PREFACE. THE following pages have been transcribed from notes made by the author from time to time in teaching Mensuration in his own classes, and are intended for those pupils only who have previously acquired some knowledge of Geometry and Algebra. Indeed it is not until a pupil has acquired this knowledge that he can take up the subject with any degree of intelligence, or derive any educational advantage from its study. The subject, however, is so important, and its results are of so much practical utility, that it is not unusual to supplement the ordinary course of arithmetic by the addition of rules and exercises on Mensuration. These rules the arithmetical pupil may follow, and the exercises he may work; but beyond taxing his memory and exercising his fingers, they can be of little or no advantage to him. On the other hand, when he enters upon the study of Mensuration with a knowledge of Geometry and Algebra, he can frame and investigate rules for himself, and thus render the subject an efficient mears of mental discipline. Besides, the results of Mensuration, so important in themselves, afford the student a ready means of illustrating and interpreting geometrical processes and algebraical formulæ. The author has to express his obligations to Mr J. J. A. BLACK, his able assistant, who has carefully wrought out the exercises proposed, and added his results in the form of answers at the end of the book. ROYAL HIGH SCHOOL, EDINBURGH, March 1873. CONTENTS. I. Having given any two sides of a right-angled triangle, to find the remaining side......... II. Given the three sides of a triangle, to find the length of the perpendicular on any of the sides from the III. Given the three sides of a triangle, to find the length of the line drawn from any of the angles to the bisection of the opposite side..... IV. Given the three sides of a triangle, to find the length of the line bisecting any of the angles......... V. Given the three sides of a triangle, to find the diameter of the circumscribing circle......................... VI. To divide a line into extreme and mean ratio... EXERCISES (1).................................... VIII. Having given the side of a regular polygon inscribed in a given circle, to find the side of the regular polygon inscribed with double the number of sides. 19 IX. Having given the side of a regular polygon inscribed in a given circle, to find the side of the regular polygon of the same number of sides circumscribing X. Given the perimeter of a regular polygon inscribed within a circle, and the perimeter of a similar cir- cumscribed polygon, to find the perimeters of the regular inscribed and circumscribed polygons of double the number of sides....... 23 3333333 Readings in English Prose, and in English Poetry. Readings in English Literature.. Class-Book of Science and Literature. Scientific Reader, forming Part I. of the Class-Book. CHAMBERS'S CHEAP REPRINTS OF ENGLISH CLASSICS, WITH NOTES, &c. Gray's Odes and Elegy....... Macaulay's Essay on Milton..........0 .0 -Winter. ....0 6 Wordsworth's Excursion-Book I....0 Shakespeare for Schools, in separate Plays, 1s. each; paper cover, 8d. First Book of Reading... 0232 .0 1 English Grammar and Com- Sen .0 6 .2 6 Lan .2 0 MANUALS for 'Specific Subjects of Instruction'-Code 1872. Sixpenny Copy-Books......each 0 6 .0 6 Graduated Writing Sheets for Twopenny Copy-Books....each 0 2 School Walls, Nos. 1 to 15......each 0 2 DRAWING. First Drawing-Book. Also in Two Parts.... Second Drawing-Book.. Drawing Lesson Books. in 18 Books .1 0 Mechanical Drawing, 3 Books, .each 0 4 3. d. each 1 6 each 2 0 2 0 0 Architectural Drawing, 3 Books, each 1 6 Isometrical Drawing, 2 Books," GEOGRAPHY, MAPS, AND ATLASES. |