# A system of practical mathematics; being no.xvi. of a new series of school-books

1845
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### –εώιεςϋλεμα

 ALGEBRA 7 Subtraction 14 Important Theorems Arts 38 39 40 41 22 Multiplication and Division of Fractions 28 Simple Equations 35 Simultaneous Equations 43 Quadratic Equations 49 Surds 55
 Geometrical Progression 65 Interest Simple 72 Promiscuous Exercises 78 Geometrical Theorems 84 Geometry of Planes 131 Solid Geometry 139 Geometrical Exercises 152 General Exercises in Algebra 164

### Ργλοωικό αποσπήσλατα

”εκΏδα 124 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
”εκΏδα 115 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth : or...
”εκΏδα 79 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
”εκΏδα 80 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a Right Angle; and the straight line which stands on the other is called a Perpendicular to it.
”εκΏδα 84 - ... is supposed . to be divided into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds. Degrees, minutes, and seconds, are designated respectively, by the characters Α ' ". For example, ten degrees, eighteen minutes, and fourteen seconds, would be written 10Α 18
”εκΏδα 80 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
”εκΏδα 136 - To draw a straight line perpendicular to a plane, from a given point above it. Let A be the given point above the plane BH ; it is required to draw from the point A a straight line perpendicular to the plane BH.
”εκΏδα 118 - ... of the base, have the same ratio which the other sides of the triangle have to one...
”εκΏδα 71 - When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents.
”εκΏδα 125 - Weigh the denser body and the compound mass, separately, both in water and out of it ; then find how much each loses in water, by subtracting its weight in water from its weight in air ; and subtract the less of these remainders from the greater. Then...