PREFACE. This Course of Practical Geometry was originally designed as a class-book for a very intelligent and influential class of persons—the members of Mechanics’ Institutions; and, as such, upon the manuscript being submitted to Prince Albert, His Royal Highness was graciously pleased to signify his permission that the work should be dedicated to himself. The Second Edition, whilst carrying out to the full the objects of the first, added that of rendering the book suitable, also, for the instruction of younger students; and so the Author had the satisfaction of seeing it introduced into many of the principal Mathematical Establishments of the Country. The Editor of the Third Edition has endeavoured to extend the usefulness of the work in both the departments for which it was designed; for that purpose he has introduced some new features, which, in his experience as a teacher, he has thought advisable. They are the following : A more extensive selection of Examples for Practice, appended to the different problems, which he has endeavoured to arrange in such a manner as to enforce the necessity of the student's constantly referring to what he had already learned: a necessary practice, which all engaged in tuition will allow is too much neglected by the generality of students, especially the younger portion. A large selection of Miscellaneous Questions has been placed at two different periods of the course, the use of which will be sufficiently obvious. The demonstrations to the second and more difficult part of the work have been simplified and enlarged, so as to render the problems capable of being understood by the tyro in Theoretical Geometry. A chapter on the construction of Scales has been added for those commencing Mathematical Drawing, and, like the other parts of the book, accompanied by examples for practice. With these alterations, it is hoped that the value of the book will be increased, and that the care taken in the revision will render it as free from errors as possible. WOOLWICH. CONTENTS. PAGE 11, 18 ADDITION of plane figures, sum ... 13, 64, 65 Altitude or height . 11, 58, 64, 65, 67 Angles, plane, right, acute, obtuse. 5, 6, 13, 38 adjacent, contiguous, alternate, vertical. 5, 11, 20, 22 at centre, at circumference, of polygons.. 10, 42, 44 equal, re-entering, salient.. exterior, interior .. 10 in circles, in segments 12, 40–42 to make, various... 17-19 Antecedent and consequent. 12 Arcs, arches, voussures.. 7, 35, 48 Area 11, 13 Base of a figure, of a drawing. a 4, 11, 64 Bisect, bisections.. 13, 16, 22 Centre, concentric and eccentric. 11, 16, 31, 34, 48 Chord, diameter, radius, secant 4, 6, 7, 18, 42, 61 Circle, circumference, circumscribe 6, 12, 32—34, 37, 48 Common, complement, supplement. 5, 7, 63 Definitions. .3—13, 30, 48, 57 Degrees 7, 18, 19, 22, 38 Describe, draw, drawing 14, 41, 46, 48, 50 Diameter, diagonal .... ... 10, 48, 75 Division, of lines, of figures 26, 27, 71–74 Ellipse, oval, diameters of 48-50 Equal, equivalent and identical, coincide. 12, 13 Figures, rectilineal, curvilineal, similar.. 7, 8, 10, 11, 41-51 Geometry, geometrical. 1, 29, 38, 48, 53 Homologous sides. 12 Inscribe, describe. 12, 33, 37, 45, 46 Instruments, mathematical 14, 27 Intersections.. 13, 21-24, 27, 33, 47–49, 76 PAGE Lines, straight, curved, mixed, etc.... Means, arithmetical, geometrical, harmonical Parallel lines, planes ; parallelograms Perimeter, periphery, term or boundary Planes, horizontal, inclined, vertical, parallel Proportion, proportionals, mean. Quadrilateral, trapezium, trapezoid. Ratio, extreme and mean, duplicate Rectangle, rhombus, rhomboid.. Scales, plain, diagonal, comparative Sector, segment, semicircle, quadrant.. 7, 29, 31, 40, 63, 68 Squares, to construct, add, subtract. 9, 36, 37, 55, 59, 65, 69, 70, 73 Superficies, concave, convex, plane . Tangents, right and curved, tangential .. 4, 12, 31—33, 35, 47, 49 Triangles, single, similar, equal... 8, 9, 21, 22, 34, 36, 54—71 |