Practical Mathematics for Technical Students Volume 1

Practical Mathematics for Technical Students Volume 1

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1917 edition. Excerpt: ...bending the following formulae are used: where, fr, f_, are stresses; M and T are respectively bending and shearing moments; and R is the radius of the shaft. CHAPTER IX. USE OF SQUARED PAPER (continued). THE LINEAR GRAPH. SLOPE. RATES. Goordinates.---Any two distinct numbers can be represented on squared paper by means of a single point. These two numbers are the coordinates of the point, and are represented by the distances of the point from two lines called the axes of coordinates, or axes of reference, or, briefly, the axes. The point of intersection of the axes is the origin. The axes are distinguished as the X (or horizontal) axis and the Y (or vertical axis). The distance of a point from the vertical axis is the abscissa. of the point, its x coordinate, or, briefly, its x; the distance of a point from the horizontal axis is its ordinate, the y coordinate of the point, or, briefly, its y. The point P in Fig. 84 is called the point (x, y). This means that the distance of P from OY is ac, and from OX is y. Consistently with previous work, if the x of a point is negative, the point is to the. left of the vertical axis; if the y of a. point is negative, the point is helow the horizontal 3x15. III II II. II ml... III IE II II II IIIIIIII El IIIIIIIIIX IIIIIIII I I Whatever y may be, x is to be 2. That is to say, the point is always to be +2 units from the vertical axis; hence, it may be anywhere on the line AB, which is parallel to OY and 2 units to its right (Fig. 86). The line AB contains every point whose x is 2, and all points where x=2 must lie on AB. Hence x=2 is represented by AB, and conversely the line AB may be called the line x=2. Similarly y=1 means the line CD, which is parallel to OX and 1 unit above it. Conversely, the...
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Product details

  • Paperback | 52 pages
  • 189 x 246 x 3mm | 109g
  • United States
  • English
  • black & white illustrations
  • 1236909704
  • 9781236909701