“And what do you understand by the term _parallel_?” “Lines are said to be parallel,” said Tom, “when they are always at the same distance from each other, and which, therefore, can never meet, though ever so far continued.” “You are quite right. What is a _square_?” “A four-sided figure, in which the sides are all equal, and its angles all right angles.” “Good again: but let me see whether you have a correct notion of the nature of an angle.” “An angle is the opening formed by two lines meeting in a point.” Mr. Seymour here acknowledged himself perfectly satisfied with his son’s answers, and said, that he should accordingly direct his attention more particularly to Louisa and Fanny; and, taking his pencil, he sketched the annexed figure. [Illustration: Fig. 1. Circle with two lines running through it.] “You perceive, Louisa,” said her father, “that the line A C makes two angles with the line B D, viz. the angle A C D and the angle A C B; and you perceive that these two angles are equal to each other.” “How can they be equal?” cried Fanny, “for the lines are of very different lengths.” “An angle, my dear girl, is not measured by the _length_ of the lines, but by their _opening_.” “But surely,” said Louisa, “that amounts to the same thing: for the longer the lines are, the greater must be the opening between them.” “Take the pair of compasses,” replied her father, “and describe a circle around these angles, making the angular point C its centre.” “To what extent am I to open them?” “That is quite immaterial; you may draw your circle of any magnitude you please, provided it cuts both the lines of the angles we are about to measure. All circles, of whatever dimensions, are supposed to be divided into 360 parts, called _degrees_; the size, but not the number, of such degrees will therefore increase with the magnitude of the circle. And since the opening of an angle is necessarily a portion of a circle, it must embrace a certain number of degrees; and two angles are, accordingly, said to be equal, when they contain an equal number of them.” “Now I understand it,” said Louisa: “as the dimensions of an angle depend upon the number of degrees contained between its lines, it evidently must be the _opening_, and not the _length_ of the lines, that determines the measure of the angle.” “Say, rather, the _value_ of the angle, for that is the usual expression: but I perceive you understand me; tell me, therefore, how many degrees are contained in each of the two angles formed by one line falling perpendicularly on another, as in the above figure.” “I perceive that the two angles together are just equal to half the circle; and, since you say that the whole circle is divided into 360 degrees, each angle must measure 90 of them, or the two together make up 180.”