English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Translation from the Latin original, "Demonstratio gemina theorematisNeutoniani, quo traditur relatio inter coefficientes cuiusvis aequationisalgebraicae et summas potestatum radicum eiusdem" (1747). E153 in the Enestromindex. In this paper Euler gives two proofs of Newton's identities, whichexpress the sums of powers of the roots of a polynomial in terms of itscoefficients. The first proof takes the derivative of a logarithm. The secondproof uses induction and the fact that in a polynomial of degree $n$, thecoefficient of $x^{n-k}$ is equal to the sum of the products of $k$ roots,times $(-1)^k$.

A double demonstration of a theorem of Newton, which gives a relation  between the coefficient of an algebraic equation and the sums of the powers  of its roots