Elements of Plane and Spherical Trigonometry: With Practical ApplicationsR. S. Davis, 1862 - 490 páginas |
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Página 55
... DIAMETER of a circle is any straight line drawn through the centre , and terminating in both directions in the circumference ; as the line A B. All the radii of a circle are equal ; all the diameters are also equal , and each is double ...
... DIAMETER of a circle is any straight line drawn through the centre , and terminating in both directions in the circumference ; as the line A B. All the radii of a circle are equal ; all the diameters are also equal , and each is double ...
Página 57
... diameter divides the circle and its circum- ference each into two equal parts . Let AEBF be a circle , and A B a diameter ; then the two parts AEB , AFB are equal . For , if the figure A E B be applied to AFB , their common base A B re ...
... diameter divides the circle and its circum- ference each into two equal parts . Let AEBF be a circle , and A B a diameter ; then the two parts AEB , AFB are equal . For , if the figure A E B be applied to AFB , their common base A B re ...
Página 58
... diameter , is a semi - circumference , and the included seg- ment is a semicircle . PROPOSITION II . THEOREM . - 172 ... diameters AB , EF are equal 58 ELEMENTS OF GEOMETRY .
... diameter , is a semi - circumference , and the included seg- ment is a semicircle . PROPOSITION II . THEOREM . - 172 ... diameters AB , EF are equal 58 ELEMENTS OF GEOMETRY .
Página 59
With Practical Applications Benjamin Greenleaf. For , since the diameters AB , EF are equal , the semicircle ADB may be A applied to the D BE C G F semicircle EGF ; and the curve line ADB will coincide with the curve line EGF ( Prop . I ...
With Practical Applications Benjamin Greenleaf. For , since the diameters AB , EF are equal , the semicircle ADB may be A applied to the D BE C G F semicircle EGF ; and the curve line ADB will coincide with the curve line EGF ( Prop . I ...
Página 66
... them is a semi - circumference . 188. Cor . Two parallel tangents meet the circumfer- ence at the extremities of the same diameter . PROPOSITION XIII . - THEOREM . 189. If two circumferences 66 ELEMENTS OF GEOMETRY .
... them is a semi - circumference . 188. Cor . Two parallel tangents meet the circumfer- ence at the extremities of the same diameter . PROPOSITION XIII . - THEOREM . 189. If two circumferences 66 ELEMENTS OF GEOMETRY .
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 79 - Two rectangles having equal altitudes are to each other as their bases.
Página 251 - The convex surface of the cylinder is equal to the circumference of its base multiplied by its altitude (Prop.
Página 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.
Página 35 - If any side of a triangle be produced, the exterior angle is equal to the sum of the two interior and opposite angles.
Página 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.
Página 303 - Equal triangles upon the same base, and upon the same side of it, are between the same parallels.
Página 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.
Página 102 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing.