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HODGES, FOSTER, AND CO., 104, GRAFTON-STREET,

PUBLISHERS TO THE UNIVERSITY.

LONDON: LONGMANS, READER, AND DYER.

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DUBLIN:

Printed at the University Press,

BY M. H. GILL.

Page.

134

FEUDAL AND ENGLISH LAW,

SCHOOL OF ENGINEERING,

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Junior Freshmen, Mathematics,

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History, Political Science, and English Literature,

Experimental and Natural Science,

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DUBLIN EXAMINATION PAPERS,

1870.

UNDERGRADUATE HONOR EXAMINATION PAPERS.

Hilary Term.

SENIOR SOPHISTERS.

Mathematics.

MR. TOWNSEND.

I. The direction angles of two complanar lines being a1 B1 y1, a2 B2 yz ; required the cosines of those of the complanar two which are equally inclined to them both.

2. The direction angles of three concurrent lines being a1 B1 y1, a2 B2 y2, a3 B3 y3; required the cosines of those of the concurrent four which are equally inclined to them all.

3. Investigate the quadratic equation whose roots are the squared semiaxes of the section of the central quadric

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4. Investigate, in the same case, the equation of the cylinder which envelopes the quadric along its conic of intersection with the plane.

5. Prove geometrically that the two rectilinear generators at any point of a ruled quadric are the two real focal lines of the cone which from the point as vertex envelopes any confocal quadric.

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