THE ELEMENTS OF EUCLID. BOOK I. DEFINITIONS. 1. A point is that which hath no parts, or which hath no mag- Book I. nitude. See Notes. II. A line is length without breadth. treme points. taken, the straight line between them lies wholly in that su perficies. VIII. “ A plane angle is the inclination of two lines to one See N. " another in a plane, which meet together, but are not in 66 the same direction.” IX. A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line. A N. B. - When several angles are at one point B, any one of them is expressed by three letters, of which the letter that • is at the vertex of the angle, that is, at the point in which the straight lines that contain the angle meet one another is put 6 between the other two letters, and one of these two is somewhere upon one of those straight lines, and the other upon the other line : Thus the angle which is contained by the straight lines AB, CB is named the angle ABC, or CBA; • that which is contained by AB, BD is named the angle ABD, 6 or DBA; and that which is contained by BD, CB is called the angle DBC, or CBD: but if there be only one angle at . a point, it may be expressed by a letter placed at that point; as the angle at E.' another straight line makes the adja- it. XII. An acute angle is that which is less than a right angle. aries. XV. A circle is a plane figure contained by one line, which Book I. is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference are equal to one another. XVI. And this point is called the centre of the circle. the centre, and terminated both ways by the circumference. XVHI. A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter. XIX. “ A segment of a circle is the figure contained by a straight line, and the circumference it cuts off.” straight lines. straight lines. which has three equal sides. XXV. An isosceles triangle is that which has (only) two sides equal. AAA Book I. XXVI. A scalene triangle is that which has three unequal sides. XXVII. A right angled triangle is that which has a right angle. tuse angle. AAA XXIX. An acute angled triangle is that which has three acute angles. XXX. Of four sided figures, a square is that which has all its sides equal, and all its angles right angles. XXXI. An oblong is that which has all its angles right angles, but has not all its sides equal. XXXII. A rhombus is that which has all its sides equal, but its angles are not right angles. XXXIII. A rhomboid is that which has its opposite sides equal to one another, but all its sides are not equal, nor its angles right angles. XXXIV. All other four sided figures besides these are call ed trapeziums. XXXV. Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways, do not meet. 5 Book I. POSTULATES. 1. Let it be granted that a straight line may be drawn from any one point to any other point. II. That a terminated straight line may be produced to any length in a straight line. III. And that a circle may be described from any centre, at ány distance from that centre. AXIOMS. 1. Things which are equal to the same are equal to one another. equal. another. VII. Things which are halves of the same, are equal to one another. which exactly fill the same space, are equal to one another. “ make the two interior angles on the same side of it taken angles. See the notes on Prop. 29. of Book I.” |