A. L. Bowley algebra applied arithmetic average binomial theorem boys calculus candidates cent centimetres centre Certificate chord circle conic course cross-ratio curve decimal distance Draw elementary equal equation Euclid examination examples experience factors feet Find forces formula fractions function Geometry girls given GRAFTON STREET graph graphical higher Highest Common Factor horizontal hyperbola idea inches knowledge laboratory Leaving Certificate length lessons logarithms Mathematics Matriculation means measurement Mechanics method obtained ordinary boy paper parabola parallel parallelogram of forces pass perpendicular plane practical problems Prove public schools pupils questions radius ratio rectangle right angles rule Secondary Schools Show sides simple square stage straight line student syllabus System of Education taken tangent taught teachers teaching text-books theorem tion triangle ABC Trigonometry University velocity vertical volume vulgar fractions weight
Página 541 - 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.
Página 594 - Mathematics, rightly viewed, possesses not only truth, but supreme beauty - a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.
Página 124 - When a straight line cuts two other straight lines, if (i) a pair of alternate angles are equal, or (ii) a pair of corresponding angles are equal, or (iii) a pair of interior angles on the same side of the cutting line are together equal to two right angles, then the two straight lines are parallel ; and the converse.
Página 125 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Página 251 - Square Measure 144 square inches = 1 square foot 9 square feet = 1 square yard...
Página 542 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C...
Página 126 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.
Página 484 - If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Página 175 - The value attached to each question is shown in brackets after the question. But a full and correct answer to an easy question will in all cases secure a larger number of marks than an incomplete or inexact answer to a more difficult one.
Página 500 - In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.