Elements of Geometry and Conic SectionsHarper, 1858 - 234 σελίδες |
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Σελίδα 178
... ordinate to the diame- ter BD . It is proved in Prop . IX . , that EG is equal to GH ; hence the entire line EH is called a double ordinate . B / G D F H 7. An abscissa is the part of a diameter intercepted be- tween its vertex and an ...
... ordinate to the diame- ter BD . It is proved in Prop . IX . , that EG is equal to GH ; hence the entire line EH is called a double ordinate . B / G D F H 7. An abscissa is the part of a diameter intercepted be- tween its vertex and an ...
Σελίδα 180
... ordinate to any diameter is parallel to the tangent at its vertex , an ordinate to the axis is perpen dicular to the axis . PROPOSITION III . THEOREM . The latus rectum is equal to four times the distance from the focus to the vertex ...
... ordinate to any diameter is parallel to the tangent at its vertex , an ordinate to the axis is perpen dicular to the axis . PROPOSITION III . THEOREM . The latus rectum is equal to four times the distance from the focus to the vertex ...
Σελίδα 181
... ordinate to the axis ; then wil BC be the subtangent , and it will be bisected at the vertex V. B For BF is equal to AF ( Prop . IV . ) ; and AF is equal to CE , which is the distance of the point A from the directrix . But CE is equal ...
... ordinate to the axis ; then wil BC be the subtangent , and it will be bisected at the vertex V. B For BF is equal to AF ( Prop . IV . ) ; and AF is equal to CE , which is the distance of the point A from the directrix . But CE is equal ...
Σελίδα 182
... ordinate AC to the axis . Make BV equal to VC ; join the points B , A , and the line BA will be the tangent required . PROPOSITION VI . THEOREM . The subnormal is equal to half the latus rectum . Let AB be a tangent to the parab- ola AV ...
... ordinate AC to the axis . Make BV equal to VC ; join the points B , A , and the line BA will be the tangent required . PROPOSITION VI . THEOREM . The subnormal is equal to half the latus rectum . Let AB be a tangent to the parab- ola AV ...
Σελίδα 183
... ordinate to the axis , is equal to the product of the latus rectum by the corresponding abscissa . Let AVC be a parabola , and A any point of the curve . From A draw the ordinate AB ; then is the square of AB equal to the product of VB ...
... ordinate to the axis , is equal to the product of the latus rectum by the corresponding abscissa . Let AVC be a parabola , and A any point of the curve . From A draw the ordinate AB ; then is the square of AB equal to the product of VB ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 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.
Σελίδα 101 - When you have proved that the three angles of every triangle are equal to two right angles...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 37 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Σελίδα 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.
Σελίδα 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.