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 14
... difference of their radii ; in which case , the centres and the point of contact lie in the same straight line . PROPOSITION VIII . THEOREM . The angle formed by two arcs of great circles , is equal to the angle formed by the tangents ...
... difference of their radii ; in which case , the centres and the point of contact lie in the same straight line . PROPOSITION VIII . THEOREM . The angle formed by two arcs of great circles , is equal to the angle formed by the tangents ...
Página 20
... difference observable , in this respect , between spheri- cal and rectilineal triangles . In the proposition now before us , as well as in Propositions XII , XIII , XIV , which treat of the comparison of triangles , it is expressly ...
... difference observable , in this respect , between spheri- cal and rectilineal triangles . In the proposition now before us , as well as in Propositions XII , XIII , XIV , which treat of the comparison of triangles , it is expressly ...
Página 22
... difference between a hemis- phere and the former triangle . PROPOSITION XIX . THEOREM . The surface of a lune is to the surface of the sphere , as the angle of this lune , is to four right angles , or as the arc which measures that ...
... difference between a hemis- phere and the former triangle . PROPOSITION XIX . THEOREM . The surface of a lune is to the surface of the sphere , as the angle of this lune , is to four right angles , or as the arc which measures that ...
Página 46
... difference . By formula ( a ) . sin . ( 0 + 6 ) For sin . cos . ß + sin . ß cos . § . substitute 180 ° -0 , the above will become sin . 180 ° - ( 4-6 ) } = sin . ( 180 ° -0 ) cos . B + sin . cos . ( 180 ° ) But sin . { 180 ° - ( 6 ...
... difference . By formula ( a ) . sin . ( 0 + 6 ) For sin . cos . ß + sin . ß cos . § . substitute 180 ° -0 , the above will become sin . 180 ° - ( 4-6 ) } = sin . ( 180 ° -0 ) cos . B + sin . cos . ( 180 ° ) But sin . { 180 ° - ( 6 ...
Página 47
... difference . By formula ( a :) sin . ( +8 ) = sin . cos . ẞ + sin . ß cos . 4 , For substitute 90 ° -4 , the above will become sin . { 90 ° — ( 8 — ẞ ) } = sin . ( 90 ° ) cos . B But , sin . { 90 ° ( 8 — ß ) } = cos . ( @ —ß ) , By ...
... difference . By formula ( a :) sin . ( +8 ) = sin . cos . ẞ + sin . ß cos . 4 , For substitute 90 ° -4 , the above will become sin . { 90 ° — ( 8 — ẞ ) } = sin . ( 90 ° ) cos . B But , sin . { 90 ° ( 8 — ß ) } = cos . ( @ —ß ) , By ...
Outras edições - Ver tudo
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.