When George Shoobridge Carr (1837-1914) wrote his Synopsis of Elementary Results he intended it as an aid to students preparing for degree-level examinations such as the Cambridge Mathematical Tripos, for which he provided private tuition. He would have been startled to see the two volumes, first published in 1880 and 1886 respectively, reissued more than a century later. Notably, in 1903 the work fell into the hands of the Indian prodigy Srinivasa Ramanujan (1887-1920) and greatly influenced his mathematical education. It is the interaction between a methodical teaching aid and the soaring spirit of a self-taught genius which gives this reissue its interest. Volume 2 contains sections on differential calculus, integral calculus, calculus of variations, differential equations, calculus of finite differences, plane coordinate geometry and solid coordinate geometry. Also included is a historically valuable index insofar as it provides references to 890 volumes of 32 periodicals dating back to 1800.The converse of the above proposition (4931), which is the theorem in Art. 356 of Salmon, is not universally true in any real sense. ... The following example from the same article is an illustration of thisa Ex.-aAny chord BB (Fig. 88) of a conic HOKD is cut harmonically by any line PKAH through P, the pole of the chord, and the tangent at K. The ellipse BKB here ... The harmonic pencil formed by PK and the tangent at K, KB and KB projects into a harmonic pencil formed by pic and the anbsp;...
|Title||:||A Synopsis of Elementary Results in Pure and Applied Mathematics: Volume 2|
|Author||:||George Shoobridge Carr|
|Publisher||:||Cambridge University Press - 2013-09-05|