Elements of Geometry and Conic SectionsHarper, 1858 - 234 sider |
Inni boken
Resultat 6-10 av 25
Side 188
Elias Loomis. 1 + ELLIPSE . Definitions . 1. AN ellipse is a plane curve , in which the sum of the dis- tances of each point from two fixed points , is equal to a given line . 2. The two fixed points are called the foci . Thus , if F , F ...
Elias Loomis. 1 + ELLIPSE . Definitions . 1. AN ellipse is a plane curve , in which the sum of the dis- tances of each point from two fixed points , is equal to a given line . 2. The two fixed points are called the foci . Thus , if F , F ...
Side 189
... ellipse at D. From any point G of the curve draw GKG / parallel to TT / and cutting DD ' in K ; then is GK an ordinate to the diameter DD ' . Ε D Τ T F Ꮐ E It is proved in Prop . XIX . , Cor . 1 , that GK is ... ellipse . Let ELLIPSE . 189.
... ellipse at D. From any point G of the curve draw GKG / parallel to TT / and cutting DD ' in K ; then is GK an ordinate to the diameter DD ' . Ε D Τ T F Ꮐ E It is proved in Prop . XIX . , Cor . 1 , that GK is ... ellipse . Let ELLIPSE . 189.
Side 190
... ellipse to the foci , is equal to the major axis . Let ADA ' be an ellipse , of which F , F are the foci , AA ' is the major axis , and D any point of the curve ; then will DF + DF be A equal to AA ' . For , by Def . 1 , the sum of the ...
... ellipse to the foci , is equal to the major axis . Let ADA ' be an ellipse , of which F , F are the foci , AA ' is the major axis , and D any point of the curve ; then will DF + DF be A equal to AA ' . For , by Def . 1 , the sum of the ...
Side 191
... ellipse ; join DF , DF ' , and FF ' . Complete the parallelogram DFD'F ' , and join DD ' . C D F Now , because the opposite sides of a parallelogram are equal , the sum of DF and DF is equal to the sum of D'F ... ellipse makes ELLIPSE . 191.
... ellipse ; join DF , DF ' , and FF ' . Complete the parallelogram DFD'F ' , and join DD ' . C D F Now , because the opposite sides of a parallelogram are equal , the sum of DF and DF is equal to the sum of D'F ... ellipse makes ELLIPSE . 191.
Side 192
... ellipse , and D any point of the curve ; if through the point D the line TT be drawn , making the angle TDF equal to T'DF ' , then will TT ' be a tangent to the ellipse at D. For if TT be not a tangent , it must meet the curve in some ...
... ellipse , and D any point of the curve ; if through the point D the line TT be drawn , making the angle TDF equal to T'DF ' , then will TT ' be a tangent to the ellipse at D. For if TT be not a tangent , it must meet the curve in some ...
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Vanlige uttrykk og setninger
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
Populære avsnitt
Side 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Side 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.
Side 101 - When you have proved that the three angles of every triangle are equal to two right angles...
Side 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.
Side 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.
Side 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.
Side 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.
Side 37 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Side 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.
Side 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.