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 - Conic sections |
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Page 9
... Geom . ) they are D B equally distant from the perpendicular CO ; therefore all the lines OM , MO , OB , are equal . Consequently , the section AMB is a circle , whose centre is O. Cor . 1. If the section passes through the centre of ...
... Geom . ) they are D B equally distant from the perpendicular CO ; therefore all the lines OM , MO , OB , are equal . Consequently , the section AMB is a circle , whose centre is O. Cor . 1. If the section passes through the centre of ...
Page 10
... Geom . ) : hence any side of the triangle ABC is less than the sum of the other two . PROPOSITION III . THEOREM . The shortest distance from one point to another , on the surface of a sphere , is the arc of the great circle which joins ...
... Geom . ) : hence any side of the triangle ABC is less than the sum of the other two . PROPOSITION III . THEOREM . The shortest distance from one point to another , on the surface of a sphere , is the arc of the great circle which joins ...
Page 11
... is less than this same circumference . Scholium . This proposition is fundamentally the same as Prop . XXII . B. I. El . S. Geom . ; for O being the centre of the sphere , a solid angle may be conceived as formed SPHERICAL GEOMETRY . 11.
... is less than this same circumference . Scholium . This proposition is fundamentally the same as Prop . XXII . B. I. El . S. Geom . ; for O being the centre of the sphere , a solid angle may be conceived as formed SPHERICAL GEOMETRY . 11.
Page 12
... Geom .; both , however , suppose that the polygon ABCDE is convex , or that no side produced will cut the figure . PROPOSITION VI . THEOREM . The poles of a great circle of the sphere , are the extremities of that diameter of the sphere ...
... Geom .; both , however , suppose that the polygon ABCDE is convex , or that no side produced will cut the figure . PROPOSITION VI . THEOREM . The poles of a great circle of the sphere , are the extremities of that diameter of the sphere ...
Page 13
... Geom . ) the line DC being perpendicular to the plane AMC , every plane DMC passing through the line DC , is perpendicu- lar to the plane AMC ; hence the angle of these planes , or ( Def . 6. ) the angle AMD , is a right angle . Cor . 2 ...
... Geom . ) the line DC being perpendicular to the plane AMC , every plane DMC passing through the line DC , is perpendicu- lar to the plane AMC ; hence the angle of these planes , or ( Def . 6. ) the angle AMD , is a right angle . Cor . 2 ...
Other editions - View all
A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ... Nathan Scholfield No preview available - 2018 |
A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ... Nathan Scholfield No preview available - 2018 |
A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ... Nathan Scholfield No preview available - 2018 |
Common terms and phrases
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
Popular passages
Page 44 - Prove that parallelograms on the same base and between the same parallels are equal in area.
Page 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.
Page 81 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 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...
Page 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.
Page 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.
Page 27 - The circumference of every circle is supposed to be divided into 360 equal parts...
Page 36 - The solidity of a cylinder is equal to the area of its base multiplied by its altitude.
Page 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.