Constructive Geometry of Plane Curves: With Numerous ExamplesMacmillan and Company, 1885 - 374 sider |
Inni boken
Resultat 1-5 av 26
Side 11
... follows of course that in any triangle if lines be drawn from the vertices ABC meeting the opposite sides in F , E , D and all passing through the same point O , AD . BF . CE = DB . FC . EA , i.e. that the continued products of the ...
... follows of course that in any triangle if lines be drawn from the vertices ABC meeting the opposite sides in F , E , D and all passing through the same point O , AD . BF . CE = DB . FC . EA , i.e. that the continued products of the ...
Side 16
... follows conversely that EA , EO , EB , EF form a harmonic pencil , as also FE , FC , FO and FA . If EO meet AB in e and CD in e ,, AeBF and Ce ̧DF are therefore harmonic ranges , and if FO meet AC in ƒf and BD in f ,, AfCE and Bf , DE ...
... follows conversely that EA , EO , EB , EF form a harmonic pencil , as also FE , FC , FO and FA . If EO meet AB in e and CD in e ,, AeBF and Ce ̧DF are therefore harmonic ranges , and if FO meet AC in ƒf and BD in f ,, AfCE and Bf , DE ...
Side 18
... follows of course that if APaQ be an harmonic range and X the centre point of PQ , XA . Xα = XP2 = XQ2 . The following relations between two pairs of conjugate points Aa and Bb , and their centre X and foci P and Q are sometimes useful ...
... follows of course that if APaQ be an harmonic range and X the centre point of PQ , XA . Xα = XP2 = XQ2 . The following relations between two pairs of conjugate points Aa and Bb , and their centre X and foci P and Q are sometimes useful ...
Side 30
... follows : - DEFINITION . If two points bé taken on a curve and a chord drawn through them ; then , if the first point remains fixed while the second , moving along the curve , approaches indefinitely near to the first , the chord in its ...
... follows : - DEFINITION . If two points bé taken on a curve and a chord drawn through them ; then , if the first point remains fixed while the second , moving along the curve , approaches indefinitely near to the first , the chord in its ...
Side 56
... follow- ing : -a point , a pair of straight lines , a circle , a parabola , an ellipse or an hyperbola . The construction of these last three curves from their definition as the sections of a cone seems à priori to be the natural way of ...
... follow- ing : -a point , a pair of straight lines , a circle , a parabola , an ellipse or an hyperbola . The construction of these last three curves from their definition as the sections of a cone seems à priori to be the natural way of ...
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Constructive Geometry of Plane Curves: With Numerous Examples Thomas Henry Eagles Uten tilgangsbegrensning - 1885 |
Constructive Geometry of Plane Curves: With Numerous Examples Thomas Henry Eagles Uten tilgangsbegrensning - 1885 |
Vanlige uttrykk og setninger
AC² anharmonic ratio asymptotes auxiliary circle bisects the angle CA² CB² centre point chord of contact circle centre circles touching cone conic conic section conjugate diameters conjugate points constant construction corresponding curvature curve being given cutting cutting CB describe a circle describe an ellipse describe an hyperbola determined directrix draw a parabola drawn equal F draw foci focus F given circle given Fig given lines given point given tangent harmonic harmonic mean homographic involution latus rectum length line joining locus major axis mean proportional opposite sides ordinate parallel pass pencil perpendicular point of contact polar pole PROBLEM Prop radical axis radius right angle second focus segments shew shewn similar triangles Similarly tangent PT three points transverse vertex vertices
Populære avsnitt
Side 28 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Side 28 - 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.
Side 303 - AB describe a segment of a circle containing an angle equal to the given angle, (in.
Side 32 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Side 99 - A conic section is the locus of a point which moves so that its distance from a fixed point, called the focus, is in a constant ratio to its distance from a fixed straight line, called the directrix.
Side 13 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Side 40 - Upon a given straight line to describe a segment of a circle which shall contain a given angle. Let AB be the given straight line.