Elements of Geometry and Mensuration: With Easy Exercises, Designed for Schools and Adult Classes |
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Page 75
... Regular Polygon is a polygon which has all its angles equal and all its sides equal . Thus a regular Pentagon , Hexagon , and Octagon will respectively present the following appearance as to form : 3 [ It does not yet appear that a ...
... Regular Polygon is a polygon which has all its angles equal and all its sides equal . Thus a regular Pentagon , Hexagon , and Octagon will respectively present the following appearance as to form : 3 [ It does not yet appear that a ...
Page 77
... regular polygon , each angle of a regular pentagon = hexagon = octagon = 6 of a right angle ; 413 3/2 ; and so on . = T D COR . 2. If ABCDEF be a portion of the perimeter of any polygon ; and if the sides AB , BC , CD , & c . , be ...
... regular polygon , each angle of a regular pentagon = hexagon = octagon = 6 of a right angle ; 413 3/2 ; and so on . = T D COR . 2. If ABCDEF be a portion of the perimeter of any polygon ; and if the sides AB , BC , CD , & c . , be ...
Page 78
... regular polygon depends only on the number , and not the length , of the sides , therefore all regular polygons of the same name have precisely the same angles , how- ever much they may differ in their other dimensions . Hence all ...
... regular polygon depends only on the number , and not the length , of the sides , therefore all regular polygons of the same name have precisely the same angles , how- ever much they may differ in their other dimensions . Hence all ...
Page 79
... regular polygon may be in- scribed in a given circle , or described about a given circle . 88. PROP . III . In every regular polygon of an even number of sides to each side there is another opposite side parallel to it ; and to each ...
... regular polygon may be in- scribed in a given circle , or described about a given circle . 88. PROP . III . In every regular polygon of an even number of sides to each side there is another opposite side parallel to it ; and to each ...
Page 82
... regular polygons of the same number of sides are proportional to the radii of their inscribed or circumscribing circles ; and their areas are proportional to the squares of those radii . ( 1 ) Let AB , ab be sides of two regular ...
... regular polygons of the same number of sides are proportional to the radii of their inscribed or circumscribing circles ; and their areas are proportional to the squares of those radii . ( 1 ) Let AB , ab be sides of two regular ...
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Common terms and phrases
ABCDEF angular points base bisect centre chain chord circular circumference circumscribed circumscribing circle compasses cone construction cubic curved cylinder describe a circle diagonal diameter distance divided draw a straight drawn edge equal angles equal arcs equilateral triangle feet find the area foot frustum given angle given circle given line given point given ratio given straight line given triangle greater height Hence hexagon inches inscribed instrument intersecting length Let ABCD magnitude measure meet number of sides opposite angle parallelogram parallelopiped perimeter perpendicular plane surface points of division prism PROB produced PROP proportional Protractor radii radius rectangle rectangle contained regular polygon right angles ruler scale segment semi-circle shew shewn similar triangles square of AB square of AC subtends suppose tangent trapezium triangle ABC unit vernier vertex whole yards
Popular passages
Page 32 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Page 19 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Page 16 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle, shall be greater than the base of the other.
Page 43 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Page 27 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Page 17 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 22 - Theorem. The greater side of every triangle is opposite to the greater angle. Let ABC be a triangle of which the side AC is greater than the side AB ; the angle ABC is also greater than the angle BCA. Because AC is greater than AB, make...
Page 223 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.
Page 128 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Page 20 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it.