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amount angles answer apparatus attention become beginning better called changes Committee composition connected consideration correct course definite direction discussion drawing effect elementary English equal examination exercise experiment expression fact field four geometry German give given grades hand high school ideas important instruction interest knowledge laboratory language Latin lead less light literature material mathematics matter means measure meeting method Michigan mind nature necessary Normal object observation obtained pass period physical plants position possible practical preparation present principles problems Professor pupils question reading reason relation secondary schools seems side student suggested taken taught teacher teaching things thought tion tube University write
Side 83 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Side 80 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Side 7 - In determining what is a reasonable punishment various considerations must be regarded ; the nature of the offense, the apparent motive and disposition of the offender, the influence of his example and conduct upon others, and the sex, age, size and strength of the pupil to be punished. Among reasonable persons, much difference prevails as to the circumstances which will justify the infliction ot punishment and the extent to which it may properly be administered.
Side 43 - Hypothesis — if two adjacent angles have their exterior sides in the same straight line, then — Conclusion — the sum of these adjacent angles is equal to two right angles.
Side 47 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it.
Side 15 - Euclid honourably shelved or buried "deeper than did ever plummet sound" out of the schoolboy's reach, morphology introduced into the elements of Algebra — projection, correlation, and motion accepted as aids to geometry — the mind of the student quickened and elevated and his faith awakened by early initiation into the ruling ideas of polarity, continuity, infinity, and familiarization with the doctrine of the imaginary and inconceivable.
Side 7 - Hence the teacher is not to be held liable on the ground of excess of punishment, unless the punishment is clearly excessive and would be held so in the general judgment of reasonable men. If the punishment be thus clearly excessive, then the master...
Side 57 - ... same extent to every pupil so long as he pursues it, no matter what the probable destination of the pupil may be, or at what point his education is to cease. Thus, for all pupils who study Latin, or history, or algebra, for example, the allotment of time and the method of instruction in a given school should be the same year by year. Not that all the pupils should pursue every subject for the same number of years; but so long as they do pursue it, they should all be treated alike.
Side 57 - ... every subject which is taught at all in a secondary school should be taught in the same way and to the same extent to every pupil so long as he pursues it, no matter what the probable destination of the pupil may be, or at what point his education is to cease.