If the school do not consist of more than 30 or 40 pupils, there will be no need of employing as monitors any but the highest class. The children should not be permitted to draw on paper, until they have become thoroughly acquainted with the figures of the five first classes. Before they attempt the sixth, they may be permitted to review the five preceding classes, drawing the figures on paper with a lead pencil. The pupils are not to be allowed the use of a rule, or any other instrument; but the monitor, to correct and prove their figures, may be furnished with a rule, dividers, square, and protracter or graduated semicircle. The rule should be a good one, with the inches and tenths of inches marked on it, that, when the pupils have become expert in making the figure, the difficulty may be increased by requiring the whole, or some part of the figure, to be of a given length or dimension. On most rules in common use, the inches are divided into quarters and eighths, but as it is our plan to apply Geometry to decimal arithmetick, such rules as are divided into tenths should be preferred. When the simplicity of decimal calculations is so evident, it is to be regretted that all our measures are not subdivided into decimal parts, as our currency is, and why our government should set so good an example in one particular, and neglect all the rest, it is not easy to determine. Although this treatise was originally designed for schools of mutual instruction, still a slight examination of it will show that there is nothing which unfits it for use in schools on any other plan. If the pupils are all taught, and their drawings examined by the instructer, they will do well; but if they are likewise required to examine and correct each other's work, they will do better; they will acquire a familiarity with the figures, and an exactness in execution, to which mere learners seldom attain. THE first class only draw right lines, triangles and perpendiculars. The corrections are made with a rule, and dividers. The four first figures drawn above, relate particularly to the first eight propositions. To ascertain if the line be straight, let the monitor draw a line through it or near it with a rule. To ascertain if a line be cut into equal parts, measure the parts with the dividers, if the eye be not sufficiently practised to detect the errours without their assistance. PROPOSITIONS. 1. Draw a right line (that is, a straight line.) fig.1. 2. Draw a right line and divide it in the centre. fig.2. 3. Draw a right line and cut it into quarters. fig.3. 4. Draw a right line and lengthen it as much farther. fig. 2. 5. Draw a right line and continue it twice its length. (fig. 4.) 6. Draw a right line and lengthen it three times its length. (fig. 3.) 7. Cut a right line into three equal parts. (fig. 4.) 8. Cut a right line into six or eight equal parts, and so on. It will be a useful exercise at this stage of the business, to show the parts of a line when divided. Thus, if required to show how much three quarters of a line are, the pupil must find one quarter, and the rest of the line will be three quarters. To find three fifths of a line, cut the line into five parts, and take three of them. A very correct idea of fractions may in this way be communicated. 9. Draw a line one inch long, then two, three, four, five, six. (fig. 5.) 10. Draw a line and divide it into inches. It is of no consequence what the length of the line is. Begin at the left, and mark, as many whole inches as there may be. 11. Draw a horizontal line. A horizontal line is one drawn from left to right, or from right to left. The surface or top of a bowl of water is horizontal or level. 12. Draw a perpendicular line. (fig. 6.) A perpendicular or vertical line is one perfectly upright, as a string will hang from a nail, or from the hand, with a weight at the end of it. (6) |