10 INTRODUCTION. 



72. Definition. The surface, 

 contained between an arc and its 

 chord, is called a segment of a circle. 



73. Definition. A chord 

 passing through the centre is 

 a diameter. 



J ^ /^ /\ 74. Definition. A trian- 

 ^^-^=- L I Z. A gle is a surface contained be- 

 tween three lines ; and these lines are understood to be 

 straight, unless the contrary is expressed. 



75. Definition. When two 

 straight lines, lying in the same 

 plane, may be produced both ways indefinitely, without 

 meeting, they are parallel. 



Scholium. The parallelism of lines is sometimes denoted by this 

 mark ||. 



76. Postulate. It is required that the length of 

 a straight line be capable of being identified, whether by 

 the effect of any object on the senses, or merely in 

 imagination, so that it may remain invariable. 



Scholium. This is practically performed by making visible marks 

 on a material surface ; although, strictly speaking, no such marks 

 remain at distances absolutely invariable, on account of changes of 

 temperature, and of other circumstances. 



77. Postulate. That a straight line of indefinite 

 length may be drawn through any two given points. 



78. Postulate. That a circle may be described on 

 any given centre with a radius equal to any given straight 

 line. 



79. Axiom. A straight line joining two points is the 

 shortest distance between them. 



