Elements of Geometry: With Practical Applications to Mensuration |
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Page 55
... RADIUS of a circle is any straight line drawn from the center to the circumference ; as the line CA , CD , or CB . 155. A DIAMETER of a circle is any straight line drawn through the center , and terminating in both directions in the ...
... RADIUS of a circle is any straight line drawn from the center to the circumference ; as the line CA , CD , or CB . 155. A DIAMETER of a circle is any straight line drawn through the center , and terminating in both directions in the ...
Page 59
... radius AC on its equal EO , since the angles AC D , E O G are equal , the radius CD will fall on OG , and the point D on G. Therefore the arcs AD and EG coincide with each other ; hence they must be equal ( Art . 34 , Ax . 14 ) ...
... radius AC on its equal EO , since the angles AC D , E O G are equal , the radius CD will fall on OG , and the point D on G. Therefore the arcs AD and EG coincide with each other ; hence they must be equal ( Art . 34 , Ax . 14 ) ...
Page 61
... radius which is perpendicular to a chord bi- sects the chord , and also the arc subtended by the chord . Let the radius C E be perpendicu- lar to the chord AB ; then will CE bisect the chord at D , and the arc AB at E. D A B E Draw the ...
... radius which is perpendicular to a chord bi- sects the chord , and also the arc subtended by the chord . Let the radius C E be perpendicu- lar to the chord AB ; then will CE bisect the chord at D , and the arc AB at E. D A B E Draw the ...
Page 62
... radius CE , which is perpendicular to the chord AB , bisects the arc A B subtended by the chord . 178. Cor . 1. Any straight line which joins the centre of the circle and the middle of the chord , or the middle of the arc , must be ...
... radius CE , which is perpendicular to the chord AB , bisects the arc A B subtended by the chord . 178. Cor . 1. Any straight line which joins the centre of the circle and the middle of the chord , or the middle of the arc , must be ...
Page 64
... radius at its termination in the circumference , is a tangent to the circle . Let the straight line BD be per- pendicular to the radius CA at its B- termination A ; then will it be a tangent to the circle . Draw from the centre C to BD ...
... radius at its termination in the circumference , is a tangent to the circle . Let the straight line BD be per- pendicular to the radius CA at its B- termination A ; then will it be a tangent to the circle . Draw from the centre C to BD ...
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Common terms and phrases
A B C ABCD adjacent angles altitude angle ACB angle equal arc A B base bisect chord circle circumference circumscribed cone convex surface cosec Cosine Cotang cylinder diagonal diameter distance divided drawn equal Prop equilateral triangle equivalent exterior angle feet formed frustum gles greater half the sum hence homologous hypothenuse inches included angle inscribed isosceles less Let ABC line A B logarithmic sine measured by half multiplied number of sides parallel parallelogram parallelopipedon pendicular perimeter perpendicular polyedron prism PROBLEM PROPOSITION pyramid quadrantal radii radius ratio rectangle regular polygon right angles right-angled triangle rods Scholium secant segment side A B similar slant height solve the triangle sphere spherical polygon spherical triangle Tang tangent THEOREM triangle ABC triangle equal trigonometric functions vertex
Popular passages
Page 59 - 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 37 - 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.
Page 120 - At a point in a given straight line to make an angle equal to a given angle.
Page 52 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Page 19 - In an isosceles triangle, the angles opposite the equal sides are equal.
Page 199 - Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes ; that is to say, as the products of their three dimensions.
Page 121 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Page 103 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Page 2 - The logarithm of any POWER of a number is equal to the product of the logarithm of the number by the exponent of the power. For let m be any number, and take the equation (Art.
Page 2 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.