A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration, Containing Many Valuable Discoveries and Impovements in Mathematical Science ...: Designed as a Text Book for Collegiate and Academic Instruction, and as a Practical Compendium on MensurationCollins brothers & Company, 1845 |
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Página 6
... Expressions for Surfaces and Solids , 180 CONIC SECTIONS . The Parabola and its Properties , The Ellipse and its Properties , The Hyperbola and its Properties , 189 197 215 SPHERICAL , GEOMETRY . SPHERICAL GEOMETRY . DEFINITIONS . 1. vi ...
... Expressions for Surfaces and Solids , 180 CONIC SECTIONS . The Parabola and its Properties , The Ellipse and its Properties , The Hyperbola and its Properties , 189 197 215 SPHERICAL , GEOMETRY . SPHERICAL GEOMETRY . DEFINITIONS . 1. vi ...
Página 23
... expression , A represents such a part of unity , as the angle of the lune is of one right angle . Scholium . The spherical ungula , bounded by the planes AMB , ANB , is to the whole solid sphere , as the angle A is to four right angles ...
... expression , A represents such a part of unity , as the angle of the lune is of one right angle . Scholium . The spherical ungula , bounded by the planes AMB , ANB , is to the whole solid sphere , as the angle A is to four right angles ...
Página 27
... expression 30 ° 20 ′ 12 " 22 " " ' , repre- sents an arc or an angle of 30 degrees 20 minutes 12 seconds 22 thirds . The circumference of any circle may in this manner be ap- plied as the measure of angles , without regard to its magni ...
... expression 30 ° 20 ′ 12 " 22 " " ' , repre- sents an arc or an angle of 30 degrees 20 minutes 12 seconds 22 thirds . The circumference of any circle may in this manner be ap- plied as the measure of angles , without regard to its magni ...
Página 46
... expression , from its great importance , is called the fundamental formula of Plane Trigonometry , and nearly the whole science may be derived from it . Given the sines and cosines of two angles , to find the sine of their difference ...
... expression , from its great importance , is called the fundamental formula of Plane Trigonometry , and nearly the whole science may be derived from it . Given the sines and cosines of two angles , to find the sine of their difference ...
Página 47
... expression , it becomes cos . ( 4-6 ) = cos . cos . ß + sin . 4 sin . B ( d ) That is , the cosine of the difference of two arcs or angles , is equal to the cosine of the first multiplied by the cosine of the second , plus sine of the ...
... expression , it becomes cos . ( 4-6 ) = cos . cos . ß + sin . 4 sin . B ( d ) That is , the cosine of the difference of two arcs or angles , is equal to the cosine of the first multiplied by the cosine of the second , plus sine of the ...
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A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ... Nathan Scholfield Pré-visualização indisponível - 2018 |
A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ... Nathan Scholfield Pré-visualização indisponível - 2018 |
A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ... Nathan Scholfield Pré-visualização indisponível - 2018 |
Palavras e frases frequentes
abscissa altitude arithmetical progression axes base bisected chord circle circular circular segment circumference cone conjugate axis construction convex surface corresponding cosec cosine cylinder described diameter distance divided draw drawn ellipse equal to half equation expression feet find the solidity formed formula Geom geometrical given height hence hyperbola inches infinite series latus rectum length logarithm major axis middle frustum minor axis multiplied ordinate parabola paraboloid parallel parallelogram perpendicular plane portion prism PROBLEM Prop PROPOSITION pyramid quadrant quantity radii radius ratio rectangle revoloidal surface right angles Scholium sector segment sides similar similar triangles sine specific gravity sphere spherical triangle spheroid spindle square straight line tangent THEOREM tion transverse axis Trigonometry ungula versed sine vertex vertical virtual centre zone
Passagens conhecidas
Página 44 - Prove that parallelograms on the same base and between the same parallels are equal in area.
Página 197 - ... is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another : 16. And this point is called the centre of the circle.
Página 81 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 219 - To find the solidity of a hyperbolic conoid, or otherwise called a hyperboloid. RULE. To the square of the radius of the base, add the square of the diameter...
Página 68 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.
Página 14 - ... this point of intersection, as a pole, and limited by the sides, produced if necessary. Let the angle BAC be formed by the two arcs AB, AC ; then it will be equal to the angle FAG formed by the tangents AF, AG, and be measured by the arc DE, described about A as a pole.
Página 27 - The circumference of every circle is supposed to be divided into 360 equal parts...
Página 36 - The solidity of a cylinder is equal to the area of its base multiplied by its altitude.
Página 7 - The radius of a sphere is a straight line, drawn from the centre to any point of the surface ; the diameter, or axis, is a line passing through this centre, and terminated on both sides by the surface.