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Algebra angles applications Arithmetic Association Beginners Calculus centre chapter circle Committee conic connection considered construction contains coordinates corresponding course curve deal definition discussion draw Edited elementary equal equation Euclid examination examples expression fact figure fixed force functions Geometry give given Hence idea interesting introduced length London Mathematical Mathematical Gazette matter means meet methods Note notice obtained original parallel pass perpendicular plane positive possible practical present principle problems Prof Professor proof properties propositions prove question ratio reference relation respectively result roots rule scale School seems sides simple Solution square straight line student suggested taken tangent teachers teaching text-book theorem theory treatment triangle volume
Página 164 - I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.
Página 56 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together •with the square...
Página 170 - I hold every man a debtor to his profession; from the which, as men of course do seek to receive countenance and profit, so ought they of duty to endeavor themselves, by way of amends, to be a help and ornament thereunto.
Página 72 - ... abstract reasoning at a more advanced point? Where would be the harm in letting a boy assume the truth of many propositions of the first four books of Euclid, letting him accept their truth partly by faith, partly by trial? Giving him the whole fifth book of Euclid by simple algebra? Letting him assume the sixth book to be axiomatic?
Página 72 - HL' : that is, AH is divided in L, so that the rectangle contained by the whole line AH and one part, is equal to the square on the other part HL.
Página 80 - The only types of factors which crop up continually are those of x*-a?, .r- ± 2ax + a-, and, generally, the quadratic function of x with numerical coefficients. In most elementary algebra books there is a chapter on Theory of Quadratic Equations, in which a good deal of attention is paid to symmetric functions of roots of quadratics. No further use is to be made of this till the analytical theory of conies is being studied.
Página 73 - Triangles upon the same base, and between the same parallels, are equal to one another.
Página 80 - VI., a certain type of diluted trigonometry which is found to be within the power of every sensible boy. He will be told what is the meaning of sine, cosine, and tangent of an acute angle, and will be set to calculate these functions for a few angles by drawing and measurement. He will then be shown where to find the functions tabulated, and his subsequent work for that term will consist largely in the use of instruments, tables, and common-sense. A considerable choice of problems is available at...
Página 80 - That the subject should be made arithmetical and practical by the constant use of instruments for drawing and measuring. 2. That a substantial course of such experimental work should precede any attack upon Euclid's text. 3. That a considerable number of Euclid's propositions should be omitted ; and in particular 4. That the second book ought to be treated slightly, and postponed till III. 35 is reached. 5. That Euclid's treatment of proportion is unsuitable for elementary work.