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19 | On transcendental progressions, that is, those whose general terms cannot be given algebraically |
| 20 | The summation of an innumerable progression |
| 25 | A general method for summing series |
| 41 | On the sums of series of reciprocals |
| 43 | On harmonic progressions |
| 46 | Universal methods of series |
| 47 | Finding the sum of any series from a given general term |
| 55 | Universal method for summation of series, further developed |
| 61 | On sums of series of reciprocals from powers of natural numbers from another discussion, in which the sums are derived principally from another source |
| 63 | Demonstration of the sum of the series 1 + 1/4 + 1/9 + 1/16 … |
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71 | A dissertation on continued fractions |
| 72 | Various observations about infinite series |
| 74 | On various methods for expressing the quadrature of a circle with verging numbers |
| 122 | On products created from infinite factors |
| 123 | Observations on continued fractions |
| 125 | Consideration of a progression suitable for finding the quadrature of a circle |
| 128 | An easy method for computing the natural and artificial sines and tangents of angles |
| 130 | Considerations on certain series |
| 189 | On the determination of series, or a new method for finding the general terms of series |
| 190 | Consideration of certain series which are gifted with particular properties |
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246 | A contribution to the calculations of sines |
| 247 | On divergent series |
| 275 | Annotations to a certain passage of Descartes for finding the quadrature of the circle |
| 280 | On progressions of arcs of circles, of which the accompanying tangents proceed by a certain law |
| 281 | A specimen of a singular algorithm |
| 326 | Analytical observations |
| 352 | Remarks on a beautiful relation between direct as well as reciprocal power series |
| 393 | On the sum of series involving the Bernoulli numbers |
| 432 | Analytical exercises |
| 447 | The summation of the progressions
sin(φλ) + sin(2φλ) + sin(3φλ) + ... + sin(nφλ);
cos(φλ) + cos(2φλ) + cos(3φλ) + ... + cos(nφλ). |
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453 | Eminent properties of series within which the general term is contained as x = (1/2)(a+b/√k)(p+q√k)n + (1/2)(a-b/√k)(p-q√k)n |
| 465 | A demonstration of a theorem of Newton on the expansion of the powers of a binomial by cases, in which the exponents are not integral numbers |
| 477 | Meditations about a singular type of series |
| 489 | On unravelling exponential formulas |
| 507 | On the infinity of infinities of orders of the infinitely large and infinitely small |
| 522 | On the formation of continuous fractions |
| 550 | On series in which the product of two consecutive terms make a given progression |
| 551 | Various methods for inquiring into the innate characters of series |
| 553 | Analytical observations |
| 555 | An examination of the use of interpolating methods in the doctrine of series |
|
561 | Various observations about angles proceeding in geometric progression |
| 562 | On how sines and cosines of multiplied angles may be expressed by products |
| 565 | On highly transcendental quantities, which may not be expressed in any way by integral formulas |
| 575 | De mirabilibus proprietatibus unciarum, quae in evolutione binomii ad potestatem quamcunqua evecti occurrunt |
| 583 | De numero memorabili in summatione progressionis harmonicae naturalis occurrente |
| 584 | De insignibus proprietatibus unciarum binomii ad uncias quorumvis polynomiorum extensis |
| 592 | On the resolution of transcendental fractions into infinitely many simple fractions |
| 593 | On the transformation of series into continued fractions, where at once this not mediocre theory is enlarged |
| 597 | A new and most easy method for summing series of reciprocals of powers |
| 613 | Dilucidationes in capita postrema calculi mei differentalis de functionibus inexplicabilibus |
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616 | On the transformation of the divergent series 1 - mx + m(m+n)x2 - m(m+n)(m+2n)x3 + etc. into a continued fraction |
| 617 | On the summation of series, in which the signs of the terms alternate |
| 636 | On the multiplication of angles which are to be obtained by factors |
| 637 | A new demonstration, with respect to which prevails the expansion of binomial powers by Newton even by fractional exponents |
| 642 | On a singular rule for differentiating and integrating, which occurs in the sums of series |
| 652 | On the general term of hypergeometric series |
| 655 | General observations about series, of which the terms arising for the sines or cosines of multiplied angles come forth |
| 661 | Several considerations about hypergeometric series |
| 663 | Plenior expositio serierum illarum memoragilium, quae ex unciis potestatum binomii formantur |
| 664 | Analytical exercises |
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684 | On the roots of the infinite equation 0 = 1 - (xx)/(n(n+1)) + (x4)/(n(n+1)(n+2)(n+3)) - (x6)/(n.....(n+5)) + etc. |
| 685 | An analytical exercise, where in particular a most general summation of series is given |
| 686 | Elucidations about the formula, in which the sines and cosines of angles are to be multiplied, where at once large difficulties are diluted |
| 703 | An easy method for finding series proceeding by the multiplication of the sines and cosines of angles, of which the use in the universal theory of astronomy is very great |
| 704 | Disquisitio ulterior super seriebus secundum multipla cuiusdam anguli progredientibus |
| 705 | Investigatio quarundam serierum, quae ad rationem peripheriae circuli ad diametrum vero proxime definiendam maxime sunt accommodatae |
| 706 | On a new type of rational and highly convergent series, by which the ratio of the periphery to the diameter is able to be expressed |
| 709 | On the expansion of the power of any polynomial 1 + x + x2 + x3 + x4 + etc. |
| 710 | Example of the transformation of singular series |
| 722 | Analytical disquisitions on the expansion of the trinomial power (1+x+xx)n |
|
726 | A demonstration of a notable theorem of numbers a twelfth part of binomial powers |
| 736 | On the summation of series contained in the form a/1 + a2/4 + a3/9 + a4/16 + a5/25 + a6/36 + etc. |
| 742 | Observations about continued fractions contained in the form S = n/(1+(n+1)/(2+(n+2)/(3+(n+3)/(4+etc.)))) |
| 743 | De serie maxime memorabili, qua potestas binomialis quaecunque exprimi potest |
| 745 | On the continued fractions of Wallis |
| 746 | A method for gathering the sums of infinite series by investigating differential formulas |
| 747 | On remarkable series, by which the sines and cosines of multiplied angles may be expressed |
| 750 | A commentary on the continued fraction by which the illustrious La Grange has expressed the binomial powers |
| 768 | De unciis potestatum binomii earumque interpolatione |
| 809 | Series maxime idoneae pro circuli quadratura proxime invenienda |
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810 | Enodatio insignis cuiusdam paradoxi circa multiplicationem angulorum observati |
| 819 | Continuation of some fragments taken from the Mathematics day book |