Elements of geometry and trigonometry . In a given circh, to inscribe a regular hexagon and an equilate-ral trianffle. 112 Suppose the problem solved,and that AB is a side of the in-scribed hexagon ; the radii AG,OB being drawn, the triangleAOB will be equilateral. For, the angle AOB is the sixthpart of four right angles ; there-fore, taking the right angle forunity, we shall have AOB = f zzI : and the two other anglesABO, BAO, of the same trian-gle, are together equal to 2—|=f ; and being mutually equal,each of them must be equal to |; hence the triangle ABO isequilateral ; therefo
Elements of geometry and trigonometry . In a given circh, to inscribe a regular hexagon and an equilate-ral trianffle. 112 Suppose the problem solved,and that AB is a side of the in-scribed hexagon ; the radii AG,OB being drawn, the triangleAOB will be equilateral. For, the angle AOB is the sixthpart of four right angles ; there-fore, taking the right angle forunity, we shall have AOB = f zzI : and the two other anglesABO, BAO, of the same trian-gle, are together equal to 2—|=f ; and being mutually equal,each of them must be equal to |; hence the triangle ABO isequilateral ; therefore the side of the inscribed hexagon is equalto the radius. Hence to inscribe a regular hexagon in a given circle, theradius must be applied six times to the circumierence ; whichwill bring us round to the point of beginning. And the hexagon ABCDEF being inscribed, the equilateraltriangle ACE may be formed by joining the vertices of thealternate angles. Scholium. The figure ABCO is a parallelogram and evena rhombus, since AB=BC=CO=AO ; hence the sum of thesquares of the diagonals AC~ + BO^ is equivalent to the sum ofthe squar
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Keywords: ., bo, bookcentury1800, booksubjectgeometry, booksubjecttrigonometry
