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22

Hamilton and Klein, Klein was more explicit about it. Hamilton in Lectures on Quaternions (1853) realized that his representation of rotations of rigid bodies by the unit quaternions was not $1$-$1$, but $2$-$1$. Klein in Lectures on the Ikosahedron and the Solution of Equations of the Fifth Degree (1888) replaced the unit quaternions by $2 × 2$ unitary ...


4

The fourth quote is found in the posthumous work "Anecdotes, Observations and Characters, of Books and Men" Vol 1 (page 158), by the historian Joseph Spence (1820). They are reported to have been uttered by Newton just before his death (1727) to Chevalier Andrew Michael Ramsey (though the latter was recorded to be in France at the time). The second probably ...


4

Before Hamilton (1847) one should cite Euler (1771), Gauss (1819), Rodrigues (1840), and Cayley (1845). Detailed references in e.g. Pujol, J., Hamilton, Rodrigues, Gauss, quaternions, and rotations: a historical reassessment, Commun. Math. Anal. 13, No. 2, 1-14 (2012). ZBL1268.01010. Specifically, to four numbers $p,q,r,s$ with $pp+qq+rr+ss=u$, Euler (1771,...


2

Trigonometric functions became "mainstream" since the publication by Ptolemy (II AD) of trigonometric tables. To be sure he did not use our modern sine and cosine, but a single trigonometric function, the chord ($=2\sin(t/2)$). Modern definitions of sine and cosine were introduced by Indian mathematicians (Surya Siddhanta (V century AD), and reached Europe ...


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