Elements of analytical geometry and the differential and integral calculus (1856)
Robinson, Horatio N. (Horatio Nelson), 1806-1867 · Cincinnati : J. Ernst · leaf 215
aw two lines to meet in the line given in position, whose sumshall he less the sum of any other two lines drawn from the samepoints to the same line. iAns. The two lines make equal angles with the( line given in position. Let A and B be the two points and ffO theline given in position. From A and £… … Then Ja^+x=BE, and Jb^+y^=AE. Now the problem requires that J a 2 -\-x^+Jb 2 -\-y^ =minimum.Whence _^_+_,^^=0. (1) But x-\-y=c. Hence dx-\-dy—0. (2) MAXIMA AND MINIMA. 207 From (2) we have dx=—dy, and this value of dx put in (1),and that equation reduced, we find ^ -. y By inspecting the figure we…
Geometry, Analytic · Calculus
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