Primary Elements of Plane and Solid Geometry: For Schools and Academies |
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Page 15
... angle DEB ( Ax . 5 ) . In the same manner it may be proved that the angle AED is equal to its opposite angle CEB . Therefore , if two straight lines , etc. THEOREM III . If a straight line intersect two parallels BOOK I. 15.
... angle DEB ( Ax . 5 ) . In the same manner it may be proved that the angle AED is equal to its opposite angle CEB . Therefore , if two straight lines , etc. THEOREM III . If a straight line intersect two parallels BOOK I. 15.
Page 16
For Schools and Academies Evan Wilhelm Evans. THEOREM III . If a straight line intersect two parallels , the corres- ponding inner and outer angles will be equal to each other ; also the alternate angles . Let the straight line EF intersect ...
For Schools and Academies Evan Wilhelm Evans. THEOREM III . If a straight line intersect two parallels , the corres- ponding inner and outer angles will be equal to each other ; also the alternate angles . Let the straight line EF intersect ...
Page 17
... intersect the two parallels AB , CD , in G and Then will BGH and H. GHD be together equal to two right angles . For ... intersecting each other be a right angle BOOK I. 17.
... intersect the two parallels AB , CD , in G and Then will BGH and H. GHD be together equal to two right angles . For ... intersecting each other be a right angle BOOK I. 17.
Page 18
For Schools and Academies Evan Wilhelm Evans. two straight lines intersecting each other be a right angle , each of the others will be a right angle . 3. Prove that the alternate outer angles EGA and FHD ( Figure to Theo . III ) are ...
For Schools and Academies Evan Wilhelm Evans. two straight lines intersecting each other be a right angle , each of the others will be a right angle . 3. Prove that the alternate outer angles EGA and FHD ( Figure to Theo . III ) are ...
Page 19
... intersects the parallels AC and BE , the angle CBE is equal to its alternate angle BCA ( Theo . III ) ; also , because AD intersects the same par- allels , the angle EBD is equal to its corresponding inner angle CAB . Therefore , the ...
... intersects the parallels AC and BE , the angle CBE is equal to its alternate angle BCA ( Theo . III ) ; also , because AD intersects the same par- allels , the angle EBD is equal to its corresponding inner angle CAB . Therefore , the ...
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...