First Lessons in Geometry: Upon the Model of Colburn's First Lessons in Arithmetic |
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Common terms and phrases
aACB AB² aBAC ABCD AC² adjacent angles angles equal angular points base and altitude BC² bisect broken line centre contain describe arcs cutting diagonals dimensions direction distance divergence divided draw equal angles equally distant equiangular equiangular polygons equilateral exterior figure GEOM Geometry given angle greater hypotenuse identical triangles inches interior angles isosceles triangle Join lelogram length less line drawn magnitudes multiplied oblique obtain the square obtuse opposite angle opposite sides paral parallel parallelogram perpendicular plane polygon PROBLEM PROPOSITION quadrilateral radius rectangle RHOMBUS right angles right triangle Show solid angles square of AC straight line subtending subtract surface tABC tABD termed THEOR three angles trapezoid triangle ABC Triangles agreeing unequal vertex zoid
Popular passages
Page 18 - For, if the wit be dull, they sharpen it; if too wandering, they fix it; if too inherent in the sense, they abstract it.
Page 23 - Of four-sided figures, a square is that which has all its sides equal, and all its angles right angles.
Page 125 - Most good practical workmen have several means for getting the cut of the mitre, and to them this demonstration will appear unnecessary, but I have seen many men make sad blunders, for want of knowing this simple rule. PROBLEM 12.
Page 22 - A CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 4 - ... Theory soon descends to guide and assist the operations of practice. To the geometrical speculations of the Greeks, we may distinctly trace whatever progress the moderns have been enabled to achieve in mechanics, navigation, and the various complicated arts of life. A refined analysis has disclosed the harmony of the celestial motions, and conducted the philosopher, through a maze of intricate phenomena, to the great laws appointed for the government of the universe.
Page 149 - In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Page 156 - Side subtending the Obtuse Angle, is Greater than the Sum of the Squares of the other two Sides, by Twice the Rectangle of the Base and the Distance of the Perpendicular from the Obtuse Angle.
Page 99 - The difference between any two sides of a triangle is less than the third side.
Page 24 - If the product of two quantities be equal to the product of two others, two of them may be made the extremes and the other two the means of a proportion.
Page 77 - A polygon of three sides is a triangle ; of four, a quadrilateral; of five, a pentagon ; of six, a hexagon ; of seven, a heptagon; of eight, an octagon; of nine, a nonagon; of ten, a decagon; of twelve, a dodecagon.