music, optics, perspective, drawing, mechanics, hydraulics, pneumatics, &c. MENSURATION. Mensuration is the art of ascertaining the contents of the su perficial areas, or planes; of solids, or substantial objects; and the lengths, breadths, &c. of various figures, either collectively or abstractedly. PLANES AND SOLIDS. The several kinds of measuring are three, viz. 1st. Lineal, by some called running measure, and is taken by a line, and it respects length without breadth; the parts of which are, 12 inches 1 foot, 3 feet 1 yard, 16 feet and a half 1 rod, pole, or perch. All kinds of ornamental work, such as cornice, frieze, &c. are measured by running measure. 2dly. Superficial, or square measure, is that which respects length and breadth; and the parts are, 144 inches 1 foot, 72 inches half a foot, 36 inches one quarter of a foot, 18 inches half a quarter of a foot, 272 feet and a quarter 1 rod, 136 feet half a rod, 1196 inches, or 9 feet, one superficial or square yard. 3dly. Solid, or cube measure, which respects, length, breadth and depth, or thickness; and the parts are, 1728 inches 1 foot, 1296 inches three quarters of a foot, 864 inches half a foot, 432 inches one quarter of a foot, and 27 feet one solid yard. Superficial Measure. To measure things that have length and breadth, such as board, glass, pavement, wainscot, and land, is to take the dimensions of the length and breadth, according to the customary methods used in each particular; for instance, board and glass are measured by the foot, the dimensions are taken in feet and inches, and the content given in fect. The dimensions of wainscoting and paving, plastering and painting, are taken in feet and inches, and the content given in yards. Of the square or superficial Content or Area. The squaring of any number is multiplying it into itself, as 12 inches multiplied by 12 inches, make 144 square inches. The superficial content or area of any thing is found four several ways, viz. by whole numbers, by Decimals, by Practice, and by Crossmultiplication; in each of which methods I shall give examples of operation. A square hath its sides perpendicular, and those that are opposite equal; but the adjadent sides are unequal boards, wainscots, ceilings, windows, doors, &c. are commonly of this figure. When any thing is to be measured, it must be considered what form or fashion it is of; and then it must be measured according to the several rules for each figure. First, if it be a square or oblong, then the length and breadth, must be multiplied one by the other, which gives the content in square measure, and that product must be divided by its proper divisor, according to the name in which the content or area is to be given. Example. Admit a board to be 12 inches broad, and 8 feet or 96 inches long, how many square or supecficial feet doth it contain? 96 12 144) 1152 (8 feet Here the length in inches is multiplied by the breadth in inches long, and the product, 1152 divided by 144 the square inches in a foot, quotes 8 feet square for the content of the board. A rule for dispatch. If the length of a board, or piece of glass, be given in feet, and the breadth in inches, multiply the one by the other, (without any reduction, and divide the product by 12; and the quotient will be the answer in feet, and the remainder will be parts of a foot. So the foregoing example might have been done sooner by dividing 96 the length, by 12 the breadth, and it quotes 8 feet for the content, as by the former way. Example. Suppose a board be 14 feet long, and 15 inches broad, what is the content in square feet? 14 feet long. 15 Inches broad. 12) 210 Feet 1701 The answer is 17 feet and . And so for any other example of this kind. f a board be 12 feet, or 150 inches long, and 15 inches broad, how many square feet doth it contain? The four methods here used are as follows: First by multiply. ing the inches together, and dividing by 144, &c. The second work is performed Decimally; the third method is by CrossMultiplication; and the last and the best is by Practice. Any of these methods may be easily understood by the use of the arithmetical part of this book, except the method by CrossMultiplication, which I shall explain here. In the example, 1 foot 3 stands under 12 feet 6; and having drawn a line, say 12 is 12, and then say crossway, 6 times 1 is 6 inches; so that line is 0 feet 6 inches; then crossway, again L say, 3 times 12 is 36 inches, the 12's in 36 is three times, or 3 feet, so that line is 3 feet 0 inches. Lastly, I multiply the inches together, saying 3 times 6 is 18, the 12's in 18 once, and there remains 6, or equal to, as in the work. If a board be wider at one end than the other, then take the breadth in the middle, or add the measure of both ends together, and take half of the mean breadth, which multiply by the length. Example. Suppose a board to be 120 inches long, and the narrow end 10 inches wide, the broadest end 34 inches wide⚫ what is its coutent in superficial feet? Add { Sum 34 broadest end 10 narrowest 44 If a board or piece of glass be ever so irregular, it may be measured very near by taking the breadth in 5 or 6 places, and add the several breadths together, dividing the total by the number of places, and the quotient will be the mean breadth: which multiply by the length, &c. Having the breadth in inches of any board, or piece of glass, to know how much the length of a board or piece of glass will make of a foot superficial? Rule. Divide 144 by the inches in breadth, and the quotient will be the length of that board that will make a foot. Example. If a board be 9 inches broad, what length of that board will make a superficial foot? 9) 144 Answer, 16 PROPER DIMENSIONS FOR JOINERS, PAINTERS, Rooms being various in their forms, take this general rule in all cases, vix, Take a line, and apply one end of it to any corner of the room; then measure the room, going into every corner with the line, till you come to the place where you first began; then see how many feet and inches the string contains, and set it down for the compass or round; then take the height by the same method. Glaziers are to take the depth and breadth of their work, and multiply one by the other, dividing by 144. Glass is measured as board. Having thus shewn the method of casting the dimensions, I come now to particulars, viz. |