OF SPACE. 



58. Definition. A line joining two 

 points is called their distance. 



59. Definition. When the distance of 

 any two or more points remains unchanged, 

 they are said to be at rest; and a space of 

 which all the points are at rest, is a quiescent 

 space. 



■Q8BP 60. Definition. 



A line which must be wholly at rest with 

 respect to any quiescent space when two of 

 its points are at rest in that space, is a straight 

 line. 



^ ^ '^ ^ ~^ Cl. Definition. 



A line which is neither a straight line, nor 

 composed of straight lines, is a curve line. 



62. Definition. A plane is a surface, 

 in which if any two points be joined by a 

 straight line, the whole of the straight line 

 will be in the surface. 



63. Definition. 

 An angle is the incli- 

 nation of two lines to eadi other. 



Scholium. An angle is sometimes denoted by this 

 mark z., and is described by three letters placed near the 

 lioes, the middle letter at the angular point. 



64. Definition. 

 When a straight line 

 standing on another 



straight line makes the adjacent angles equal, 

 they are called right angles, 



65. Definition. A straight line between 

 two right angles is called a perpendicular to 

 the line on which it stands. 



6G. Definition. 

 When a plane surface 

 is contained by a 

 circumference, such 

 that all straight lines drawn to it from a 

 certain point in the plane'are equal, the sur- 

 face is a circle. 



VOL. II, 



G7. Definition. The point equally dis- 

 tant from the circumference, is called the 

 centre. 



G8. Definition, Any straight line 

 drawn from the centre to the circumference, 

 is called a radius. 



69. Definition. The term circle also 

 often implies the circumference, and not the 

 circular surface. 



70. Definition. A portion of the cir- 

 cumference of a circle is called an arc. 



71. Definition. A straight line joining 

 the extremities of an arc, is its chord. 



72. Definition, 

 The surface con- 

 tained between an arc and its chord is called 

 a segment of a circle. 



73. Definition. 

 A chord passings 

 through the centre 

 is a diameter. 



ilA^ 



74. Defini- 

 tion. A trian- 

 gle is a surface contained between three lines ; 

 and these lines are understood to be straight, 

 unless the contrary is expressed. 



75. Definition. ^^g^^^B ~ 



When two straight ^^^^^ 



hnes, lying in the same jdane, may be pro- 

 duced both ways indefinitely, without meet- 

 ing, they are parallel. 



Scholium. The parallelism of lines is sometimes de- 

 noted by this mark II . 



7G. Postulate. It is required that the 

 length of a straight line be capable of being 

 identified, whether by the effect of any ob- 

 ject on the senses, or merely in imagination, 

 so that it may remain invariable. 



Scholium. This is practically performed by making 

 \isible marks on a material surface; although, strictly 

 speaking, no such marks remain at distances absolutely 

 C - 



