School Science and Mathematics, Volume 11

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Smith & Turton, 1911 - Education
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Page 352 - Any proof of a Proposition will be accepted which appears to the Examiners to form part of a systematic treatment of the subject...
Page 776 - MATHEMATICS. Remittances should be made by Post Office Money Order, Express Order, or Bank Draft. If personal checks are sent, please add ten cents for collection. SCHOOL SCIENCE AND MATHEMATICS is the "official organ" of the folloicing associations and is sent free to all members who have paid their dues.
Page 274 - Al Antimony Sb Argon A Arsenic As Barium Ba Bismuth Bi Boron B Bromine Br Cadmium Cd Caesium Cs CALCIUM Ca...
Page 348 - Sir David Brewster's Translation." In the same article DeMorgan gives utterance to a difficulty experienced by young students, which has been referred to by many writers in different countries, the reductio ad absurdum. DeMorgan says : " The most serious embarrassment in the purely reasoning part is the reductio ad absurdum, or indirect demonstration. This form of argument is generally the last to be clearly understood, though it occurs almost on the threshold of the ' Elements.' We may find the...
Page 436 - Through a given point one line and only one can be drawn parallel to a given line. The question of limits is considered later. It is not deemed desirable to postulate explicitly the existence of such concepts as point, line, and angle, nor to assume that a line drawn through a point in a triangle must cut the perimeter twice, nor to add a postulate of continuity.
Page 434 - There is also the assumption that if unequals are added to unequals in the same order the sums are unequal in the same order, and that if unequals are subtracted from equals the remainders are unequal in the reverse order, these being the only ones relating to inequalities that are needed in elementary geometry.
Page 529 - An oblique prism is equivalent to a right prism whose base is a right section of the oblique prism, and whose altitude is equal to a lateral edge of the oblique prism. Hyp. OM is a right section of oblique prism AD', and OM ' a right prism whose altitude is equal to a lateral edge of AD'. To prove AD' =0= GM' . Proof. The lateral edges of GM
Page 510 - ... this way, loci problems may and should be introduced at certain stages of the subject. For example, in Book I: The locus of a point equidistant from two fixed points, equidistant from two intersecting lines, or from two parallel lines, or at a given distance from a fixed line. In the book on circles, the locus of all points equidistant from a fixed point, the locus of the centers of circles of fixed radius and tangent to a given line, the locus of the centers of all circles tangent to two parallel...
Page 274 - Hydrogen H Indium In Iodine I Iridium Ir Iron Fe Krypton Kr Lanthanum La Lead Pb Lithium...
Page 332 - This is useful in fortification ; ' ' you cannot play at billiards without this.' ' You only look through a telescope like a Hottentot until this proposition is read,' with many such powerful strokes of rhetoric to the same purpose. And upon such terms, and with such inducements, who would not be a mathematician? Who would go to work with all that apparatus which I have described as necessary for understanding Euclid, when he has only to take a pleasant walk with Clairaut upon the flowery banks of...

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