ^^drawn perpendicular to f </and through A and B will give the true tangent points, /and g. Problem 41 (fig. 85). To draw a circle tangent to a given lineA B at a given point C in it, and which shall also pass through afixed point D -uithout the line. If C? be the point in the line A CAand D the point withoutthe line, from C draw C O perpendicular to A CB. Join C and B
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectrailroa, bookyear1887
