Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry and Mensuration : Accompanied with All the Necessary Logarithmic and Trigonometric TablesD. Appleton, 1860 - 443 σελίδες |
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Σελίδα vii
... sine and cosine of the sum and difference of two arcs Numerical values of sines , tangents , etc ..... CHAPTER II . Explanation of Table I. of logarithms ..... Arithmetical calculations by logarithms .. Arithmetical complement ...
... sine and cosine of the sum and difference of two arcs Numerical values of sines , tangents , etc ..... CHAPTER II . Explanation of Table I. of logarithms ..... Arithmetical calculations by logarithms .. Arithmetical complement ...
Σελίδα 4
... sine A = ; sine C = b h h B The tangent of either of the acute angles is the quotient ob- tained by dividing the side opposite the angle by the adjacent side . Thus , P b tangent A = ; tangent C = b Ρ . The secant of either of the acute ...
... sine A = ; sine C = b h h B The tangent of either of the acute angles is the quotient ob- tained by dividing the side opposite the angle by the adjacent side . Thus , P b tangent A = ; tangent C = b Ρ . The secant of either of the acute ...
Σελίδα 5
... sine of that angle . Thus , C , D , is the sine of the angle CAC1 . For we have ( § 8 ) defined the sine of this angle to be the quo- tient obtained by dividing CD1 by AC1 , which quotient be- comes C , D ,, since the divisor is the ...
... sine of that angle . Thus , C , D , is the sine of the angle CAC1 . For we have ( § 8 ) defined the sine of this angle to be the quo- tient obtained by dividing CD1 by AC1 , which quotient be- comes C , D ,, since the divisor is the ...
Σελίδα 7
... counted in the positive direction ( §9 ) is the arc , CD the sine , CH the cosine , BE the tangent , GF the cotangent , AE the secant , and AF the cosecant . The algebraic sines of these lines will be as follows §11 . ] 7 TRIGONOMETRY .
... counted in the positive direction ( §9 ) is the arc , CD the sine , CH the cosine , BE the tangent , GF the cotangent , AE the secant , and AF the cosecant . The algebraic sines of these lines will be as follows §11 . ] 7 TRIGONOMETRY .
Σελίδα 8
... Sine and cosecant , + + Cosine and secant , + Tangent and cotangent , + + 1 + 1 § 12. By carefully inspecting the diagrams of § 11 , we see that denoting any arc when considered as positive by a , it will , when counted in an opposite ...
... Sine and cosecant , + + Cosine and secant , + Tangent and cotangent , + + 1 + 1 § 12. By carefully inspecting the diagrams of § 11 , we see that denoting any arc when considered as positive by a , it will , when counted in an opposite ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
a+b+c ABCD altitude angles equal apothem base bisecting centre chord circle circumference circumscribed circle cone consequently corresponding cosec Cosine Cotang cubic cylinder decimal denote diameter dicular distance divided draw drawn equally distant equation exterior angles feet figure frustum given angle given line gives greater half hence hypotenuse inches included angle inscribed circle intersection logarithm measure middle point multiplied number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedral angle polyedron prism PROBLEM proportion pyramid quadrant quadrilateral radii radius ratio rectangle regular polygon respectively equal right angles right-angled triangle Scholium secant similar similar triangles Sine slant height solid sphere spherical triangle square straight line subtract suppose surface Tang Tangent THEOREM three sides triangle ABC volume
Δημοφιλή αποσπάσματα
Σελίδα 113 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Σελίδα 31 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.
Σελίδα 112 - ALSO THE AREA OF THE TRIANGLE FORMED BY THE CHORD OF THE SEGMENT AND THE RADII OF THE SECTOR. THEN...
Σελίδα 33 - 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.
Σελίδα 80 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Σελίδα 139 - 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.
Σελίδα 15 - The sum of all the angles of a polygon is equal to twice as many right angles as the polygon has sides, less two.
Σελίδα 174 - The radius of a sphere is a straight line, drawn from the centre to any point of the...
Σελίδα 107 - ... similar figures are to each other as the squares of their homologous sides.
Σελίδα 180 - Every section of a sphere, made by a plane, is a circle.