Calendar: 1849-1850 Page 289

GENERAL LITERATURE AND SCIENCE 287 The product of the sum of two squares hy double square is also the sum of two squares Write down the general term of -f bx cx2 71 yt a2 Prove the formula cos --- and also the 6c geometrical theorem on which the demonstration is founded being an acute angle If four straight lines are proportionals the similarly described rectilinear figures are also proportionals and the converse OI 4ף If -b be then &- Jjtfi 91 Find χ and when- λ ύ 10 cargo is sold for £2200 and 12 per cent is lost whereas it was expected to gain 10 per cent for what was the cargo sold below its value 11 Given the perimeter and area 72מ of triangle and angle shew that cot 12 Expand aT according to the powers of and show that the series is convergent after the rth term when first is greater than 13 Find the number of solutions in the equation- 4- 4- 23 110 14 If ρ be the perpendicular from the centre of circle radius on the side of regular inscribed pentagon and if be the side of regular decagon inscribed in the same circle r3 pz- d3 15 In garden there are three square plots one of which is equ to half the size of the other two find their magnitude when it is known that the border of the largest is more than 10 but less than 20 feet long 16 Three observers are at known and equal distances from an elevated object find its height