The Mathematical MiscellanyC. Gill., 1836 |
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algebraic axes becomes bisects Catlin centre chord co-efficients co-ordinates cone const constant cos² cosec cubes curve cylinder denote diameter difference distance divide drawn dt dt dx dy dx² ellipse elliptic functions equal equation factors formula fraction function give given circles given point Hamilton College hence integer integral intersection locus logarithms Macully multiplied Murray Co negative odd number parabola Paul's College Peirce perpendicular plane polar equation positive Prof Professor quantities QUESTION VIII radii radius required to find right angles roots SECOND SOLUTION sides sin² sphere square substituting suppose surface tangent tangent circles tion triangle values velocity vertex vertical whole number x₁ y₁
Popular passages
Page 180 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Page 16 - 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 351 - 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 344 - In any trinomial square (Art. 108), the middle term is twice the product of the square roots of the first and third terms...
Page 344 - 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 256 - 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 296 - 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 265 - ... 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...