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REVIEW. u Still pleased to praise, yet not afraid to blame."—Pope •
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Art * I *—Systematic Education , 8 fC . ( Continued from p . 521 . ) THE Mathematical and Philosophical part of the work fell na =-turally to our lamented friend Mr , Joyce , whose multiplied labours m this walk , had before entitled him to
the grateful acknowledgments of the rising generation . After a few observations on the importance and utility of mathematical science in general , as an exercise of the faculties of the mind , as well as for its various
useful applications , he proceeds to the History and Principles of Arithmetic , gives a short review of the principal school books , Vyse , Hutton , Molyneux , Bonnycastle , and his own , the . particular recommendation of which is , that it contains a greater variety of
examples tending to afford much useful information applicable to the advancing stages of life , and that it applies logarithms with great advantage to the calculating of annuities , reversions , &c ~ The larger works of Malcolm and Mair are also deservedly praised .
Algebra is in like manner historically traced , its general principles explained , and 1 he practical treatises of Bonnycastle and Bridge recommended ; after either of which the student is directed to Maclaurin ,
bimpson , Euler , &c , then to the mathematical repositories of Dodson and Ley bourn , and to the works of Clairaut , D'Alembert , Landen , Waring , &c « , and the Scriptores Logarithmici . We were surprised at the unfavourable mention of Mr . Frend ' s
Algebra , which appears to us the only book which gives a clear idea of ne ^ gative quantities , or makes the change of the sign in multiplication at all intelligible ; and whatever may become of his proposed change in the
mode of notation , ( and we admit the difficulty of effecting a change in thiese respects even for the better , ) we should be very glad to see a practical eAetmehtary book , with a sufficient number of examples , constructed Upon his principles . .
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Geometry is traced from the Egypr tians to modern times , and its universal application pointed oat . The several editions of Euclid are reviewed , from Barrow to Playfair , as are also
the compendiums of Simpson , Payne , Cowley , &c , and the extensive plan of Professor Leslie , only in part executed , which is considered as proper to be made rather a second than a first
book by those who are studying without the aid of a preceptor . Handsome mention is made of the treatises of Reynard and Keith , and the chap * ter concludes with some judicious
remarks on the best mode of studying geometry . Trigonometry is traced from Hipparchus to the completion of the Logarithmic Tables : and the distinction is noted between the ancient mode of
resolving trigonometrical questions by chords , and the modern one by sines , &c . The advantages respectively pos * sessed by the geometrical and algebraic modes of investigation are pointed out ; the three cases , which include all the varieties that can happen ,
stated ; and the modes of solution , by geometrical construction , arithmetical computation , and extension upon the scale , are described . The practical treatises are those of Martin , Ashworth , Simson and Simpson , Vince , Woodhouse , Bridge , Bonnycastle , Keith , & . c . ; in Spherical
Trigonometry , Kelly , and the late excellent George Walker ' Doctrine of the Sphere , " which has at no time been appreciated as it deserves . " The Logarithmic Tables of Hutton and Taylor are recommended , and the Tables Portatives of Callet , stereotyped by Didot . Some remarks conclude the
chapter on the centesimal computation of the French , which , though it would , no doubt , facilitate calculation , would render useless ail existing trigonometrical and astronomical works , as well as all the valuable mathematical instruments .
Conic Sections , after -being traced front Apollonius , are recommended to be studied in the works of Simson , Hamilton , T . Newton or Vmce , It
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Review. U Still Pleased To Praise, Yet Not Afraid To Blame."—Pope •
REVIEW . u Still pleased to praise , yet not afraid to blame . "—Pope
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Citation
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Monthly Repository (1806-1838) and Unitarian Chronicle (1832-1833), Sept. 2, 1818, page 573, in the Nineteenth-Century Serials Edition (2008; 2018) ncse.ac.uk/periodicals/mruc/issues/vm2-ncseproduct2480/page/37/
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