New Elementary Geometry: With Practical Applications ; a Shorter Course Upon the Basis of the Larger Work |
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Page 8
... Solid , or Volume , is that which has length , breadth , and thickness . ANGLES AND LINES . 10. An Angle is the difference in the direction of two lines , which meet at a point ; as the angle A. The point of meeting , A , is the ver ...
... Solid , or Volume , is that which has length , breadth , and thickness . ANGLES AND LINES . 10. An Angle is the difference in the direction of two lines , which meet at a point ; as the angle A. The point of meeting , A , is the ver ...
Page 111
... solid , or volume , bounded by planes . The bounding planes are called the faces of the polyedron ; and the lines of intersection of the faces are called the edges of the polyedron . 258. A Prism is a polyedron having two of its faces ...
... solid , or volume , bounded by planes . The bounding planes are called the faces of the polyedron ; and the lines of intersection of the faces are called the edges of the polyedron . 258. A Prism is a polyedron having two of its faces ...
Page 122
... solid AG into 15 small paral- I lelopipedons , all equal to each other , hav- ing equal bases and equal altitudes ... Solid AG : Solid A L :: AE : A I. For , if this proportion is not correct , suppose we have Solid A G : Solid A L ...
... solid AG into 15 small paral- I lelopipedons , all equal to each other , hav- ing equal bases and equal altitudes ... Solid AG : Solid A L :: AE : A I. For , if this proportion is not correct , suppose we have Solid A G : Solid A L ...
Page 123
... Solid AG : Solid A Q :: A B : AO , Solid A Q : Solid A K : : AD : AM . Multiplying together the corresponding terms of these pro- portions , and omitting , in the result , the common factor Solid A Q , we shall have , Solid AG ...
... Solid AG : Solid A Q :: A B : AO , Solid A Q : Solid A K : : AD : AM . Multiplying together the corresponding terms of these pro- portions , and omitting , in the result , the common factor Solid A Q , we shall have , Solid AG ...
Page 124
... Solid AG : Solid A K :: ABCD : AM NO . But the two parallelopipedons AK , AZ , having the same base , AMNO , are to each other as their altitudes , A Е , A X ( Theo . XII . ) ; hence we have Solid AK : Solid A Z : : A E : A Х ...
... Solid AG : Solid A K :: ABCD : AM NO . But the two parallelopipedons AK , AZ , having the same base , AMNO , are to each other as their altitudes , A Е , A X ( Theo . XII . ) ; hence we have Solid AK : Solid A Z : : A E : A Х ...
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Common terms and phrases
A B C A B equal ABCD ABCDEF adjacent angles allel alternate angles altitude angle ACD angle BAC antecedent base multiplied bases ABC bisect chord circumference cone consequently convex surface cylinder diagonal diameter divided draw the straight equal and parallel equal angles equal bases equal Theo equiangular equivalent feet formed four right angles frustum given straight line greater Greenleaf's half the sum homologous sides hypothenuse included angle inscribed angle inscribed circle interior angles intersection Let ABC line CD magnitudes mean proportional measured by half meet number of sides opposite parallelogram parallelopipedon perimeter perpendicular polyedron prism quadrilateral radii radius ratio rectangle regular polygon rhombus right angles Theo Scholium secant line side A B side BC slant hight Solid sphere square described tangent THEOREM third triangles ABC triangular triangular prism vertex volume
Popular passages
Page 23 - 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 29 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 83 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing these angles proportional, are similar.
Page 85 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Page 61 - At a point in a given straight line to make an angle equal to a given angle.
Page 57 - The angle formed by a tangent and a chord is measured by half the intercepted arc.
Page 62 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Page 117 - If two angles not in the same plane have their sides parallel and lying in the same direction, these angles will be equal, and their planes will be parallel. Let...
Page 100 - The circumferences of circles are to each other as their radii, and their areas are to each other as the squares of their radii. Let C denote the circumference of one of ^ the circles, R its radius OA, A its area; and let C...
Page 88 - Similar polygons may be divided into the same number of triangles similar each to each, and similarly situated.