Elements of Geometry and Conic SectionsHarper, 1849 - 226 páginas |
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Página 7
... Hyperbola 44 · 57 83 98 . 112 • 127 148 • € 166 177 188 205 N.B. When reference is made to a Proposition in the same Book , only the number of the Proposition is given ; but when the Proposition is found in a different Book , the number ...
... Hyperbola 44 · 57 83 98 . 112 • 127 148 • € 166 177 188 205 N.B. When reference is made to a Proposition in the same Book , only the number of the Proposition is given ; but when the Proposition is found in a different Book , the number ...
Página 177
... Hyperbola . PARABOLA . Definitions . B 1. A parabola is a plane curve , every point of which is equally distant from a fixed point , and a given straight line . 2. The fixed point is called the focus of the parabola , and the given ...
... Hyperbola . PARABOLA . Definitions . B 1. A parabola is a plane curve , every point of which is equally distant from a fixed point , and a given straight line . 2. The fixed point is called the focus of the parabola , and the given ...
Página 204
... the circle is represented by TAC ' ; hence the area of the ellipse is equal to TACX BC , which is a mean proportional between the two circles described on the axes . HYPERBOLA . Definitions . 1. AN hyperbola is a plane 204 CONIC SECTIONS .
... the circle is represented by TAC ' ; hence the area of the ellipse is equal to TACX BC , which is a mean proportional between the two circles described on the axes . HYPERBOLA . Definitions . 1. AN hyperbola is a plane 204 CONIC SECTIONS .
Página 205
... hyperbola , of which F and F are the foci . If the point D ' moves about F ' in such a manner that D'F - D'F ' is F always equal to DF - DF , the point D ' will describe a sec- ond hyperbola similar to the first . The two curves are ...
... hyperbola , of which F and F are the foci . If the point D ' moves about F ' in such a manner that D'F - D'F ' is F always equal to DF - DF , the point D ' will describe a sec- ond hyperbola similar to the first . The two curves are ...
Página 206
... hyperbola at D. From any point G of the curve draw GKG parallel to TT ' and cut- ting DD ' produced in K ; then FA is GK an ordinate to the di- ameter DD ' . It is proved , in Prop . XIX . , Cor . 1 , that GK is equal to D ' B E D F H T ...
... hyperbola at D. From any point G of the curve draw GKG parallel to TT ' and cut- ting DD ' produced in K ; then FA is GK an ordinate to the di- ameter DD ' . It is proved , in Prop . XIX . , Cor . 1 , that GK is equal to D ' B E D F H T ...
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ELEMENTS OF GEOMETRY & CONIC S Elias 1811-1889 Loomis,Making of America Project Sin vista previa disponible - 2016 |
Términos y frases comunes
75 cents ABCD AC is equal allel altitude angle ABC angle ACB angle BAC Anthon's base BCDEF bisected chord circle circumference cone contained 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 greater Hence Prop hyperbola inscribed intersection join latus rectum Let ABC lines AC major axis mean proportional measured by half meet Muslin 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 Sheep extra side AC similar slant height solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC vertex vertices
Pasajes populares
Página 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Página 27 - VIf two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the...
Página 11 - A rhombus, is that which has all its sides equal, but its angles are not right angles.
Página 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.
Página 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.
Página 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.
Página 15 - 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.
Página 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.
Página 148 - I.), that every section of a sphere made by a plane is a circle.