/(?f Gardeners, &c. 19 

 p R o p o S IT I o N XIL 



To frame an Hexagon regular upon a right Line given. 



Let A B be the right Line given, from the Ends 

 A and B, and from the Interval A B defcribe the 

 Arches AC, B C^ and from the SedHon C defcribe 

 the Circle A B E F G: Bring fix times the Line 

 AB within the Circumference, and you ihall have 

 an Hexagon regular, A B E F G D, fram\l upon 

 aright Line given, A B. Fig. i, 2. 



K B. It is to be here obferv'd, that the Semidi- 

 ameter of an Hexap;on, is always one Side oi it. 

 And this is the eaueil to make of all Polvgonar Fi- 

 gures. 



This is alfo the Foundation from which' all Poly- 

 gonar Figures are fram'd, as wilLappear in Fig. ^, 

 ''' ' The FraBicecn the Gro::i:d 



Is every Way anfw^erable to.-that ou.th^e E^pgr. 



'' • p R^ o p o s I TT^t) K - xift: -^;' : 



The Hexagon being the Foundation, on' \v1iicli all 

 Pol3rg.^nar' Figures are built, 'here follows a Mc 

 thod, Upon 'any right Line given ^ to defcribe fiich a 

 Polygon as fhdl he reqmrd\ from an Hejidgon to a 

 Dodecagon^ or Figure of 12 Sides, •'.-Vt 

 Cut the Line A B into two equally in O^ elevate 

 the Perpendicular O I from the Point B ^ defcribe 

 the Arch A C ^ divide A C into fix Parts equally, 

 M N O P Q.R-, this may make anHeptagoh'if 

 3^ou will. Then from the Point C, and the Inter- 

 val of one Part, C M, defcribe the Arch, D M J), 

 fhall be the Center, to defcribe a Circle capable of 

 containing feven times the Line A B ^ and fo on, 

 of any of the reft, as will more plainly appear by 

 a little Pradice. Fig. 3. 



C 2 



