Elements of Plane and Spherical Trigonometry: With Practical ApplicationsR. S. Davis, 1862 - 490 Seiten |
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Seite 55
... CHORD of an arc is the straight line joining its extremities ; E thus EF is the chord of the arc EGF . Ꭰ B C F G 158. The SEGMENT of a circle is the part of BOOK III THE CIRCLE, AND THE MEASURE OF ANGLES.
... CHORD of an arc is the straight line joining its extremities ; E thus EF is the chord of the arc EGF . Ꭰ B C F G 158. The SEGMENT of a circle is the part of BOOK III THE CIRCLE, AND THE MEASURE OF ANGLES.
Seite 56
... chord E F. 159. The SECTOR of a circle is the part of a circle included between an Ꭰ B C E F G arc , and the two ... chords ; as the angle ABC . 165. An INSCRIBED POLYGON is one which has the vertices 56 ELEMENTS OF GEOMETRY .
... chord E F. 159. The SECTOR of a circle is the part of a circle included between an Ꭰ B C E F G arc , and the two ... chords ; as the angle ABC . 165. An INSCRIBED POLYGON is one which has the vertices 56 ELEMENTS OF GEOMETRY .
Seite 58
... chords ; and , conversely , equal chords subtend equal arcs . Let A DB and EGF be two equal circles , and let the arc AD be equal to EG ; then will the chord AD be equal to the chord E G. For , since the diameters AB , EF are equal 58 ...
... chords ; and , conversely , equal chords subtend equal arcs . Let A DB and EGF be two equal circles , and let the arc AD be equal to EG ; then will the chord AD be equal to the chord E G. For , since the diameters AB , EF are equal 58 ...
Seite 59
... chord AD is equal to the chord EG ( Art . 34 , Ax . 11 ) . Conversely , if the chord A D is equal to the chord E G , the arcs A D , E G will be equal . For , if the radii CD , OG are drawn , the triangles ACD , EOG , having the three ...
... chord AD is equal to the chord EG ( Art . 34 , Ax . 11 ) . Conversely , if the chord A D is equal to the chord E G , the arcs A D , E G will be equal . For , if the radii CD , OG are drawn , the triangles ACD , EOG , having the three ...
Seite 60
... chord which subtends the greater arc is the greater . A B D Conversely , if the chord AB be greater than the chord AD , the arc A B will be greater than the arc AD . For the triangles ACB , ACD have two sides , AC , CB , in the one ...
... chord which subtends the greater arc is the greater . A B D Conversely , if the chord AB be greater than the chord AD , the arc A B will be greater than the arc AD . For the triangles ACB , ACD have two sides , AC , CB , in the one ...
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Häufige Begriffe und Wortgruppen
A B C ABCD adjacent angles altitude angle ACB angle equal base bisect centre 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 interior angles 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 Required the area 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
Beliebte Passagen
Seite 28 - 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.
Seite 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.
Seite 79 - Two rectangles having equal altitudes are to each other as their bases.
Seite 251 - The convex surface of the cylinder is equal to the circumference of its base multiplied by its altitude (Prop.
Seite 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.
Seite 35 - If any side of a triangle be produced, the exterior angle is equal to the sum of the two interior and opposite angles.
Seite 168 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.
Seite 303 - Equal triangles upon the same base, and upon the same side of it, are between the same parallels.
Seite 4 - 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. 9) M=a*, then, raising both sides to the wth power, we have Mm = (a")m = a"" . Therefore, log (M m) = xm = (log M) X »»12.
Seite 102 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing.