Elements of Geometry and Trigonometry: From the Works of A.M. LegendreA.S. Barnes, 1874 - 455 Seiten |
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Seite 59
... 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 . 5. A CHORD is a straight line joining the extremities of an arc . Any chord belongs to two ...
... 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 . 5. A CHORD is a straight line joining the extremities of an arc . Any chord belongs to two ...
Seite 63
... radii CD and OG . The triangles ACD and EOG have all the sides of the one equal to the cor- responding sides of the other ; they are , therefore , equal in all their parts : hence , the angle ACD is equal to EOG . If , now , the sector ...
... radii CD and OG . The triangles ACD and EOG have all the sides of the one equal to the cor- responding sides of the other ; they are , therefore , equal in all their parts : hence , the angle ACD is equal to EOG . If , now , the sector ...
Seite 64
... radii CA and CB . Then , the right - angled triangles CDA and CDB will have the hypothenuse CA equal to CB , and the side CD common ; the triangles are , therefore , parts hence , AD is equal to DB . Α equal in all their Again , because ...
... radii CA and CB . Then , the right - angled triangles CDA and CDB will have the hypothenuse CA equal to CB , and the side CD common ; the triangles are , therefore , parts hence , AD is equal to DB . Α equal in all their Again , because ...
Seite 71
... radii . Let the circumferences , whose centres are C and D , intersect at A : then will CD be less than the sum , and greater than the difference of the radii of the two circles . For , draw AC and AD , forming the triangle ACD . Then ...
... radii . Let the circumferences , whose centres are C and D , intersect at A : then will CD be less than the sum , and greater than the difference of the radii of the two circles . For , draw AC and AD , forming the triangle ACD . Then ...
Seite 72
... radii , one will be tangent to the other internally . Let C and D be the centres of two circles , and let the distance between these centres be equal to the difference of the radii : then will the one be tangent to the other in ...
... radii , one will be tangent to the other internally . Let C and D be the centres of two circles , and let the distance between these centres be equal to the difference of the radii : then will the one be tangent to the other in ...
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Häufige Begriffe und Wortgruppen
AB² ABCD AC² adjacent angles altitude apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine slant height sphere spherical polygon spherical triangle square subtracted Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence
Beliebte Passagen
Seite 126 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Seite 59 - 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 18 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.
Seite 104 - 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 6 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Seite 28 - If two triangles have two sides of the one equal to two sides of the...
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 99 - The area of a parallelogram is equal to the product of its base and altitude.
Seite 172 - If two planes are perpendicular to 'each other, a straight line drawn in one of them, perpendicular to their intersection, will be perpendicular to the other.
Seite 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.