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
... Diameter of a 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 ,. 130 130 131 131 132 138 Area of the Surface of a Prism , Area of CONTENTS . vii.
... Diameter of a 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 ,. 130 130 131 131 132 138 Area of the Surface of a Prism , Area of CONTENTS . vii.
Seite 61
... DIAMETER is a straight line drawn through the centre and terminating in the circumference . All radii of the same circle are equal . All diameters are also equal , and each is double the radius . 4. An ARC is any part of a circumference ...
... DIAMETER is a straight line drawn through the centre and terminating in the circumference . All radii of the same circle are equal . All diameters are also equal , and each is double the radius . 4. An ARC is any part of a circumference ...
Seite 62
... when its circumference touches each of the sides of the polygon . © о POSTULATE . A circumference can be described from any point as a centre , and with any radius . PROPOSITION I. THEOREM . Any diameter divides the circle , 62 GEOMETRY .
... when its circumference touches each of the sides of the polygon . © о POSTULATE . A circumference can be described from any point as a centre , and with any radius . PROPOSITION I. THEOREM . Any diameter divides the circle , 62 GEOMETRY .
Seite 63
... diameter divides the circle , and also its circumference , into two equal parts . Let AEBF be a circle , and AB any diameter : then will it divide the circle . and its circumference into two equal parts . For , let AFB be applied to AEB ...
... diameter divides the circle , and also its circumference , into two equal parts . Let AEBF be a circle , and AB any diameter : then will it divide the circle . and its circumference into two equal parts . For , let AFB be applied to AEB ...
Seite 64
... diameters AB D M A N B E and EF . If the semicircle ADB be applied to the semi- circle EGF , it will coincide with it , and the semi - circum- ference ADB will coincide with the semi - circumference EGF . But the part AMD is equal to ...
... diameters AB D M A N B E and EF . If the semicircle ADB be applied to the semi- circle EGF , it will coincide with it , and the semi - circum- ference ADB will coincide with the semi - circumference EGF . But the part AMD is equal to ...
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Häufige Begriffe und Wortgruppen
AB² AC² altitude angle is equal apothem Applying logarithms axis base and altitude base multiplied bisects centre chord circumference cone consequently convex surface corresponding cosec cosine cotangent cylinder denote diagonals diameter distance divided draw drawn edges equal altitudes equal in volume equilateral feet find the area formula frustum given line given point greater hence homologous hypothenuse included angle inscribed circle inscribed polygon intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROBLEM.-To PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium segment similar sine slant height sphere spherical angle spherical polygon spherical triangle square straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence
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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.