Elements of Geometry: With NotesJ. Souter, 1827 - 208 sider |
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Side 113
... regular polygons . PROPOSITION I. THEOREM . Two regular polygons of the same number of sides are similar . For the ... polygon is the same submultiple of their sum ; and equi - submultiples of equal magnitudes being equal , the angles of the ...
... regular polygons . PROPOSITION I. THEOREM . Two regular polygons of the same number of sides are similar . For the ... polygon is the same submultiple of their sum ; and equi - submultiples of equal magnitudes being equal , the angles of the ...
Side 114
... polygon to have more than four sides . Then , the angles of this polygon being each greater than a right angle ... regular polygon the diagonal , cutting off three sides , is parallel to the middle one , and , further , that the dia ...
... polygon to have more than four sides . Then , the angles of this polygon being each greater than a right angle ... regular polygon the diagonal , cutting off three sides , is parallel to the middle one , and , further , that the dia ...
Side 115
... polygon , are all equal , being subtended by equal chords . Scholium . It may be remarked that in regular polygons the centre of the inscribed and circumscribed circles is called also the centre of the polygon , and that the ...
... polygon , are all equal , being subtended by equal chords . Scholium . It may be remarked that in regular polygons the centre of the inscribed and circumscribed circles is called also the centre of the polygon , and that the ...
Side 116
... regular poly- gons ( Prop . II . ) . The converse of this proposition is as follows : -If the sur face of a polygon be equivalent to the rectangle of its perime- ter and another line , this line will be half the radius of the in ...
... regular poly- gons ( Prop . II . ) . The converse of this proposition is as follows : -If the sur face of a polygon be equivalent to the rectangle of its perime- ter and another line , this line will be half the radius of the in ...
Side 118
... regular poly- gons of the same number of sides . The converse of this proposition is not true . It It may be enunciated thus : -If the perimeters of two polygons are to each other as the lines R , R ' , and their surfaces as R2 , R2 ...
... regular poly- gons of the same number of sides . The converse of this proposition is not true . It It may be enunciated thus : -If the perimeters of two polygons are to each other as the lines R , R ' , and their surfaces as R2 , R2 ...
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AB² adjacent angles altitude angle ABC angle ACB angle BAC angles equal antecedent base centre chord circ circle circum circumference circumscribed polygon coincide consequently Prop construction Converse of Prop corollary demonstration described diagonals diameter divided draw equal angles equal Prop equal to AC equimultiples equivalent Euclid exterior angle follows four right angles geometry given straight line gonal greater half hence homologous sides hypothenuse hypothesis included angle inscribed angle inscribed polygon intersect isosceles triangle join Legendre less line drawn magnitudes meet multiple number of sides obtuse opposite angles parallel perimeter perpendicular PROBLEM proportion PROPOSITION XII quadrilateral radii rectangle rectangle contained regular polygon respectively equal rhomboid right angled triangle Scholium side BC similar polygons similar triangles submultiple subtended surface tangent THEOREM three angles tiple triangle ABC vertex VIII