Elementary Treatise on Geometry

Elementary Treatise on Geometry

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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. 1830 edition. Excerpt: ...determine the length of a line? 2. How do you find out which of two lines is the greater? 3. How can you measure a surface? 4. What do you call the area of a surface? 5. If you take one of the sides of a triangle for the basis, how do you determine the height of the triangle? 6. How is the height of a parallelogram determined? How that of a rectangle? A rhombus? A square? 7. When do you call a triangle equal to a square? to a parallelogram? to a rectangle, &c? 8. When can you call two geometrical figures equal to one another, though these figures do not coincide with each other? 9. Can you now repeat the different principles respecting the areas of geometrical figures, which you have learned in this section? Ans. 1. The area of a rectangle is found by multiplying its basis, given in miles, rods, feet, inches, &c, by its height, expressed in units of the same kind. 2. The area of a square is found by multiplying one of its sides by itself. 3. If a parallelogram stands on the same basis as a rectangle, and has its height equal to the height of that rectangle, the area of the parallelogram is equal to the area of the rectangle. 4. The areas of all parallelograms, which have equal bases and heights, are equal to one another. 5. Parallelograms upon equal bases and between the same parallels, are equal to one another. 6. The area of a parallelogram is found by multiplying the basis given in rods, feet, inches, &c, by the height, expressed in units of the same kind. 7. The area of a rhombus or lozenge is found like that of a parallelogram. 8. The areas of parallelograms are to each other, as the products obtained by multiplying the bases of the parallelograms by their heights. 0. Rectangles, or parallelograms which have equal bases, are to...
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Product details

  • Paperback | 44 pages
  • 189 x 246 x 2mm | 95g
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236526465
  • 9781236526465