This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1890 Excerpt: ...about the triangle. (6) Show that the tangent line to the circle of eq. (267) has the equation r = a(ii cos 6 +i2 sin 6) + wa(i2 cos 6--ii sin 6), of which the scalar form is rp = a2. Also the equations of the tangent and normal to (269) are respectively (r--e)(p--e) = a2 and (r--e) (p--e) = 0. (7) Find what the ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1890 Excerpt: ...about the triangle. (6) Show that the tangent line to the circle of eq. (267) has the equation r = a(ii cos 6 +i2 sin 6) + wa(i2 cos 6--ii sin 6), of which the scalar form is rp = a2. Also the equations of the tangent and normal to (269) are respectively (r--e)(p--e) = a2 and (r--e) (p--e) = 0. (7) Find what the equation op = a2 represents when p is not the vector to a point on the circle. 84. The parabola. The equations -rXtl + yh (272) represent a parabola; for, eliminating x, we have which shows that the abscissa varies as the square of the ordinate, a property of the parabola. Differentiating (273), we have a vector parallel to the tangent at the end of p; hence the equation of the tangent may be written in which y is to be taken as constant. Eliminating y from (273), we have the scalar form of the equation, viz.: or, as it may be written, p(i2-pi2-4aii) = 0. In this latter form we see that the vector i2. pi2--4aii is always perpendicular to p. Let r = i2. pi2--4aii; then rii =--4a, and it appears that the locus of the end of r drawn outward from the origin is a right line parallel to i2, at a distance of 4 a to the left of the origin; also, ri2 = pi2, so that the projections of p and cr on i2 are equal. The following proposition is a consequence, viz.: If a right-angle triangle have its rectangular vertex fixed, and one of the other vertices moves on a right line to which the hypotenuse remains perpendicular, then the third vertex generates a parabola. To find the locus of the middle points of a system of parallel chords, i.e. a diameter. Let e be parallel to the chords, and let the equation of some chord be p = pi + xe, in which pi satisfies eq. (275). Substitute this value of p in (275) to find the other end of the chord; therefore (5) Show that...
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PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
