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. 1891 Excerpt: ...each chord, such pairs of tangents will form a series in involution and will determine, by their intersection with any tangent to the curve, an involute range. Find the centre and constant of the involution ( 11, 15, 27). 9. As a particular case, shew that (1) the tangent at the vertex of a parabola is divided by 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. 1891 Excerpt: ...each chord, such pairs of tangents will form a series in involution and will determine, by their intersection with any tangent to the curve, an involute range. Find the centre and constant of the involution ( 11, 15, 27). 9. As a particular case, shew that (1) the tangent at the vertex of a parabola is divided by the pairs of tangents at the ends of focal chords into an involute range, (2) that any other tangent of the same group is also divided in involution by the remaining tangents. Find the centre and constant of involution in each case. 10. If from any centre three pairs of rays be drawn parallel respectively to the three pairs of opposite sides of a complete quadrangle, they will form three pairs of rays of an involute pencil. If two of the three pairs of opposite sides meet at right angles, the third pair will also meet at right angles; or the three perpendiculars let fall from the three apices of a triangle upon the opposite sides meet in a point, hereafter termed the centre of altitude of the triangle ( 25). 11. The sides of a triangle and the line at infinity in the same plane form a complete quadrilateral whose three pairs of opposite apices are projected from the centre of altitude of the triangle by three pairs of normal rays in involution ( 25). 12. If a parabola be enveloped by a complete quadrilateral whose fourth side is the tangent at infinity, the centre of the rectangular involute pencil projecting the three pairs of opposite apices of the quadrilateral will coincide with the centre of altitude of the triangle formed by the first three sides (Ex. 11). 13. The tangents at the ends of a focal chord meet at right angles in the directrix ( 30, 36). 14. The locus of the centres of altitude of the triangles ...
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Add this copy of Geometry of Position to cart. $50.10, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2011 by Nabu Press.
