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Hints, theoretical, elucidatory, and practical, for the use of teachers of elementary mathematics, and of self-taught students; with especial ... also a selection of miscellaneous tab - Softcover
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Inhaltsangabe
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1840 Excerpt: ...often produce practical results of great value; and are here simply alluded to, though briefly, because they serve to convince a student of acumen and research, who will not satisfy himself with gliding over the surface of things; how admirable is the fecundity of even this region of truth, and what is the corresponding reward of those who do not rest satisfied with a hasty glance at what lies before them. Let it be observed, also, that converse and contrary propositions are not to be confounded. Two propositions are contrary to one another, when one affirms what the other denies, or denies what it affirms. Thus, if it be affirmed, that three and four are seven, it is a contrary proposition that three and four are eight. (e.) Once more, with respect to the first book of the elements, notice that it, like most of those which follow, supplies various examples of the fecundity to which allusion has just been made, that almost creative power of generalizing, which so frequently appears in the researches of geometers. For example, in tracing the properties of triangles, with regard to their sides and angles, taking of the six data three and three together, there will be found twenty combinations; of which, prop. 4 involves three, while prop. 8 involves only one, and prop. 26 nine; the remaining seven have not fallen under the contemplation of Euclid. The synopses of the data of triangles by Lawson, Leybourn, and Farey, have added very greatly to the rich varieties of this kind of classification. (A similar course, of greater or less extent, according to circumstances, may be adopted at the end of each book of the elements.) These and other matters, which might have been specified, but which will occur to the experienced teacher, are not verbal niceties, but are ...
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Reseña del editor
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1840 Excerpt: ...often produce practical results of great value; and are here simply alluded to, though briefly, because they serve to convince a student of acumen and research, who will not satisfy himself with gliding over the surface of things; how admirable is the fecundity of even this region of truth, and what is the corresponding reward of those who do not rest satisfied with a hasty glance at what lies before them. Let it be observed, also, that converse and contrary propositions are not to be confounded. Two propositions are contrary to one another, when one affirms what the other denies, or denies what it affirms. Thus, if it be affirmed, that three and four are seven, it is a contrary proposition that three and four are eight. (e.) Once more, with respect to the first book of the elements, notice that it, like most of those which follow, supplies various examples of the fecundity to which allusion has just been made, that almost creative power of generalizing, which so frequently appears in the researches of geometers. For example, in tracing the properties of triangles, with regard to their sides and angles, taking of the six data three and three together, there will be found twenty combinations; of which, prop. 4 involves three, while prop. 8 involves only one, and prop. 26 nine; the remaining seven have not fallen under the contemplation of Euclid. The synopses of the data of triangles by Lawson, Leybourn, and Farey, have added very greatly to the rich varieties of this kind of classification. (A similar course, of greater or less extent, according to circumstances, may be adopted at the end of each book of the elements.) These and other matters, which might have been specified, but which will occur to the experienced teacher, are not verbal niceties, but are ...
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- VerlagRareBooksClub.com
- Erscheinungsdatum2012
- ISBN 10 0217158099
- ISBN 13 9780217158091
- EinbandTapa blanda
- SpracheEnglisch
- Anzahl der Seiten36
- Kontakt zum HerstellerNicht verfügbar
(Keine Angebote verfügbar)
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