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 8
... vertex is the centre . The base of the pyramid is the spherical polygon intercepted by the same planes . 12. A zone is the portion of the surface of the sphere in- cluded between two parallel planes , which form its bases . One of those ...
... vertex is the centre . The base of the pyramid is the spherical polygon intercepted by the same planes . 12. A zone is the portion of the surface of the sphere in- cluded between two parallel planes , which form its bases . One of those ...
Página 15
... vertices as poles and included between their sides : hence it is easy to make an angle of this kind equal to a given ... vertices of the three angles of a spherical triangle , as poles , three arcs be described forming a second triangle ...
... vertices as poles and included between their sides : hence it is easy to make an angle of this kind equal to a given ... vertices of the three angles of a spherical triangle , as poles , three arcs be described forming a second triangle ...
Página 16
... vertices of the two angles of a given spherical tri- angle , as poles , the circumference of two circles be described which shall pass through the third angle of the triangle ; if then , through the other point in which those ...
... vertices of the two angles of a given spherical tri- angle , as poles , the circumference of two circles be described which shall pass through the third angle of the triangle ; if then , through the other point in which those ...
Página 18
... vertex A to the middle point D of the base , the two triangles ABD , ACD will have all the sides of the one respectively equal to the corresponding sides of the other , namely , AD common , BD = DC , and AB = AC : hence , by the last ...
... vertex A to the middle point D of the base , the two triangles ABD , ACD will have all the sides of the one respectively equal to the corresponding sides of the other , namely , AD common , BD = DC , and AB = AC : hence , by the last ...
Página 19
... vertex of an isos- celes spherical triangle to the middle of the base , is at right an- gles to the base , and bisects the vertical angle . PROPOSITION XVI . THEOREM . In any spherical triangle , the greater side is opposite the great ...
... vertex of an isos- celes spherical triangle to the middle of the base , is at right an- gles to the base , and bisects the vertical angle . PROPOSITION XVI . THEOREM . In any spherical triangle , the greater side is opposite the great ...
Otras ediciones - Ver todas
A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ... Nathan Scholfield Sin vista previa disponible - 2018 |
A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ... Nathan Scholfield Sin vista previa disponible - 2018 |
A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ... Nathan Scholfield Sin vista previa disponible - 2018 |
Términos y frases comunes
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
Pasajes populares
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.