Descriptive Geometry: With Numerous Problems and Practical Applications

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D. Van Nostrand, 1922 - 118 стор.
 

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Сторінка 7 - While it belongs to the geometry of the ancients by the character of its solutions, on the other hand it approaches the geometry of the moderns by the nature of the questions which compose it. These questions are in fact eminently remarkable for that generality which...
Сторінка 38 - ... resistance does not continue. The elastic resistance is raised by the sliding, and consequently the sliding is limited. A stress-strain curve can be drawn which shows the increase of the limit of elastic resistance p with sliding ; the rate of increase of the former at any point may be measured by observing the angle which the tangent to the curve at that point makes with the axis of strain ; I will call this angle <f>.
Сторінка 7 - A mathematical problem may usually be attacked by what is termed in military parlance the method of "systematic approach;" that is to say, its solution may be gradually felt for, even though the successive steps leading to that solution cannot be clearly foreseen. But a Descriptive Geometry problem must be seen through and through before it can be attempted. The entire scope of its conditions, as well as each step toward its solution, must be grasped by the imagination. It must be "taken by assault.
Сторінка 35 - The three most famous of these problems are the squaring of the circle, the duplication of the cube, and the trisection of an angle. Many well-meaning, self-appointed, and self-anointed mathematicians, and a motley assortment of lunatics and cranks, knowing neither history nor mathematics, supply an abundant crop of "solutions" of these insoluble problems each year.
Сторінка 37 - The ordinary helix is a curve generated by a point moving on the surface of a cylinder of revolution, so as to cut all the elements at a constant angle.
Сторінка 57 - PL 16. If the axes are in the same plane, they will either intersect each other or be parallel. We shall first consider the case in which they intersect. Let the horizontal plane be taken perpendicular to the axis of one surface, and the vertical plane parallel to the plane...
Сторінка 12 - ... the distance from the horizontal projection of the point to the axis, and the other side is equal to the distance from the point in space to H.
Сторінка 30 - An ellipse is a curve which is the locus of a point that moves in a plane so that the sum of its distances from two fixed points in the plane is constant.
Сторінка 55 - G, through the vertex of the cone parallel to the elements of the cylinder, will be a line of each auxiliary plane.
Сторінка 29 - A normal to a curve at any point is the perpendicular to the tangent to the curve at the point of tangency.

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