CIRCULAR MEASURE. 34. For what is Circular Measure used? For measuring angles, land, latitude and longitude, the motion of the heavenly bodies, etc. 35. What are the denominations? Signs, degrees, minutes, and seconds NOTE.-Signs as a measure are used only in Astronomy. The Circumference of a Circle is the curve line by which it is bounded. It is divided into 360°. 38. What is the Diameter? The Diameter is a straight line drawn through the centre, terminating at each end in the circumference. 39. What is the Radius ? The Radius is a straight line drawn from the center to the circumference, and is equal to half the diameter. 40. What is an Arc of a Circle? An Arc of a Circle is any part of the circumference. In the preceding figure, A DE B F is the circumference; A B the diameter; C A, C D, C E, etc., are radii; A D, D E, etc., are arcs. Draw a circle. Draw a diameter. Draw another diameter perpendicular to the first. NOTE. These two diameters divide the circumference into four equal parts, called quadrants. 41. How many degrees in a quadrant ? Ninety. 42. How many and what angles do these two diameters form? Four right angles. 43. How many degrees in a right angle? Ninety. MEASUREMENT OF TIME. 44. What are the denominations of Time? Centuries, years, months, weeks, days, hours, minutes, NOTE.-In most business transactions, 30 days are considered a month. Four weeks are sometimes called a lunar month. 45. What is a common year? A common year is one which contains 365 days. 46. What is a solar year? A solar year is the time in which the earth revolves around the sun, and equals 365 d. 5h. 48 min. and 49.7 sec. NOTE. The excess of the solar above the common year is about 6 hours, or 4 of a day, nearly; hence, in 4 years, it amounts to about I day. 47. What is a leap year? A leap year is one which contains 366 days. 48. How caused, and why so called? It is caused by the excess of a solar above a common year; and is so called because it leaps over the limit, or runs on one day more than a common year. This day is given to February, because it is the shortest month; hence, in leap years, February has 29 days. 49. What is a civil year? A civil year is the year adopted by government for computing time, and includes both common and leap years as they occur. 50. How is the civil year divided? It is divided into 12 calendar months, viz.: January (Jan.), the first month, has 31 days. NOTE.-The following couplet will aid the learner in remembering the months that have 30 days each: "Thirty days hath September, April, June, and November." Each of the other months has 31 days, except February, which in common years has 28 days, but in leap years, 29. 51. Into how many seasons is the year divided? Four, viz.: Spring, Summer, Autumn, and Winter. 52. Name the months of each season? Spring consists of March, April, and May. NOTE. The terms folio, quarto, octavo, etc., denote the number of leaves into which a sheet of paper is folded in making books. Aliquot Parts of a Dollar, or 100 Cents. REDUCTION. 1. What is Reduction? Reduction is changing a number from one denomination to another, without altering its value. It is of two kinds, Ascending and Descending. 2. What is Reduction Descending? Reduction Descending is changing higher denominations to lower; as, feet to inches, etc. 3. What is Reduction Ascending? Reduction Ascending is changing lower denominations to higher; as, inches to feet, etc. To Reduce Higher Denominations to Lower. 1. How many farthings are there in £16, 5s. 4d. 2 far.? OPERATION. £16, 58. 4d. 2 far. 20 3258. 12 3904d. ANALYSIS. Since there are 20s. in a pound, there must be 20 times as many shillings as pounds, plus the given shillings. Now 20 times 16 are 320s., and 320s.+58.=325s. Again, since there are 12d. in a shilling, there must be 12 times as many pence as shillings, plus the given pence. Now 12 times 325 are 3900, and 3900d. +4d.=3904d. Finally, since there are 4 far. in a penny, there are 4 times as many farthings as pence, plus the given farthings. Now 4 times 3904 are 15616 far., and 15616 far. + 2 far. 15618 far. Therefore, etc. 4 15618 far. Ans. 4. How reduce higher denominations to lower? Multiply the highest denomination by the number required of the next lower to make one of the higher, and to the product add the lower denomination. Proceed in this manner with the successive denominations, till the one required is reached. |