## Memoirs on Mathematics and Mathematical Physics: An Extensive Collection Of. From the Philosophical Transactions, the Transactions of the Royal Irish Academy, Comptes-rendus de L'Académie Des Sciences, Mémoires de L'Académie Des Sciences de St. Pétersbourg [Petrograd], Liouville's Journal, Etc., with Numberous Plates and Other Illustrations, Notes and MS. Lists of Contents by Lord Justice Stirling, Volume 8 |

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### Common terms and phrases

Abel's theorem apply arbitrary constants ascending powers axes axis becomes canonizant carrés conjugate considered contain coordinates corresponding criteria cubical parabola curve d'après D'où definite integral degré dénominateur denote determined développement differential coefficients differential equations discriminant disturbing function donne elements elliptic functions epicene equa equal roots équations Error explicitly expressed in terms factor facultative finite formule fraction continue given Hence imaginary roots infinite invariants J. J. Sylvester l'équation l'expression l'on les valeurs limits Mémoires method méthode negative nombre observed obtained original pair peut plane positive principal plane probability problem proper fractions qu'on quantities random lines rational function real roots réduites represent respect result second member série solution somme substitution suivant suppose symbol tangent theorem tion trans-rotatory transformation trouve trouver valeurs données values vanish variables variation-index variations vis viva zero

### Popular passages

Page 627 - Ei$x, y)* becomes to a factor pres identical with the primitive (a, b, c, d, e\x, y)4, so that all the first minors of the matrix a, 6, c, d, e, f A, B, C, D, E, F vanish.

Page 579 - As all roads are said to lead to Rome, so I find, in my own case at least, that all algebraic inquiries sooner or later end at the Capitol of Modern Algebra over whose shining portal is inscribed "Theory of Invariants.

Page 581 - I suppose the sign to be so taken as to render positive the term which is a power of the product of the first and last coefficients ; and it may be well to remember that with this definition the number of real roots in any equation =0 or 1 to modulus 4 when the discriminant is positive, and =2 or 3 when the discriminant is...

Page 642 - This is not the first unconscious plagiarism I have been guilty of towards this eminent man whose friendship I am proud to claim. A more glaring case occurs in a note by me in the " Comptes Rendus," on the twentyseven straight lines of cubic surfaces, where I believe I have followed (like one walking in his sleep), down to the very nomenclature and notation, the substance of a portion of a paper inserted by Schlafli in the " Mathematical Journal," which bears my name as one of the editors upon the...

Page 191 - He is maintaining the hypothesis (consonant with our theory) that "errors (of observation) in rerum naturd result from the superposition of a large number of minuter errors arising from a number of independent sources." He proceeds: "In coarse and rude observations the errors proceed from a very few principal causes, and in this case, consequently, our hypothesis will probably represent the facts only imperfectly, and the frequency of the errors will only approximate roughly and vaguely to the law...

Page 192 - But when astronomers, not content with the degree of accuracy they had reached, prosecuted their researches into the remaining sources of error, they found that not three or four, but a great number of minor sources of error of nearly co-ordinate importance began to reveal themselves, having been till then masked and overshadowed by the graver errors which had been now approximately removed...

Page 605 - Mr Cayley, of whom it may be so truly said, whether the matter he takes in hand be great or small, " nihil tetigit quod non ornavit," suggests the following independent proof of this. Taking unity as the length of the contour, fixing the extremity of one of the lines, and calling...

Page 300 - X, then also dX dT ~j : r~" — "> dp dp the differentiation with respect to p being in each case performed only so far as p appears explicitly in the function. The value of...

Page 206 - Quant aux différentielles qui contiennent une racine carrée d'une fonction du quatrième degré, cette méthode de réduction fournit un rapprochement très intéressant de la construction des valeurs irrationnelles, avec la règle et le compas, et l'intégration des différentielles sous forme finie. En terminant...

Page 225 - This paper has for its object the investigation of the general analytical conditions of a method for the solution of questions in the Theory of Probabilities, which was published in a work entitled " An Investigation of the Laws of Thought, &c.