## A theorem relating to neutral series. From the Trans., Cambr. phil. society |

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absolute alternating series approach in ratio approach to straightness AUGUSTUS DE MORGAN az+1 az+l Cavalieri commencement cot oo curve cycle of terms deferred convergent series difficulty diminish without limit divided Earnshaw finite fixed neutrality give grade of infinity Hence increases without limit increasing terms infinite sums infinitely deferred convergent infinitely deferred neutral infinitely small compared last ratio last terms law of formation limit of convergency limit of summation limit of variation limiting form limiting ratio logn logra mathematica1 MATHEMATICS IN UNIVERSITY method neutral limit NEUTRAL SERIES neutral-form limit number of increasing number of terms odd number Poisson and Fourier preceding divergent series Pz+1 pz+l Q„+l ratio of equality RELATING TO NEUTRAL series a0 series is infinite series vanishes supposed three following terms TRINITY COLLEGE ultimate neutrality ultimately equal undulation unity variation of a0

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Page 11 - I have come to a settled conclusion that great points belong to those who made great points of them. The history of mathematical discovery is vexed with, neverending disturbances arising out of claims of priority, which mean that this person threw the thing away before that person used it. In many cases it is by no means certain that this person ever saw in his own words or formulae what that person enables us to see. Giving due moral blame to any one...

Page 12 - Sea • As many lines close in the Dial's centre ; So may a thousand actions, once afoot, End in one purpose, and be all well borne Without defeat.

Page 11 - ... see. Giving due moral blame to any one who consciously suppresses a hint which he knows he has taken, I consider that an inventor who is the first user has a position from which a hundred previous inventors cannot dislodge him, nor do anything but enhance his merit as the inventor of the use, most often the more difficult invention of th...

Page 11 - Sterinus, and Des Cartes, without finding anything which offered a chance if the search were pursued. But if, which is possible, any anticipation of a case or two should be discovered or even the theorem itself, unapplied, I should not the less give it the name of Cavalieri. I have come to a settled conclusion that great points belong to those who made great points of them. The history of mathematical discovery is vexed with, neverending disturbances arising out of claims of priority, which mean...