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First lessons in Plane Geometry. Together with an application of them to the ...
Francis Joseph Grund
Uten tilgangsbegrensning - 1830
ABCD adding adjacent angles angle opposite bases basis bear called centre chord circle circumference common consequently construct the triangle contain DEMON demonstration describe diameter difference distance divided division draw draw the lines drawn dropped equal equal angles expressed extended extremities figure follows foot formed four fourth term geometrical proportion give given greater half height hypothenuse inches included inscribed instance isosceles Join legs length less line AC line CD manner mean measure meets minutes multiply number of sides opposite parallel parallelogram perpendicular polygon ABCDEF principle PROBLEM proportion prove quadrilateral Query radii radius ratio rectangle regular polygon relation remaining sides Remark right angles Sect side AC similar smaller SOLUTION square square inches stands straight line surface tangent three sides triangle ABC truth vertex whole
Side 195 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Side 211 - HDG, the corresponding sides are proportional (page 70, 4thly) ; therefore we have the proportion ED : DG =AD : HD (II.) This last proportion has the first ratio common with the first proportion ; consequently the two remaining ratios are in a geometrical proportion (Theory of Prop., Prin. 3d) ; that is, we have AD : HD = DG: BD; and as, in...
Side 173 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Side 176 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Side 175 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.