Elements of Geometry |
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Page 123
... prism . 369. The equal and parallel polygons ABCDE , FGHIK , are called the bases of the prism . The other planes taken together , constitute the lateral or convex surface of the prism . The equal straight lines AF , BG , CH , & c ...
... prism . 369. The equal and parallel polygons ABCDE , FGHIK , are called the bases of the prism . The other planes taken together , constitute the lateral or convex surface of the prism . The equal straight lines AF , BG , CH , & c ...
Page 124
... prism . In every other case the prism is oblique , and the altitude is less than the side . 372. A prism is triangular , quadrangular , pentagonal , hexago- nal , & c . , according as the base is a triangle , a quadrilateral , a ...
... prism . In every other case the prism is oblique , and the altitude is less than the side . 372. A prism is triangular , quadrangular , pentagonal , hexago- nal , & c . , according as the base is a triangle , a quadrilateral , a ...
Page 128
... prisms are equal , when three planes containing a solid angle of the one are equal to three planes containing a solid ... prism abci . For , let the base ABCDE be placed upon the base a b c d e , the two bases will coincide . But the ...
... prisms are equal , when three planes containing a solid angle of the one are equal to three planes containing a solid ... prism abci . For , let the base ABCDE be placed upon the base a b c d e , the two bases will coincide . But the ...
Page 129
... prisms , which have equal bases and equal altitudes , are equal . For , since the side AB = ab , and the altitude BG = b g , the rectangle ABGF = abgf ; the same may be proved with respect to the rectangles BGHC , bghc ; thus the three ...
... prisms , which have equal bases and equal altitudes , are equal . For , since the side AB = ab , and the altitude BG = b g , the rectangle ABGF = abgf ; the same may be proved with respect to the rectangles BGHC , bghc ; thus the three ...
Page 130
... ABD - HEF is a prism . The same may be proved with respect to the solid GHF - BCD . We say now that these two prisms are symmetrical with each other . Upon the base ABD make the prism ABD - E'F'H 130 Elements of Geometry .
... ABD - HEF is a prism . The same may be proved with respect to the solid GHF - BCD . We say now that these two prisms are symmetrical with each other . Upon the base ABD make the prism ABD - E'F'H 130 Elements of Geometry .
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAD angles equal base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle intersection isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence
Popular passages
Page 65 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 21 - 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 ii - Co. of the said district, have deposited in this office the title of a book, the right whereof they claim as proprietors, in the words following, to wit : " Tadeuskund, the Last King of the Lenape. An Historical Tale." In conformity to the Act of the Congress of the United States...
Page 63 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 22 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page ii - States entitled an act for the encouragement of learning hy securing the copies of maps, charts and books to the author., and proprietors of such copies during the times therein mentioned, and also to an act entitled an act supplementary to an act, entitled an act for the encouragement of learning by securing the copies of maps, charts and books to the authors and proprietors of such copies during the times therein mentioned and extending the benefits thereof to the arts of designing, engraving and...
Page 80 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 164 - If two triangles have two sides and the inchtded angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects.
Page 24 - In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs.
Page 153 - XVII.) ; hence two similar pyramids are to each other as the cubes of their homologous sides.