TABLE I. The Amount of an Annuity of 17. at Compound Interest. Yrs. at 3 perc.2 per c. 4 per c. 41 per c. 5 per c. 6 per c. 1.0000 1.0000 2.0450 2.0500 2.0600 3.1216 7.6625 7.7794 7.8983 8 9 10 13 14 8.8923 9.0517 9.2142 9.3800 10.1591 10.3685 10.5828 10.802 11 0266 11.4913 11.4639 11.7314 12.0061 12.2582 12.5779 13.1808) 11 12.8078 13.1420 13,4864 13.841 14.2068 14.9716 12 14.1920 14.6020 15.0258 15.4640 15.9171 16.8699 15 6178 16.1130 16.6268 17.1599 17.7130 18.8821 17.0863 17.6770 18.29.9 18.9321 19.5986 21.0151) 15 18.5989 19.2957 20.3236 20.7841 21.5786 23.2760 16 20.1569 20.9710 21.8245 22.7193 23.6575 25.6725 17 21.7616 22.7050 23.6975 24.7417 25.8404 28.2129 23.4141 24.4997 25.6454 26.8551 28.1324 30.9057 25.1169 26-3572 27.6712 29.0636 30.5390 33.7600 26.8704 28.2797 29.7781 31.3714 33.0660 36.7856 21 28.6765 30.2695 31.9692 33.7831 35.7193) 39.9927 18 19 20 TABLE II. The present Value of an Annuity of 17. Yrs. at 3 perc.3 per c.14 per c. 4 per c. 5 per c. 6 per c. 11.2340 10.8378 10.1059 To find the Amount of any annuity forborn a certain number of years. TAKE out the amount of 11. from the first table, for the proposed rate and time; then multiply it by the given annuity; and the product will be the amount, for the same number of years, and rate of interest.-And the converse to find the rate or time. Exam. To find how much an annuity of 50l. will amount to in 20 years, at 31 per cent. compound interest. On the line of 20 years, and in the column of 34 per cent. stands 28 2797, which is the amount of an annuity of 11. for the 20 years. Then 28.2797 x 50 gives 1413-985/ = : 14131. 19s. 8d. for the answer required. To find the present Value of any annuity for any number of years.-Proceed here by the 2d table, in the same manner as above for the 1st table, and the present worth required will be found. Exam. 1. To find the present value of an annuity of 501. which is to continue 20 years, at 3 per cent.-By the table, the present value of 11. for the given rate and time, is 14.2124; therefore 14-2124 × 50=710 62. or710l. 12s. 4d. the present value required. Exam. 2. To find the present value of an annuity of 201. to commence 10 years hence, and then to continue for 11 years longer, or to terminate 21 years hence, at 4 per cent. interest. In such cases as this, we have to find the difference between the present values of two equal annuities, for the two given times; which therefore will be done by subtracting the tabular value of the one period from that of the other, and then multiplying by the given annuity. Thus, tabular value for 21 years 14.0292 10 years 8.1109 ditto for GEOMETRY. DEFINITIONS. 1. A POINT is that which has position, but no magnitude, nor dimensions ; neither length, breadth, nor thickness. 2. A Line is length, without breadth or thick ness. 3. A Surface or Superficies, is an extension or a figure, of two dimensions, length and breadth; but without thickness. 4. A Body or Solid, is a figure of three dimensions, namely, length, breadth, and depth, or thickness. 5. Lines are either Right, or Curved, or Mixed of these two. 6. A Right Line, or Straight Line, lies all in the same direction, between its extremities; and is the shortest distance between two points. When a line is mentioned simply, it means a Right line. 7. A Curve continually changes its direction between its extreme points. 8. Lines are either Parallel, Oblique, Perpendicular, or Tangential. 9. Parallel Lines are always at the same perpendicular distance; and they never meet though ever so far produced. 10. Oblique lines change their distance, and would meet, if produced on the side of the least distance. 11. One line is Perpendicular to another, when it inclines not more on the one side than the the other, or when the angles on both sides of it are equal. 12. A line or circle is Tangential, or a Tangent to a circle, or other curve, when it touches it, without cutting, when both are produced. 13. An Angle is the inclination or opening of two lines, having different directions, and meeting in a point. 14 Angles are Right or Oblique, Acute or Obtuse. 15. A Right Angle is that which is made by one line perpendicular to another. Or when the angles on each side are equal to one another, they are right angles. 16. An Oblique Angle is that which is made by two oblique lines; and is either less or greater than a right angle. 17. An Acute Angle is less than a right angle. 18. An Obtuse Angle is greater than a right angle. 19. Superficies are either Plane or Curved. EN 20. A Plane Superficies, or a Plane, is that with which a right line may, every way coincide. Or, if the line touch the plane in two points, it will touch it in every point. But, if not, it is curved. 21. Plane figures are bounded either by right lines or curves. 22. Plane figures that are bounded by right lines have bames according to the number of their sides, or of their angles; for they have as many sides as angles; the least number being three. 23. A figure of three sides and angles is called a Triangle. And it receives particular denominations from the relations of its sides and angles. 24. An Equilateral Triangle is that whose three sides are all equal. 25. An Isosceles Triangle is that which has two sides equal. 26. A 26. A Scalene Triangle is that whose three sides are all unequal. 27. A Right-angled Triangle is that which has one right-angle. 28. Other triangles are Oblique-angled, and are either Obtuse or Acute 29. An Obtuse-angled Triangle has one obtuse angle. 30. An Acute-angled Triangle has all its three angles acute. 31. A figure of Four sides and angles is called a Quadrangle, or a Quadrilateral. 32. A Parallelogram is a quadrilateral which has both its pairs of opposite sides parallel. And it takes the following particular names, viz. Rectangle, Square, Rhombus, Rhomboid. 33. A Rectangle is a parallelogram having a right angle. 34. A square is an equilateral rectangle ; having its length and breadth equal. 35. A Rhomboid is an oblique-angled parallelogram. 36. A Rhombus is an equilateral rhomboid; having all its sides equal, but its angles oblique. 37. A Trapezium is a quadrilateral which hath not its opposite sides parallel. 38. A Trapezoid has only one pair of opposite sides parallel. 39. A Diagonal is a line joining any two opposite angles of a quadrilateral. 40. Plane figures that have more than four sides, are, in general, called Polygons: and they receive other particular names, according to the number of their sides or angles, Thus, 41. A Pentagon is a polygon of five sides; a Hexagon, of six sides; a Heptagon, seven; an Octagon, eight; a Nonagon, nine; a Decagon, ten; an Undecagon, eleven; and a Dodecagon, twelve sides. 42. A |