14,25 breadth. 24,5 length. 7125 5700 2850 349,125 Rule. Multiply the length by the breadth, and cut off as many places to the right hand as there are decimals in the length and breadth. Suppose a board or piece of glass be in the form of figure the first, called the rhombus, that is, in the shape of a common pane of glass, or diamond square. Rule. To measure which, multiply the breadth A B, by the length of any of the sides (for they are all equal) and cut off as many places to the right hand as there are decimal places in both multiplicand and multiplier, as hinted before. As suppose one breadth A B, 8 feet 38 parts, and the length of the sides to be 8 feet 52 parts, then the work will appear thus: ft. P. 8,52 8,38 6816 2556 6816 Here the multiplication as in whole number, and the content or answer is found to be 71 square feet, and 4 inches. 71,3976 3976 is separated by a comma, as above directed, and are so many 10,000 parts of a foot. Again, admit a piece of measurement to be in the form of a rhomboides: its length 17 feet 25 parts, and its breadth 8 feet 58 parts. Once more. Suppose a board, piece of glass, pavement or piece of land, to represent, or be in the form of a triangle, or three-cornered figure, expressed as in the shape of figure the third. Every triangle is half an oblong, whose length and breadth is equal to the perpendicular and base. Note. The dotted line is the perpendicular, the bottom line the base, and the line from the top of the perpendicular to the left angle of the base is called the hypothenuse. The measuring of a triangle hath already been shewn, and therefore I shall desist speaking any further thereto. The fourth figure is called a trapezium, and consists of 4 sides. This figure, before it can be measured, must be divided into two triangles, viz. by a line drawn from one angle or corner, to the angle opposite to it, as in the figure. Suppose the dimensions of the trapezium before described to be, viz. the base 16 feet 67: the one perpendicular 12 feet 50, and the other 9 feet 68, (as in figure 5,) what is the content? The operation. One perpendicular 13,50 Add The other 9,68 The sum is 22,18 The half sum is 11,09 which multiply the whole base 16,67 produces 184,8703 which is, 184 feet, and 1870% of a foot, equal to 10 inches. Note, 1. If two sides of a trapezium are parallel, that is, equidistant, then add them together, and half the sum multiplied by the nearest distance between those two sides gives the content. Or, if you measure in the middle between two sides or lines that are of equal length, the answer will be the same. 2. The painting, plastering, &c. of irregular pieces in the forms of triangles or not, if divided as above, may be measured as before; and brought into yards (if the content is to be so giver in) by dividing by 9, as before shewn. REGULAR FIGURES. Figures that have more than 4 sides are called polygons, and those of them that have their sides and angles equal, called regular polygons. 14,25 breadth. 24,5 length. 7125 5700 2850 349,125 Rule.-Multiply the length by the breadth, and cut off as many places to the right hand as there are decimals in the length and breadth. Suppose a board or piece of glass be in the form of figure the first, called the rhombus, that is, in the shape of a common pane of glass, or diamond square. Rule. To measure which, multiply the breadth A B, by the length of any of the sides (for they are all equal) and cut off as many places to the right hand as there are decimal places in both multiplicand and multiplier, as hinted before. As suppose one breadth A B, 8 feet 38 parts, and the length of the sides to be 8 feet 52 parts, then the work will appear thus: ft. P. 8,52 8,38 6816 2556 6816 Here the multiplication as in whole number, and the content or answer is found to be 71 square feet, and 4 inches. 71,3976 3976 is separated by a comma, as above directed, and are so many 10,000 parts of a foot. Again, admit a piece of measurement to be in the form of a rhomboides: its length 17 feet 25 parts, and its breadth 8 feet 58 parts. |