First Lessons in Geometry Upon the Model of Colburn's First Lessons in ArithmeticD. Appleton and Company, 1859 |
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Common terms and phrases
AB² aBAC ABCD AC² adjacent angles altitude angle ABC angles equal angular points Arithmetic base and altitude BC² bend bisect breadth broken line centre contain curve describe arcs cutting diagonal diedral angles difference dimensions direction distance distinct straight lines divergence divided draw equal angles equiangular polygons equilateral exterior fall figure GEOM Geometry given angle greater hypotenuse identical triangles inches interior angles isosceles triangle Join lelogram length less Let AC line drawn magnitudes Mary Howitt multiplied oblique obtuse paral parallel parallelogram perpendicular plane polygon PROBLEM produced PROPOSITION quadrilateral radius reckoned rectangle Required RHOMBUS right angles right triangle rods Show solid angles subtending subtract surface tABC tABD termed THEOR theorem triangle ABC Triangles agreeing unequal vertex vols zoid
Popular passages
Page 18 - In the mathematics I can report no deficience, except it be that men do not sufficiently understand the excellent use of the pure mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual. For, if the wit be too dull, they sharpen it ; if too wandering, they fix it ; if too inherent in the sense, they abstract it.
Page 123 - 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 93 - Any exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Page 147 - In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Page 21 - ... that the angle inscribed in a semicircle is a right angle, and to have testified his joy by a sacrifice to the Muses!
Page 154 - 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 97 - The difference between any two sides of a triangle is less than the third side.
Page 23 - Of four-sided figures, a square is that which has all its sides equal, and all its angles right angles.
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.