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 |
From inside the book
Results 1-5 of 29
Page 8
... zone or of a segment is the distance between the two parallel planes , which form the bases of the zone or segment . 15. Whilst the semicircle DAE ( Def . 1. ) revolving round its diameter DE , describes the sphere , any circular sector ...
... zone or of a segment is the distance between the two parallel planes , which form the bases of the zone or segment . 15. Whilst the semicircle DAE ( Def . 1. ) revolving round its diameter DE , describes the sphere , any circular sector ...
Page 185
... zone is required , it may be ex- pressed by the product of the altitude of the zone multiplied by the circumference of the sphere ; let h = the altitude , and we have 2 rh for the spherical surface of the zone , ( 2. ) The solidity of ...
... zone is required , it may be ex- pressed by the product of the altitude of the zone multiplied by the circumference of the sphere ; let h = the altitude , and we have 2 rh for the spherical surface of the zone , ( 2. ) The solidity of ...
Page 186
... zone of the sphere , its surface , formula ( 2 , Art . 9 , ) will be 2r ' « × h = 2rhx , ( 2 ) The surface of the corresponding zone of the polyedroid , will be 2r'Xh = 2r'h , ( P. XVIII . Cor . B. III . El . S. G. ) - ( 3. ) And hence ...
... zone of the sphere , its surface , formula ( 2 , Art . 9 , ) will be 2r ' « × h = 2rhx , ( 2 ) The surface of the corresponding zone of the polyedroid , will be 2r'Xh = 2r'h , ( P. XVIII . Cor . B. III . El . S. G. ) - ( 3. ) And hence ...
Page 188
... zones are the convex surfaces , the altitude of each segment being 327 miles , and the radius of the base 1575,28 miles ? Ans ... zone is the convex surface , the radii of the bases be- ing 3628,86 miles , and the altitude 3150,6 ? Ans ...
... zones are the convex surfaces , the altitude of each segment being 327 miles , and the radius of the base 1575,28 miles ? Ans ... zone is the convex surface , the radii of the bases be- ing 3628,86 miles , and the altitude 3150,6 ? Ans ...
Page 6
... Zones , To find the Circumference of a Circle , or any Arc , • 182 . 182 186 Mensuration of the Ellipse , Mensuration of the Parabola , Mensuration of the Hyperbola , To find the Area of any Plane Surface by Equi - distant Ordinates ...
... Zones , To find the Circumference of a Circle , or any Arc , • 182 . 182 186 Mensuration of the Ellipse , Mensuration of the Parabola , Mensuration of the Hyperbola , To find the Area of any Plane Surface by Equi - distant Ordinates ...
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.