Elements of Geometry and Conic Sections |
From inside the book
Results 1-5 of 11
Page 166
... cone is the cir- cle described by that side containing the right angle , which revolves . 4. The axis of a cone is the fixed straight line about which the triangle revolves . The hypothenuse of the triangle describes the convex surface ...
... cone is the cir- cle described by that side containing the right angle , which revolves . 4. The axis of a cone is the fixed straight line about which the triangle revolves . The hypothenuse of the triangle describes the convex surface ...
Page 168
... cone is equal to the product of halj its side , by the circumference of its base . Let A - BCDEFG be a cone whose base is the circle BDEG , and its side AB ; then will its convex surface be equal to the product of half its side by the ...
... cone is equal to the product of halj its side , by the circumference of its base . Let A - BCDEFG be a cone whose base is the circle BDEG , and its side AB ; then will its convex surface be equal to the product of half its side by the ...
Page 169
... cone by 2πR × 4S , or πRS . PROPOSITION IV . THEOREM . The convex surface of a frustum of a cone is equal to the product of its side , by half the sum of the circumferences of its two bases . Let BDF - bdf be a frustum of a cone whose ...
... cone by 2πR × 4S , or πRS . PROPOSITION IV . THEOREM . The convex surface of a frustum of a cone is equal to the product of its side , by half the sum of the circumferences of its two bases . Let BDF - bdf be a frustum of a cone whose ...
Page 170
Elias Loomis. PROPOSITION V. THEOREM . The solidity of a cone is equal to one third of the product of its base and altitude . Let A - BCDF be a cone whose base is the circle BCDEFG , and AH its altitude ; the solidity of the cone will be ...
Elias Loomis. PROPOSITION V. THEOREM . The solidity of a cone is equal to one third of the product of its base and altitude . Let A - BCDF be a cone whose base is the circle BCDEFG , and AH its altitude ; the solidity of the cone will be ...
Page 171
... cone . Hence the frustum of a cone is equivalent to the sum of three cones , having the same altitude with the frustum , and whose bases are the lower base of the frustum , its upper base , and a mean proportional between them . hard ...
... cone . Hence the frustum of a cone is equivalent to the sum of three cones , having the same altitude with the frustum , and whose bases are the lower base of the frustum , its upper base , and a mean proportional between them . hard ...
Common terms and phrases
ABCD AC is equal allel altitude angle ABC angle ACB angle BAC base BCDEF bisected chord circle circumference cone convex surface curve described diameter dicular draw drawn ellipse equal angles equal to AC equally distant equiangular equivalent exterior angle foci four right angles frustum given angle greater Hence Prop hyperbola inscribed intersection join latus rectum less Let ABC lines AC major axis mean proportional measured by half meet number of sides ordinate parabola parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN principal vertex prism PROPOSITION pyramid radii radius ratio rectangle regular polygon right angles Prop Scholium segment side BC similar similar triangles solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC triangle DEF vertex vertices VIII
Popular passages
Page 17 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal.
Page 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Page 63 - IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the' rectangle contained by the parts.
Page 18 - BC common to the two triangles, which is adjacent to their equal angles ; therefore their other sides shall be equal, each to each, and the third angle of the one to the third angle of the other, (26.
Page 101 - When you have proved that the three angles of every triangle are equal to two right angles...
Page 10 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Page 37 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Page 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 15 - Wherefore, when a straight line, &c. QED PROP. XIV. THEOR. If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Page 30 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.