Elements of Plane and Spherical Trigonometry: With Practical ApplicationsR. S. Davis, 1862 - 490 páginas |
Dentro del libro
Resultados 1-5 de 78
Página 49
... C :: B : D. : For , since the magnitudes are in proportion , A C B = D and multiplying each member of this equation by B C ' have AX B BX C - СХВ DX C ' we which , reduced to the lowest terms , gives whence 5 BOOK II . 49.
... C :: B : D. : For , since the magnitudes are in proportion , A C B = D and multiplying each member of this equation by B C ' have AX B BX C - СХВ DX C ' we which , reduced to the lowest terms , gives whence 5 BOOK II . 49.
Página 51
... Multiplying each side of this equation by any number , m , we have therefore mxAX Bmx BX A ; ( m × A ) × B = ( m × B ) × A. Hence , by Prop . II . , mx A : m X B :: A : B. PROPOSITION X. - THEOREM . 144. Magnitudes which are ...
... Multiplying each side of this equation by any number , m , we have therefore mxAX Bmx BX A ; ( m × A ) × B = ( m × B ) × A. Hence , by Prop . II . , mx A : m X B :: A : B. PROPOSITION X. - THEOREM . 144. Magnitudes which are ...
Página 53
... Multiplying together the corresponding members of these equations , we have AX DX EX HBX CXFX G. Hence , by Prop . II . , AXE : BX F :: CX G : DX H. PROPOSITION XIV . - THEOREM . 150. If three magnitudes are proportionals , the first ...
... Multiplying together the corresponding members of these equations , we have AX DX EX HBX CXFX G. Hence , by Prop . II . , AXE : BX F :: CX G : DX H. PROPOSITION XIV . - THEOREM . 150. If three magnitudes are proportionals , the first ...
Página 81
... multiplied by their altitudes . H D C G F B A Let ABCD , AEGF be two rectangles ; then will ABCD be to AEGF as A B multiplied by AD is to AE multiplied by AF . E Having placed the two rectangles so that the angles at A are verti- cal ...
... multiplied by their altitudes . H D C G F B A Let ABCD , AEGF be two rectangles ; then will ABCD be to AEGF as A B multiplied by AD is to AE multiplied by AF . E Having placed the two rectangles so that the angles at A are verti- cal ...
Página 106
... multiplying together the corresponding terms of these proportions , and omitting the common term ABE , we have ( Prop . XIII . Bk . II . ) , ABC : ADE :: ABX AC : ADX AE . 273. Cor . If the rectangles of the sides containing the equal ...
... multiplying together the corresponding terms of these proportions , and omitting the common term ABE , we have ( Prop . XIII . Bk . II . ) , ABC : ADE :: ABX AC : ADX AE . 273. Cor . If the rectangles of the sides containing the equal ...
Otras ediciones - Ver todas
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.