## 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 Mensuration, Parts 3-4Collins brothers & Company, 1845 - Conic sections |

### 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 asymptotes axes base bisected chord circle circular circular segment circumference circumscribing prism cone Conic Sections conical construction convex surface corresponding cosec cosine cylinder described distance divided draw drawn ellipse equal to half equation equidistant formed formula frustum Geom geometrical given height hence hyperbola inches latus rectum length logarithm major axis minor axis multiplied by one-third ordinates parabola paraboloid parallel parallelogram perpendicular plane portion principal vertex Prop proportional PROPOSITION pyramid quadrant quantity radii radius ratio rectangle represent revoloidal curve revoloidal surface right angles right revoloid Scholium sector segment sides similar similar triangles sine solidity space sphere spherical spheroid spindle square straight line tangent THEOREM tion trian triangle ungula versed sine vertex virtual centre

### 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.