A Synopsis of the Principal Formulae and Results of Pure Mathematics

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J. & J.J. Deighton, 1829 - Mathematics - 358 pages
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Page 112 - THEOREM. Every section of a sphere, made by a plane, is a circle.
Page 4 - Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.
Page 4 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.
Page 347 - Si, the formula assigned by Thomson to the mineral from Ireland, named " Anhydrous silicate of iron." Now, this slag had evidently been in a position favourable to the absorption of oxygen, namely, the...
Page 4 - To reduce a fraction to its lowest terms, divide both the numerator and denominator by their greatest common divisor.
Page 4 - The same quantity may be added to, or subtracted from, both sides of an equation. To...
Page 343 - The immutability, no less than the symmetry of its notation, (which should ever be guarded with a jealousy commensurate to its vital importance,) facilitates the translation of an expression into common language at any stage of an operation, - disburdens the memory of all the load of the previous steps, - and at the same time, affords it a considerable assistance in retaining the results.
Page 46 - These criteria were derived by a new transformation, namely the one which yields an equation whose roots are the squares of the differences of the roots of the given...
Page 161 - Straight line and circle. A straight line cannot cut a circle in more than two points. In fact, an unlimited straight line may (i) cut a circle in two points, eg AB or CD in fig.
Page 2 - Tiie square root of a quantity cannot be partly rational and partly a quadratic surd. If possible, let...

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