## An Essay Upon the Study of Geometry in Common Schools |

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An Essay Upon the Study of Geometry in Common Schools (1847) Stephen Chase No preview available - 2008 |

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abstract accurate additional angles right application Arithmetic attention become better clear common schools comparing confined connect consideration continue convenient correct count curved defined definition demonstration difficulty diffusion direct disci distinct distinguish early easy elementary enunciation Euclid exact expressed extend extremes fact faculties familiar father felt four frequently furnishes gain habits higher hundred ideas illustrations important intellectual intelligent interest INTRODUCTION knowledge known learned less lesson magnitudes mathematical means memory mental habits merely mind nature never object occur parallel particular perfectly philosophers pline points practical preparation present principles proof proper sphere properties propositions pupil reach Reading reasoning rectangle regarded relations remark remembered respect result right angles secure simplicity Spelling square straight line study of Geometry teacher teaching text-book thing thought till treatise triangle true truth universal whole young youth

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Page 18 - Men do not sufficiently understand the excellent use of the pure mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual. For if the wit be too dull, they sharpen it; if two wandering, they fix it ; if too inherent in the sense, they abstract it.

Page 21 - We first hear of it, as an occult and mysterious science, among the Egyptian priests. We next find it in Greece, among the philosophers and learned men; — cultivated by Thales, Pythagoras, Plato, and their schools, and by Euclid, Archimedes, and Apollonius. Thales is said to have brought it into Greece, about six hundred years before the Christian era ; he is also said, which indicates the state of the science at that time, to have himself discovered that the angle inscribed in a semicircle is...

Page 22 - A definition should equally avoid excess and defect. It should express neither too much nor too little. It should be so full as perfectly to identify the object defined, but should not include properties the possibility of whose combination is yet to be proved. Thus, Legendre's definition of the circumference of a circle as " a curved line, all the points of which are equally distant from an interior point, called the centre...

Page 8 - ... Harvard University Monroe C. Gutman Library of the Graduate School of Education HARVARD UNIVERSITY GRADUATE SCHOOl OF EDUCATION MONROE C.

Page 24 - If the product of two quantities be equal to the product of two other quantities, two of them " (any two, of course) " may be made the extremes, and the other two the means, of a proportion " ; eg 4 X 8 = 2 X 16 ; then, making 4 and 2 the extremes, we have 4 : 8 = 16 : 2 ; or, as the product of the extremes is equal to that of the means, 4 X 2 = 8 X 16, or 8 = 128. It should be, the two factors of one product may be made the extremes, &c. Nor is this a mere captious objection. I have repeatedly...

Page 13 - Geometry is admirably adapted to the power» of the youthful mind. Its ideas are elementary. The ideas of form and size are among the earliest which children acquire. Why should we not continue to direct their attention to ideas so early awakened? Why should we not extend their knowledge of subjects, towards which the mind so...

Page 21 - Apollonius distinguished themselves in the higher departments of mathematical science ; Apollonius, particularly, by a most valuable treatise on the Conic Sections. Archimedes, " the most profound and inventive genius of antiquity...

Page 21 - Now, during all this time, and for many centuries after, the knowledge of Geometry was confined to the philosophers, — to the few. Out of the schools of philosophy, among the mass of the community, such science was utterly unknown. The universal diffusion of knowledge, as of all other blessings, * Дог ÎTOV ста, (tai TOV K&r/ioi/ (tipmrw.

Page 19 - ... respectability in society, they need this invigorating discipline. And we can scarce estimate too highly the advantage in educating the next generation, if mothers generally had the benefit of such training, so as to excite their children, by the true intellectual stimulus of sympathy, to the same habits of exact thinking and reasoning.

Page 19 - Shall we gain any thing by delaying till young men come into the higher schools and the colleges? till bad habits are fully formed, and confirmed by long practice \ Again, multitudes who never enter the halls of a college, many who never enjoy the instructions even...