MENSURATION FOR The Use of Schools. WITH NUMEROUS EXAMPLES. BY SEPTIMUS TEBAY, B.A., GRAMMAR SCHOOL, RIVINGTON. PREFACE. THE object of the present work is to enable boys to acquire a moderate knowledge of Mensuration in a reasonable time. All difficult and useless matter has been avoided. The examples for the most part are easy, and the rules are concise; those depending on the circle are only first approximations; but the rules are handy, and the results are always sufficiently accurate in practice. A description of the Plotting Scale is given with a view to make this useful instrument more familiarly known to boys, who meet with it in cases of instruments; but rarely know the use of it. Some prominence is given to the method of finding the content of an irregular area by seven equidistant ordinates, first given by the late Mr Thomas Weddle, in the Cambridge and Dublin Mathematical Journal, New Series, Vol. ix. p. 79. When the first, second, third, fourth, or fifth order of differences of the ordinates is constant, this method will furnish the area of the figure exactly. The tables of triangles will be useful in the construction of problems for class practice. A few examples are added on the application of Algebra to Geometry, to induce the aspiring student to step out from the beaten path of Arithmetic; for no one must consider himself proficient till he can investigate his own methods. |