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Geometrical 'InJlruBions 



PROPOSITION XYIII. 



Whhin a Circle glven^ to defcribe an Ejineagon^ or 

 Figure of mne Sides. 



Let BCD be the Circle propounded, within 

 which one would infcribe an tnnea gon. 

 The Pra^ice upon Paper. 



Draw the half Diameter A B froih the End B, 

 and from the interval B A defcribe the Arch C A 

 D ^ draw the right Line C D onwards to F ^ make 

 the Line E F equal to A B. From the Point E de- 

 fcribe F G, and from the Point F defcribe EG-, 

 draw the right Line A G, and D H fhall be the 

 ninth Part ot' that Circle. Fig. i, 2. 

 The Fraclice on the Ground 



Being done by a Line, as the Praftice on the 

 Paper is by Compaffes, there is little Occafion to 

 repeat it, but to refer to Figure 4. 



PROPOSITION XIX. 

 j4 Line being given^ to fnd the Center of a Circle^ and 

 ■ to make an Eniwagon, or Figure of nine Sides, 

 Draw the Line A B, and a Line perpendicular 

 from the Middle thereof, as has been before taught •, 

 drav/ the Arch A (), and divide it into fix equal 

 Parts ^ or, which is lefs Trouble, take the half of 

 it, and fet up to P, which is the Center of this 

 Circle, upon which you are to make this Ennea- 

 gon, or Figure of nine Sides, ev^ry Side being 

 tgnal toA B. Fig. ?. 



The Pra&ice on the Ground 

 Continues ftill the fame-, and from this Rule of 

 anHeiagone, is any Pol3^gonar Figure to 20, ^o, 

 or 40 Sides, made upon a given Line •, from what 

 has been faid likev/ife of given Circles, may the 

 Side of any Polygon be found-, and with this I 

 ihall conclude this Point. 



