The Mathematical Miscellany

C. Gill., 1836 - Mathematics

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Page 180 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Page 14 - A, B, C, D, E play together on this condition, that he who loses shall give to all the rest as much as they already have. First A loses, then B, then C, then D, and at last also E. All lose in turn, and yet at the end of the 5th game they all have the same sum, viz.
Page 349 - A banker borrows money at 3^ per cent, per annum, and pays the interest at the end of the year ; he lends it out at the rate of 5 per cent, per annum, but receives the interest quarterly, and by this means gains £200 a-year ; how much does he borrow ? 15. A person spends in the 1st year n times the interest of his property ; in the 2nd year 2...
Page 342 - In any trinomial square (Art. 108), the middle term is twice the product of the square roots of the first and third terms...
Page 342 - Thus, the square of the sum, of any two quantities is equal to the sum of their squares plus twice their product.
Page 60 - ... 9. If any two numbers be separately divided by 9 or 3, and the two remainders multiplied together, and that product divided by 9 or 3, the last remainder will be the same as if you divided the product of the first two numbers by 9 or 3. 10. If any number ending...
Page 254 - An Elementary Treatise on Sound ; being the Second Volume of a Course of Natural Philosophy, designed for the Use of High Schools and Colleges.
Page 294 - A diameter of a curve is the locus of the middle points of a series of parallel chords. 149. To find the diameter of a given system of parallel chords in a parabola. Let 0 be the inclination of the chords to the axis of the parabola ; let x, y...
Page 263 - ... catholics baptised their children at the parish church after the Reformation. Neither Leland in 1538, nor Camden, who visited Manchester more than forty years later, makes even a guess at the population. All accounts, however, agree that it was a populous town till the pestilential epidemics, towards the close of the sixteenth and the early part of the seventeenth century, destroyed so many of its people and so much of its prosperity, that in 1645 parliament voted 1,oool. to its relief, as to...