“You are quite right, and I beg you to remember, that an angle of 90 degrees, is called a _right_ angle, and that, when one line is perpendicular to another, it will always form, as you have just seen, a right angle on either side.” “I now understand,” said Louisa, “what is meant BY lines being at _right angles to each other_: But, papa,” continued she, “what are _obtuse_ and _acute_ angles, of which I have so often heard you speak?” [Illustration: Fig. 2. An acute (A) and an obtuse (B) angle.] Mr. Seymour replied, that he could better explain their nature by a drawing, than by any verbal description. “Here,” said he, “is an acute angle, A; and here an obtuse one, B: the former, you perceive, is one that contains less than 90 degrees; the latter, one which contains more, and is consequently greater than a right angle.” Louisa fully comprehended the explanation, and observed, that she should remember, whenever an angle measured less than a _right_ angle, that it was _acute_, and when more, _obtuse_. “But you have not yet explained to me,” she continued, “the meaning of a _triangle_.” “That is a term denoting a figure of three sides, and angles. I dare say Tom can describe the several kinds of triangles.” Tom accordingly took the pencil, and drew a set of figures, of which the annexed are faithful copies. [Illustration: Fig. 3. Three triangles, labeled A, B, and C.] “A,” said he, “is an _Equi-lateral_ triangle; its three sides being all equal. B is a _Right-angled_ triangle, having one right angle. C represents an _Obtuse-angled_ triangle, it having one obtuse angle. An _Acute-angled_ triangle is one in which all the three angles are acute, as represented in figure A.” “As you have succeeded so well in your explanation of a triangle, let us see whether you can describe the nature of a circle.” “It is a round line, every part of which is equally distant from the centre.” “And which round line,” said Mr. Seymour, “is frequently called the _circumference_. What is the diameter?” “A straight line drawn through the centre, and terminating in the circumference on both sides.” “And an arc?” said Mr. Seymour. “Any portion of the circumference.” “Now let me ask you, what name is given to a line which joins any two opposite angles of a four-sided figure?” “The _diagonal_, papa.” “You are quite right,” said Mr. Seymour; and, turning towards the girls, he desired them to remember that term, as they would frequently hear it mentioned during their investigation into the nature of “Compound Forces.” “I really think,” continued their father, “that Tom is as capable of instructing you in these elementary principles as myself; I shall, therefore, desire you, my dear boy, to conclude this lecture during my absence; remember, that by teaching others we always instruct ourselves: but before I quit you, I will give you a riddle to solve, for I well know that you all delight in an enigma.” “Indeed do we,” said Louisa.