MATHEMATICa PLANE GEOMETRY. 



[DEFINITIONS. 



An Mil* angle 

 U that which is 

 greater than a 

 right angle. 



An aeute angle is that 

 which U lea than a 

 right angle. 



XI. 



A figure in that which is enclosed by 

 one or more boundaries. 



XII. 



A circle is a plane figure en- 

 closed by one line, which is called 

 the rircumjertnee of the circle : it 

 is such, that all straight lines, 

 drawn from a certain point with- 

 in the figure to the circum- 

 ference, are equal to one another. 



XIII. 



This point is called the centre 

 of the circle. 



And any line drawn from the centre to the circumference U called 

 a radiut at the circle. 



XIV. 



A diameter of a circle is a straight line drawn through 

 the centre, and terminated both ways by the circum- 

 ference. 



A radio* is therefore hall the diameter, or a itmidiamtter. 



XV. 



A semicircle is the figure contained by a diameter and 

 the part of the circumference cut off by the diameter. 



XVI. 



Rectilineal figures are those which are enclosed by 

 straight lines only. 



XVII. 



Trilateral figures, or triaiujles, are enclosed by three 

 straight lines. 



XVIII. 



Quadrilateral figures, by four straight lines. 



XIX. 



Multilateral figures, or polygons, by more than four 

 straight lines. 



The term polTiron, howerer, 1* often employed a* a general name fcr 

 rectilineal Airures of all kinds, without rrgrard to the number of the 

 sides; so that the rectilineal figures denned above may, without 

 Impropriety, be called polygons of three and of four aide* re- 

 spectiTely. 



XX. 



An eipiilittrral triangle is that which 

 has ite three sides equal 



XXL 



An isosceles triangle has two of its sides 

 equal. 



XXII. 



A tcaltne triangle has its three sides 

 unequal. 



XXIII. 



A right-angled triangle has one of its 

 angles a right angle. 



XXIV. 



An obtnse-angled triangle 

 has one of its angles obtuse, 

 or greater than a right angle. 



xxv. 



An acute-anyled triangle has each 

 of its angles acute, or less than a 

 right angle. 



* 



xxvi. 



Of four-sided figures, a iquare is that 

 which has all its sides equal, and all its 

 angles right angles. 



If the four aides are rqital, and only anf of the 

 angle* affirmed to be ritcht, the other three angles 

 mut be ritcht, of necessity, as will be hereafter 

 proved ; this definition ia therefore redundant. 



XXVII. 



A rectangle is that which has all its four 

 angles right angles, whether its sides be 

 equal or not. 



XXVIIL 



A rhombus is that which has all its 

 sides equal, but its angles are not 

 right angles. 



XXIX. 



A rhomboid is that which has its oppo- 

 site sides equal to one another, but all its 

 sides are not equal, nor its angles right 

 angles. 



XXX. 



Parallel straight lines are __^_ 



such as are in the same 



plane, and which, being 



produced ever so far both 

 ways, do not meet. 



XXXI. 



If each pair of opposite sides * . 



of a quadrilateral be parallel .s ^/^ 



lines, the figure is called a ^_ ' 



parallelogram. 



It will be Ken hereafter that square*, rectangles, rhombuses, and 

 rhomboids, are all parallelogram!. 



XXX IL 



All other four- 

 sided figures, besides 

 those here defined, 

 are called trapeziums. 



XXXIII. 



A line drawn across 

 a figure, joining two 

 opposite corners, or 

 vertices, is called a 

 diagonal. 



POSTULATES. 



I. 



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 prolonged to 

 any length in a straight line. 



