according added angle answers appears arch arising base become circle coefficient common compound consequently CONSTRUCTION continued cube DEMONSTRATION denominator denoted describe determined difference divided divisible divisor draw equal equation evident example expressed extracting extremes factors figure former four fourth fraction given gives greater half Hence interest join known latter least likewise manner means measure meeting method Moreover multiplied negative observed operation parallel perpendicular positive preceding PROBLEM progression proportion proposed quantities question quotient radius ratio reason rectangle reduced remain represented respectively root rule sides simple sine square stand substituted subtracted supposed taken thence theorem thing third tion triangle true unknown whence wherein whereof whole
Page 241 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.
Page 64 - ... then, by adding, or subtracting, the two equations thus obtained, as the case may require, there will arise a new equation, with only one unknown quantity in it, which may be resolved as before.
Page 251 - ... the sum of the segments of the base is to the sum of the sides as the difference of the sides to the difference of the segments of the base.
Page 87 - A composition of copper and tin containing 100 cubic inches weighed 505 ounces. How many ounces of each metal did it contain, supposing a cubic inch of copper to weigh of ounces, and a cubic inch of tin to weigh 4т ounces ? Ans. 420 of copper, and
Page 88 - ... half of what he had left, and half a sheep over ; and, soon after this, a third party met him, and used him in the same manner, and then he had only five sheep left. It is required to find what number of sheep he had at first, Ans, 47 sheep.
Page 254 - The following particular directions, however, may be of some use. 1st, In preparing the figure, by drawing lines, let them be either parallel or perpendicular to other lines in the figure, or so as to form similar triangles. And if an angle be given, it will be proper to let the perpendicular be opposite to that angle, and to fall from one end of a given line, if possible.