Mathesis enucleata, or, The elements of the mathematicks by J. Christ. Sturmius ; made English by J.R. and R.S.S.

SCHOLIƲM II.

NOW therefore as we have Practical Rules to determine A∣rithmetically the sides of the Pentagon and Decagon, so also they may be found Geometrically by what we have demon∣strated. For if the Semidiameter CB (Fig. 96. N. 1.) be divided into 2 parts, EC will =½ a; and erecting perpendicularly the Radius CD=aDE will = 〈 math 〉〈 math 〉. Moreover if you cut of EF equal to it, FC will be = 〈 math 〉〈 math 〉= to the side of the Decagon, by Consect. 1. Having therefore drawn DF, which is equal in Power to the Radius or Side of the Hexagon DC, and the side of the Decagon FC together, by the Pythag. Theorem

it will be the side of the Pentagon sought. Much to the same purpose is also this other new Construction of the same Problem, wherein BG (Numb. 2.) is the side of the Hexagon BD the side of the Square, to which GF is made equal, so that FC is that side of the Decagon, and DF of the Pentagon; which we thus demonstrate after our way: Having bisected GH the side of an Equil. Triangle, the Square of GE will be 〈 math 〉〈 math 〉, by Prop. 48. which being subtracted from the Square of GF=2 aa, viz. 〈 math 〉〈 math 〉 aa, by Prop. 49. there will remain for the Square of EF 〈 math 〉〈 math 〉 aa, and for the line EF 〈 math 〉〈 math 〉, and for FC 〈 math 〉〈 math 〉, which is the side of the Decagon, as DF of the Pentagon, after the same way as before.