Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in an Appendix, the Theory of ProjectionBaldwin and Cradock, 1830 - 272 Seiten |
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Seite 26
... hyperbola , con- choïd , and cissoïd , ) any given angle may be trisected , or divided into three equal parts ; but such constructions , not being effected by the two species of lines which are the subject of these Ele- ments , are for ...
... hyperbola , con- choïd , and cissoïd , ) any given angle may be trisected , or divided into three equal parts ; but such constructions , not being effected by the two species of lines which are the subject of these Ele- ments , are for ...
Seite 214
... usually appropriated to the other plane sections , viz . the ellipse ( def . 10 , ) , the parabola ( def . 11. ) , and the hyperbola ( def . 12. ) . Let the plane a be cut the axis of the 214 [ Appendix . GEOMETRY . t.
... usually appropriated to the other plane sections , viz . the ellipse ( def . 10 , ) , the parabola ( def . 11. ) , and the hyperbola ( def . 12. ) . Let the plane a be cut the axis of the 214 [ Appendix . GEOMETRY . t.
Seite 215
... hyper- bola . because a part of each is intercepted be- tween the vertical plane and the plane of the conic section ; and because there are two slant sides in each surface which lie in the vertical plane , and therefore cannot be ...
... hyper- bola . because a part of each is intercepted be- tween the vertical plane and the plane of the conic section ; and because there are two slant sides in each surface which lie in the vertical plane , and therefore cannot be ...
Seite 216
... hyperbola ( 1. ) : for the plane which passes through V pa- rallel to the circular section , falls entirely without the cone , so that no point of the conic section is found in that plane . Cor . 3. And so , the projection of every ...
... hyperbola ( 1. ) : for the plane which passes through V pa- rallel to the circular section , falls entirely without the cone , so that no point of the conic section is found in that plane . Cor . 3. And so , the projection of every ...
Seite 217
... hyper- bola , and the straight line A A ' , which is intercepted between them , is called the principal diameter or transverse axis of the ellipse or hyperbola . In the parabola , the axis cuts the curve in one point , A , only ; and ...
... hyper- bola , and the straight line A A ' , which is intercepted between them , is called the principal diameter or transverse axis of the ellipse or hyperbola . In the parabola , the axis cuts the curve in one point , A , only ; and ...
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Häufige Begriffe und Wortgruppen
A B C a² b² ABCD altitude asymptote axes axis base bisected centre chord circle circumference circumscribed co-ordinates common section conic section contained convex surface curve cylinder describe diameter difference dihedral angle distance divided draw drawn ellipse equal angles equation frustum given line given point given straight line gles greater hence hyperbola hypotenuse inscribed intersection join Latus Rectum less likewise locus magnitudes meet parabola parallel parallelogram parallelopiped pass pendicular perimeter perpendicular perspective projection pole prism produced projection PROP pyramid radii radius ratio rectangle rectangular rectilineal figure regular polygon right angles Scholium segment similar solid angles solid content sphere spherical angle spherical arc spherical triangle square tangent tion touch triangle ABC vertex vertical y₁
Beliebte Passagen
Seite 196 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Seite 64 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Seite 20 - In every triangle, the square of the side subtending any of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle. Let ABC be any triangle, and the angle at B one of its acute angles ; and upon BC, one of the sides containing it, let fall the perpendicular...
Seite 10 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Seite 189 - ... shall be greater than the base of the other. Let ABC, DEF be two triangles, which have the two sides AB, AC, equal to the two DE, DF, each to each, viz.
Seite 1 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Seite 84 - The angle at the centre of a circle is double of the angle at the circumference, upon the same base, that is, upon the same part of the circumference.
Seite 78 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Seite 79 - EQUAL straight lines in a circle are equally distant from the centre ; and those which are equally distant from the centre, are equal to one another.
Seite 264 - IF two straight lines cut one another, the vertical, or opposite, angles shall be equal.