Primary Elements of Plane and Solid Geometry: For Schools and Academies |
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Page 39
... inscribed in a circle when all its sides are chords of that circle . A CIRCLE is said to be inscribed in a polygon when all the sides of the polygon are tangents to the circle . When one figure is inscribed in another , the latter is ...
... inscribed in a circle when all its sides are chords of that circle . A CIRCLE is said to be inscribed in a polygon when all the sides of the polygon are tangents to the circle . When one figure is inscribed in another , the latter is ...
Page 43
... inscribed angle is measured by half the arc on which it stands . Let ACB be an angle in- scribed in a circle . It is meas- ured by half the arc AEB . First , suppose the center D to be within the angle . Draw the diameter CE ; also ...
... inscribed angle is measured by half the arc on which it stands . Let ACB be an angle in- scribed in a circle . It is meas- ured by half the arc AEB . First , suppose the center D to be within the angle . Draw the diameter CE ; also ...
Page 44
... inscribed angle , etc. Cor . 1. Angles inscribed in the same segment , as AEC and ADC , are equal ; for they are measured by half the same arc ABC . A E B Cor . 2. Any angle inscribed in a semicircle is a right angle ; being measured by ...
... inscribed angle , etc. Cor . 1. Angles inscribed in the same segment , as AEC and ADC , are equal ; for they are measured by half the same arc ABC . A E B Cor . 2. Any angle inscribed in a semicircle is a right angle ; being measured by ...
Page 45
... inscribed angle , it is measured by half the arc FE ( Theo . XXVI ) ; therefore , the remaining angle ABF is meas- ured by half the remaining arc BF . Again , because CBE is measured by half the semi- circumference BDE , and EBF by half ...
... inscribed angle , it is measured by half the arc FE ( Theo . XXVI ) ; therefore , the remaining angle ABF is meas- ured by half the remaining arc BF . Again , because CBE is measured by half the semi- circumference BDE , and EBF by half ...
Page 46
... sides of the regular poly- gon , will be tangents to that circle ( Theo . XXIII ) , and the circle will be inscribed in the polygon ( Def . 7 , Sec . VIII ) . THEOREM XXIX . The area of a circle is equal 46 GEOMETRY .
... sides of the regular poly- gon , will be tangents to that circle ( Theo . XXIII ) , and the circle will be inscribed in the polygon ( Def . 7 , Sec . VIII ) . THEOREM XXIX . The area of a circle is equal 46 GEOMETRY .
Other editions - View all
Primary Elements of Plane and Solid Geometry: For Schools and Academies E W (Evan Wilhelm) 1827-1874 Evans No preview available - 2021 |
Primary Elements of Plane and Solid Geometry: For Schools and Academies E. W. 1827-1874 Evans No preview available - 2016 |
Common terms and phrases
AB² ABCDEF allel alternate angles altitude angle BAC angles ABC apothegm base multiplied bisect called chord circle circumference cone consequently convex surface diagonals diameter divided draw Eclectic Reader equal Theo equal to half equivalent frustum Geometry given point half the arc half the product Hence hypotenuse included angle inscribed angle intersect isosceles triangle Let ABCD let fall McGuffey's measured by half mutually equiangular mutually equilateral number of equal number of sides opposite parallelogram perimeter perpendicular perpendicular distance prism proportion proved Published by W. B. quadrilateral radii radius Ray's rectangle regular inscribed regular polygon regular pyramid right angles right parallelopiped right-angled triangle Schol semicircle side BC slant hight solidity square straight line SUPT tangent THEOREM trapezoid triangles ABC triangles are equal triangular vertex W. B. SMITH
Popular passages
Page 69 - If from a point without a circle, a tangent and a secant be drawn, the tangent will be a mean proportional between the secant and its external segment.
Page 42 - The circumference of every circle is supposed to' be divided into 360 equal parts, called degrees ; each degree into 60 minutes, and each minute into 60 seconds. Degrees, minutes, and seconds are designated by the characters °, ', ". Thus 23° 14' 35" is read 23 degrees, 14 minutes, and 35 seconds.
Page 21 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Page 47 - It follows, then, that the area of a circle is equal to half the product of its circumference and its radius.
Page 72 - The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and R
Page 33 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Page 38 - The area of a regular polygon is equal to half the product of its apothem and perimeter.
Page 52 - PROBLEM VII. Two angles of a triangle being given, to find the third angle. The three angles of every triangle are together equal to two right angles (Prop.
Page 30 - The area of a rectangle is equal to the product of its base and altitude.
Page 69 - 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. either the sides adjacent to the equal...