# Calendar: 1852-1853 Page 333

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GENERAL LITERATURE AND SCIENCE 320 14 Prove the equation u2 -f- in spirals and apply it to the ellipse the perpendicular on the tangent being from the centre if 15 Trace the curve ×™ -axy -ax2y- -x4 0t and show that it has cusp at the origin 16 If parallels be drawn to the base of triangle and per- pendiculars to the sides be drawn from their extremities the locus of their intersection will be straight line passing through the vertex III -Cije Ctrtfor $criott The questions upon this subject were the same as those set for the Senior Classical Scholarship See page 319 JUNIOR MATHEMATICAL SCHOLARSHIP In given triangle inscribe parallelogram similar to given parallelogram Define harmonic proportion and divide given finite straight line harmonically Parallelograms upon the same base and between the same parallels are equal to one another If straight line be divided into any two parts the square of the whole line is equal to the squares of the two parts together with twice the rectangle contained by the parts Upon given straight line to describe segment of circle which shall contain an angle equal to given rectilineal angle

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