Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United StatesA.S. Barnes, 1885 - 512 Seiten |
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Seite vii
... Circle , .... To find the Length of an Arc ,. Area of a Circle , .... Area of a Sector , Area of a Segment ,. Area of a Circular Ring , 129 130 130 131 131 132 138 Area of the Surface of a Prism , Area of CONTENTS . vii.
... Circle , .... To find the Length of an Arc ,. Area of a Circle , .... Area of a Sector , Area of a Segment ,. Area of a Circular Ring , 129 130 130 131 131 132 138 Area of the Surface of a Prism , Area of CONTENTS . vii.
Seite viii
... Prism , Area of the Surface of a Pyramid , Area of the Frustum of a Cone , .. Area of the Surface of a Sphere ,. Area of a Zone , Area of a Spherical Polygon ,. Volume of a Prism , Volume of a Pyramid , .. Volume of the Frustum of a ...
... Prism , Area of the Surface of a Pyramid , Area of the Frustum of a Cone , .. Area of the Surface of a Sphere ,. Area of a Zone , Area of a Spherical Polygon ,. Volume of a Prism , Volume of a Pyramid , .. Volume of the Frustum of a ...
Seite 189
... prism ; the lines in which the lateral faces meet , are called lateral edges , and the lines in which the lateral faces meet either base are called basal edges of the prism . 3. The ALTITUDE of a prism is the perpendicular dis- tance ...
... prism ; the lines in which the lateral faces meet , are called lateral edges , and the lines in which the lateral faces meet either base are called basal edges of the prism . 3. The ALTITUDE of a prism is the perpendicular dis- tance ...
Seite 190
... PRISM is one whose lateral edges are oblique to the planes of the bases . In this case , any lateral edge is greater than the altitude . 6. Prisms are named from the number of sides of their bases ; a triangular prism is one whose bases ...
... PRISM is one whose lateral edges are oblique to the planes of the bases . In this case , any lateral edge is greater than the altitude . 6. Prisms are named from the number of sides of their bases ; a triangular prism is one whose bases ...
Seite 192
... prism is equal to the perim- eter of either base multiplied by the altitude . Let ABCDE - K be a right prism : then is its convex sur- face equal to , ( AB + BC + CD + DE + EA ) × AF . For , the convex surface is equal to the sum of all ...
... prism is equal to the perim- eter of either base multiplied by the altitude . Let ABCDE - K be a right prism : then is its convex sur- face equal to , ( AB + BC + CD + DE + EA ) × AF . For , the convex surface is equal to the sum of all ...
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Häufige Begriffe und Wortgruppen
ABCD AC² adjacent angles altitude apothem Applying logarithms bisects centre chord circle circumference circumscribed cone consequently convex surface cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle inscribed intersection isosceles less Let ABC log sin lower base lune mantissa number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron principle demonstrated prism PROBLEM.-In PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment semi-circumference similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square straight line subtracting supplement Tang tangent THEOREM THEOREM.-Show tri-rectangular triangle ABC triangular prism triedral angle upper base vertex vertices volume whence
Beliebte Passagen
Seite 28 - If two triangles have two sides of the one equal to two sides of the...
Seite 90 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Seite 18 - Things which are equal to the same thing, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.
Seite 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Seite 253 - For, the point A being the pole of the arc EF, the distance AE is a 'quadrant ; the point C being the pole of the arc DE, the distance CE is likewise a quadrant : hence the point E is...
Seite 61 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Seite 94 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Seite 126 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Seite 46 - 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.
Seite 125 - THEOREM. Similar triangles are to each other as the squares of their homologous sides.