Logarithmic Table of Numbers from 1 to 10000 A Table of Logarithmic Sines, Tangents, Secants, and Versed Sines, to every Degree and Minute of the A Table of Logarithmic Sines, Tangents, and Secants, for every Point, half Point, and Quarter Point of the Mariners Compass, 118 To find the Area of a Rectangle, To find the Area of a Rhombus, or Rhomboid, To find the Length or Breadth of a given Parallelogram, 121 To find the Area of a Triangle, To find the Area of a Trapezoid, Te find the Area of a Trapezium, To find the Area of an irregular Polygon, To find the Area of the Cycloid, To find the Sine and Co-line of an Arch, To find the Tangent and Co-tangent of an Arch, To find the Secant and Co-fecant of an Arch, To find the Superficies of a Cube, To find the Solidity of a Cube, To find the Superficies of a Parallelopipedon or Prism, 175 To find the Solidity of a Parallelopipedon, Prism, and Cy- 179 Ta 176 178 To find the Superficies of the Frustum of a Cone, 180 To find the Solidity of the Fruftum of a Cone or Pyramid, 187 To find the Solidity of the Prismoid, To find the Solidity of a Wedge, To find the Superficies of a Sphere, To find the Solidity of a Sphere, To find the Superficies of any Zone, To find the Solidity of the Segment of a Sphere, To find the Solidity of the middle Zone of a Sphere, 196 To find the Area of a circular Spindle, To find the Solidity of a circular Spindle, To find the Solidity of the middle Zone of a circular Spin- To find the Area and Solidity of the five regular Bodies, 206 To find the Surface and Solidity of a cylindric Ring, 207 Of the Parabola and its parts, Of the Hyperbola and its parts, To find the Content of a Field, Of dividing or laying out of Ground, To GEOMETRICAL DEFINITIONS. i. A point is that which has no parts, neither length, breadth, nor thickness. 2. A line is length, without breadth or thickness. 3. A surface, or superficies, is that which has length and breadth, without thickness. 4. A solid is that which has length, breadth, and thickness. 5. Points are the extremities of a line. 6. Lines are the boundaries of a superficies. 7. Superficies are the boundaries of a solid. 8. A straight line lies evenly between its extreme points. See plate I. fig. 1. 9. Parallel lines are such as are in the same plane, and keep the fame distance, though produced ever so far. 10. An angle is the inclination of two lines of different directions, and meeting in a point. See plate 1. fig. 2. N. B. When two lines, AB, and BC, meet in any point, B, the angle, may be exprefled by three letters, putting other two, thus : ABC, or CBA. 11. When one straight line falls upon another straight line, so as to make the adjacent angles equal to one another, each of them is a right angle and the straight line which falls upon the other is perpendicular to it. See plate 1. fig. 3. 12. An angle which is less than a right angie, is called an acute angle. See plate 1. fig. 4. 13. An angle which is greater than a right angle, is called. an obtuse angle. Plate 1. fig. 5. 14. A figure is that which is inclosed by one or more boundaries. 15. A triangle is bounded by three straight lines. 16. Quadrilateral figures are bounded by four straight lines. 17. Polygons are bounded by more than four straight lines. 18. An equilateral triangle is that which has all its fides equal. Plate i. fig. 6. 19. An isosceles triangle is that which has two of its fides equal. Plate 1. fig. 7. 20. A scalene triangle is that whose sides are all unequal. Plate 1. fig. 8. 21. A right-angled triangle is that which has one right angle. Plate 1. fig. 9. 22. The longest side of a right-angled triangle is called the hypothenuse. 23. An acute angled triangle is that whose angles are all acute. Plate 1. fig. 10. 24. An obtuse angled triangle is that which has one obtuse angle. See plate 1. fig. u. 25. A Tquare is a figure whose fides are equal, and all its angles right angles. See plate 1. fig. 12. 26. An oblong is that whose parallel sides only are equal, and all its angles right angles. Plate 1. fig. 13. 27. A rhombus is that which has all its fides equal, but its angles not right angles. Plate 1. fig. 12. 28. A rhomboid is that whose opposite sides only are equal, but its angles not right angles. Plate 1. fig. 13. 29. A trapezium is a four-sided figure, which has none of its sides parallel. Plate 1. fig. 14. 30. A trapezoid is a quadrilateral figure, with two of its sides parallel. Plate 1. fig. 15: 31. A diagonal is a straight line, which joins any two oppofate angles of a quadrilateral figure. Plate 1. fig. 16. |