## Exercises on mensuration |

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8th square adjacent angle equal base beginning called circle circumference cone contain Curved line bending cylinder denote described diagonal diameter direction distance divided draw Draw a Horizontal drawn equal parts taken Exercises feet feet 6 inches fifth figure Find find the area five foot four fourth given greater half height is equal hexagon horizontal line Horizontal Straight line inches inclination inscribed Join lateral surface length less lower measure meet nine ninth parallel perimeter point of division Q-Have Q-How many lesser Q-What proportion Q-Which is greatest Questions radii radius rect rectangle equal rectangle whose height rectangles taken right angle round seven seventh Shew side sixth Slanting line Slate sphere squa square divided square inches third total surface triangle Twice upper extremity upright line Upright Straight line volume whole square yards

### Popular passages

Page 134 - ... by equal regular polygons of either three, four, or six sides. 262. A plane surface may be entirely covered by a combination of squares and regular octagons having the same side, or by dodecagons and equilateral triangles having the same side.

Page 136 - From this it readily follows that all the three lines drawn from the angles of a triangle to the middle of the opposite sides, pass through one and the same point.

Page 137 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.

Page 108 - ... respectively, on a side and the volume of a prism of the same altitude whose base is a section of the frustum parallel to its bases and equidistant from them.

Page 68 - Find the area of a sector of a circle whose radius is 21 feet, the length of the arc being 15 feet.

Page 132 - Prove that the area of the regular hexagon inscribed in a circle is twice the area of the inscribed equilateral triangle. Verify this fact by cutting a regular hexagon out of paper, and folding it. Ex. 1195. The side of an equilateral triangle circumscribed about a circle is twice the side of an inscribed equilateral triangle.

Page 134 - A = the side of the similar circumscribed polygon, then, 2aR 2AR -a-) V(4R 3 +A 3 ) 272. If o = the side of a regular polygon inscribed in a circle whose radius is R,, and a...

Page 9 - Large School-room Maps of England, Scotland, Ireland, Europe, Palestine, Asia, Africa, and North and South America, unvarnished, each, 12s.

Page 114 - Find the radius of a sphere which has the same volume as a cone whose height = h, and radius of base 6.

Page 63 - Show that the areas of similar triangles are to each other as the squares of the homologous sides.