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 & Company, 1872 - 455 Seiten |
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Seite vii
... Diameter of a Circle , To find the length of an Arc , 116 117 .... Area of a Circle , .... 117 Area of a Sector , ..... Area of a Segment , ..... Area of a Circular Ring , ... 118 118 119 ... ... Area of the Surface of a Prism , Area ...
... Diameter of a Circle , To find the length of an Arc , 116 117 .... Area of a Circle , .... 117 Area of a Sector , ..... Area of a Segment , ..... Area of a Circular Ring , ... 118 118 119 ... ... Area of the Surface of a Prism , Area ...
Seite 59
... 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 60
... its circumference touches all of the sides of the polygon . POSTULATE . ооо A circumference can be described from any point as a centre and with any radius . PROPOSITION I. THEOREM . Any diameter divides the circle , 60 GEOMETRY .
... its circumference touches all of the sides of the polygon . POSTULATE . ооо A circumference can be described from any point as a centre and with any radius . PROPOSITION I. THEOREM . Any diameter divides the circle , 60 GEOMETRY .
Seite 61
... 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 . A F B For , let AFB be applied to ...
... 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 . A F B For , let AFB be applied to ...
Seite 62
... diameters AB and EF ADB be applied to the semi - circle EGF , it will coincide with it , and the semi - circumference ADB will coincide with the semi - circumference EGF But the part AMD is equal to the part ENG , by hypothesis : hence ...
... diameters AB and EF ADB be applied to the semi - circle EGF , it will coincide with it , and the semi - circumference ADB will coincide with the semi - circumference EGF But the part AMD is equal to the part ENG , by hypothesis : hence ...
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Häufige Begriffe und Wortgruppen
AB² ABCD AC² adjacent angles altitude apothem Applying logarithms centre chord circle circumference circumscribed complement cone consequently convex surface cosec cosine Cotang cylinder decimal denote diameter difference distance divided draw drawn edges equal to AC Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection isosceles less Let ABC log sin lower base lune mantissa number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polar triangle pole polyedral angle polyedron prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right-angled triangle Scholium segment semi-circumference side BC similar sine six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triedral angle upper base vertex vertices volume whence
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Seite 101 - The area of a parallelogram is equal to the product of its base and altitude.
Seite 92 - PROBLEM XV. To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect the angles A and B, by the lines AO and BO, meeting in the point 0 (Prob.
Seite 48 - 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 45 - In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference.
Seite 106 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Seite 33 - THEOREM. If two angles of a triangle are equal, the sides opposite to them are also equal, and consequently, the triangle is isosceles.
Seite 18 - A SCALENE TRIANGLE is one which has no two of its sides equal ; as the triangle GH I.
Seite 30 - If two triangles have two sides of the one equal to two sides of the other, each to each, and the included angles unequal, the third sides will be unequal; and the greater side will belong to the triangle which has the greater included angle.
Seite 8 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Seite 156 - DE, are like parts of the circumferences to which they belong, and similar sectors, as A CH and 'D OE, are like parts of the circles to which they belong : hence, similar arcs are to each other as their radii, and similar sectors are to each other as the squares of their radii.