Elements of Geometry and Conic SectionsHarper, 1858 - 234 Seiten |
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Seite 7
... Hyperbola 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 of the Book is also specified ...
... Hyperbola 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 of the Book is also specified ...
Seite 177
... Hyperbola . PARABOLA . Definitions . 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 straight ...
... Hyperbola . PARABOLA . Definitions . 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 straight ...
Seite 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 .
Seite 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 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 F always equal to DF - DF , the point D ' will describe a sec- ond hyperbola similar to the first . The two curves are ...
Seite 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 F T ' FB ...
... 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 F T ' FB ...
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Häufige Begriffe und Wortgruppen
ABCD AC is equal allel altitude angle ABC angle ACB angle BAC base BCDEF bisected chord circle circumference cone convex surface curve described diagonals diameter draw ellipse equal angles equal to AC equally distant equiangular equilateral equivalent exterior angle foci four right angles frustum given angle given point greater hyperbola hypothenuse inscribed intersect join latus rectum Let ABC lines AC Loomis major axis mean proportional measured by half meet number of sides ordinate parabola parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN prism Professor of Mathematics PROPOSITION pyramid radii radius ratio rectangle regular polygon right angles Prop Scholium segment side AC similar similar triangles slant height solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC vertex vertices
Beliebte Passagen
Seite 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Seite 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, their third sides will be equal, and their other angles will be equal, each to each.
Seite 101 - When you have proved that the three angles of every triangle are equal to two right angles...
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 37 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Seite 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.
Seite 44 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.