## A Synopsis of the Principal Formulae and Results of Pure Mathematics |

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A Synopsis of the Principal Formulæ and Results of Pure Mathematics Charles Brooke No preview available - 2015 |

A Synopsis of the Principal Formulae and Results of Pure Mathematics ... Charles Brooke No preview available - 2017 |

### Common terms and phrases

a.cos a.sin A=log according angle applied arbitrary arcs Assume axis b.sin becomes Biot centre circle co-ordinates conjugate const constant containing corresponding cos x cosc cosec curve determined diameter differential coefficients differential equation dimensions divided divisor eliminating ellipse equal expressed factor formulæ fraction functions given given equation hyperbola impossible integral intersection least Let the equation log Sin method multiplying negative obtained origin parabola parallel particular perpendicular plane pole positive possible powers preceding prime number proposed putting quadratic quantities radius reduced referred remainders render represent respectively result roots satisfy sides signs sin x solution square straight line substituting Suppose surface tangent theorem transformed triangle values variables vers

### Popular passages

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...