## A Treatise of Algebra: Wherein the Principles are Demonstrated ... To which is Added, the Geometrical Construction of a Great Number of Linear and Plane Problems ... |

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2aac acac acº annuity arch arithmetical progression base become bisect centre circle co-sine coefficient common difference completing the square consequently CONSTRUCTION cube cube root DEMONSTRATION denominator denoted by ac divided divisor draw equa equal example expressed fore fraction given angle given ratio gives half Hence JMethod of Calculation known likewise manner method moidores multiplied negative number of terms parallel perpendicular PROBLEM proposed Q. E. D. JMethod quadratic equation quotient radical quantities radius rectangle remain right-angled right-line segments sides similar triangles sine square root substituted subtracted supposed surd tangent thence theorem third tion trapezium triangle ABC trigonometry unknown quantity value of ac whence the angle whereof whole number

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Side 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.

Side 53 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.

Side 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.

Side 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.

Side 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

Side 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.

Side 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.