## The Collected Mathematical Papers of James Joseph Sylvester ...University Press, 1912 |

### Contents

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### Common terms and phrases

1+hx A₁ algebraical arithmetical series asymptotic aura autre ax² B₁ c'est-à-dire coefficients Comptes Rendus condition conséquemment consequently contain corresponding d'une degré degree denote determinant deux differential equation Differential Invariants diviseurs donnée éléments équation être expressed F₁ facteur factor Farey series formula fraction given graph Hence homographic invariant involution isobaric l'autre l'équation l'on latent roots Lecture letters linéaire linear functions Mathematics matrices multiplied nombre parfait nombres premiers obtain operator P₁ pair partitions peut prime numbers Principiant protomorphs pure reciprocant qu'on quadratic quadratic function quadric quantic quantity quaternions quelconque racines rational integral regular graph Schwarzian Derivative sera seront solution somme substitution suppose Sylvester theorem théorème theory u₁ unity valeur vanish variables write Y₁ zero

### Popular passages

Page xvii - An Essay on the application of Mathematical Analysis to the Theories of Electricity and Magnetism...

Page xviii - How charming is divine Philosophy! Not harsh and crabbed, as dull fools suppose, But musical as is Apollo's lute, And a perpetual feast of nectar'd sweets, Where no crude surfeit reigns.

Page 273 - My Lord, I have undertaken this long journey purposely to see your person, and to know by what engine of wit or ingenuity you came first to think of this most excellent help unto Astronomy, viz. the Logarithms ; but, my lord, being by you found out, I wonder nobody else found it out before, when, now being known, it appears so easy.' He was nobly entertained by the Lord Napier ; and every summer after that, during the Laird's being alive, this venerable man went purposely to Scotland to visit him.

Page xix - In song and dance about the sacred Hill — Mystical dance, which yonder starry sphere Of planets and of fixed in all her wheels Resembles nearest; mazes intricate, Eccentric, intervolved, yet regular Then most when most irregular they seem; And in their motions harmony divine So smooths her charming tones that God's own ear Listens delighted.

Page xx - The Principles of pure D'ism, in opposition to the Dot-age of the University.

Page 273 - Marr therewith who went into Scotland before Mr Briggs purposely to be there when these two so learned persons should meet. Mr Briggs appoints a certain day when to meet at Edinburgh ; but, failing thereof, Merchiston was fearful he would not come. It happened one day as John Marr and the Lord Napier were speaking of Mr Briggs,

Page 276 - Then said he unto me, Prophesy unto the wind, prophesy, son of man, and say to the wind, Thus saith the Lord GOD ; Come from the four winds, 0 breath, and breathe upon these slain, that they may live.

Page 273 - Merchiston, made public his logarithms, Mr. Briggs, then reader of the astronomy lectures at Gresham College, in London, was so surprised with admiration of them, that he could have no quietness in himself, until he had seen that noble person...

Page 594 - ... represent an infinitude of primes. I have sometimes thought that the profound mystery which envelops our conceptions relative to prime numbers depends upon the limitation of our faculties in regard to time, which like space may be in its essence poly-dimensional, and that this and such sort of truths would become self-evident to a being whose mode of perception is according to superficially as distinguished from our own limitation to linearly extended time.

Page 582 - Perhaps I may, without immodesty, lay claim to the appellation of the mathematical Adam, as I believe that I have given more names (passed into general circulation...