Practical, plane and solid geometry, for elementary students; Adapted to the requirements of the revised South Kensington syllabus
Joseph Harrison
Paperback
(RareBooksClub.com, March 6, 2012)
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. 1907 Excerpt: ... energy, temperature, etc. In these we have only magnitude to consider. In other cases, although we may be dealing with directed quantities, yet the conditions may be such as to require only one aspect to be taken into account. For instance we might have a problem involving the speed of a railway train, the direction of motion being ignored; or another problem requiring us to know the direction of the sun's rays, but taking no notice of the sun's distance, or the speed of light. In most of the problems which have been considered in the preceding chapters we have been concerned mainly with the magnitudes of lines, angles, and figures, irrespective of any properties of direction which these might possess. In the present section we are to pay special attention to the association of magnitude and direction in one and the same quantity, and it is a distinctive feature of the problems that both factors shall come into the account. 114. How directed quantities may be represented.--To take a simple case, suppose we wished to specify the position of a point in a plane relatively to another point in the plane. For instance, how might a resident in Liverpool describe the position of Manchester? It would be sufficient to state that Manchester was 30 miles distant in a direction 10 to the north of east. Or, as it might be written, 30 miles E. by 10 N., or 30 miles E. io N. This is a statement of a length and an angle and is the numerical specification of the relative position in question. In the graphical representation, we should first indicate the cardinal points of the compass, or mark say which was East. We should then draw a line in the proper direction, and cut off a segment 30 miles long to scale, specifying the latter. And finally we should place an arrowhead on...