A Synopsis of the Principal Formulae and Results of Pure Mathematics

Charles Brooke

J. & J.J. Deighton, 1829 - 358 σελίδες

Περιεχόμενα

• ART 13 Definitions and rules: 1
• Surds: 2
• Greatest common divisor 1012 Fractions: 3
• 55: 6
• 1315 Equations simple and quadratic 16 17 Ratios and proportion: 7
• Arithmetical progression: 8
• Harmonical progression 21 Figurate and polygonal numbers: 10
• Geometrical progression: 11
• Permutations and combinations: 13
• Binomial theorem: 14
• Polynomial theorem: 17
• Indeterminate coefficients: 22
• Logarithms 30 31 Continued fractions: 29
• 56: 33
• General properties of equations: 36
• Transformation of equations: 38
• Elimination: 40
• Depression of equations: 43
• Symmetrical functions of the roots of equations 39 The equation of differences: 46
• Limits of the roots of equations: 48
• Commensurable roots: 50
• Incommensurable roots: 51
• Quadratic factors: 52
• Impossible roots: 53
• Application of the theory of equations to surds: 54
• 22: 60
• 36 38 40 43: 74
• 5053: 80
• ib 54: 82
• 1 2: 88
• 13: 100
• 19: 136
• 20: 142
• 22: 149
• 4 5: 155
• DIFFERENTIAL CALCULUS: 193
• INTEGRAL CALCULUS: 204
• APPLICATION OF THE DIFFERENTIAL AND INTEGRAL: 263
• 14 15: 269
• Cubature: 275
• CALCULUS OF VARIATIONS: 288
• 25: 294
• 2 3: 297
• Inverse method of differences: 309
• 26 27: 310
• 29: 316
• Equations of mixed differences: 318
• Theory of generating functions: 326
• APPENDIX: 341

Δημοφιλή αποσπάσματα

Σελίδα 112 - THEOREM. Every section of a sphere, made by a plane, is a circle.

Σελίδα 4 - Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.

Σελίδα 4 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.

Σελίδα 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...

Σελίδα 4 - To reduce a fraction to its lowest terms, divide both the numerator and denominator by their greatest common divisor.

Σελίδα 4 - The same quantity may be added to, or subtracted from, both sides of an equation. To...

Σελίδα 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.

Σελίδα 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...

Σελίδα 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.

Σελίδα 2 - Tiie square root of a quantity cannot be partly rational and partly a quadratic surd. If possible, let...

Πληροφορίες βιβλιογραφίας

• Τίτλος: A Synopsis of the Principal Formulae and Results of Pure Mathematics
• Συγγραφέας: Charles Brooke
• Εκδότης: J. & J.J. Deighton, 1829
• Πρωτότυπο από: το Πανεπιστήμιο του Μίτσιγκαν
• Ψηφιοποιήθηκε στις: 8 Ιουν. 2007
• Μέγεθος: 358 σελίδες