Constructive geometry of plane curves |
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Side ix
... harmonic mean between two given lines . 13 12 . To find the third term of an harmonic progression , the first two terms being given 14 Harmonic range and harmonic pencil ib . Harmonic properties of a complete quadrilateral 16 13 . Two ...
... harmonic mean between two given lines . 13 12 . To find the third term of an harmonic progression , the first two terms being given 14 Harmonic range and harmonic pencil ib . Harmonic properties of a complete quadrilateral 16 13 . Two ...
Side xiv
... Harmonic Properties . 88. To determine the centre of curvature at any point of a given 139 · 140 · 141 ellipse CHAPTER V. THE HYPERBOLA . 145 89 . To describe an hyperbola , the foci and a vertex , the vertices and a focus , or the axes ...
... Harmonic Properties . 88. To determine the centre of curvature at any point of a given 139 · 140 · 141 ellipse CHAPTER V. THE HYPERBOLA . 145 89 . To describe an hyperbola , the foci and a vertex , the vertices and a focus , or the axes ...
Side xviii
... Involute of circle 292 294 · 296 ib . • 297 299 CHAPTER XII . MISCELLANEOUS CURVES . 153. Harmonic Curve or Curve of Sines 305 ib . Tangent and normal . PROBLEM 154. Ovals of Cassini Tangent and normal . 155. xviii CONTENTS .
... Involute of circle 292 294 · 296 ib . • 297 299 CHAPTER XII . MISCELLANEOUS CURVES . 153. Harmonic Curve or Curve of Sines 305 ib . Tangent and normal . PROBLEM 154. Ovals of Cassini Tangent and normal . 155. xviii CONTENTS .
Side 12
... nearly equal magnitude should be selected , since the intersections of lines cutting at very acute angles cannot be accurately determined . DEFINITION . Three magnitudes are said to be in harmonic 12 EXTRACTION OF SQUARE ROOT .
... nearly equal magnitude should be selected , since the intersections of lines cutting at very acute angles cannot be accurately determined . DEFINITION . Three magnitudes are said to be in harmonic 12 EXTRACTION OF SQUARE ROOT .
Side 13
... harmonic progression and the lines be superimposed with a common extremity as in that fig.:— AB AD :: BC : CD . then The reciprocals of magnitudes in harmonic progression are in arithmetic progression and conversely : -for , if AB , AC ...
... harmonic progression and the lines be superimposed with a common extremity as in that fig.:— AB AD :: BC : CD . then The reciprocals of magnitudes in harmonic progression are in arithmetic progression and conversely : -for , if AB , AC ...
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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 |
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 centre point chord of contact circle centre circles touching cone conic conic section conjugate diameters conjugate points construction corresponding curve being given cutting cutting CB describe a circle describe an ellipse describe an hyperbola determined draw a parabola ellipse equal fixed point foci focus F given circle given Fig given lines given point given tangent harmonic mean homographic involution latus rectum length line joining locus major axis mean proportional meet the directrix opposite sides ordinate pass pencil perpendicular point of contact point of intersection polar pole PROBLEM Prop radical axis radius reduces to Prob right angle second focus segment shew shewn similar triangles Similarly tangent PT three given vertex vertices
Populære avsnitt
Side 11 - ... the first is to the third as the difference between the first and second is to the difference between the second and third, the quantities a, b, c, are said to be in harmonical proportion.
Side 26 - 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 358 - TRIGONOMETRY. By Rev. JB LOCK, MA, Senior Fellow, Assistant Tutor and Lecturer in Mathematics, of Gonville -and Caius College, Cambridge ; late Assistant-Master at Eton. Globe 8vo.
Side 358 - AND BESSEL'S FUNCTIONS. Crown 8vo. WILSON (JM)— ELEMENTARY GEOMETRY. Books I. to V. Containing the Subjects of Euclid's first Six Books. Following the Syllabus of the Geometrical Association. By JM WILSON, MA, Head Master of Clifton College. New Edition. Extra fcap. 8vo. 4?.
Side 287 - AB describe a segment of a circle containing an angle equal to the given angle, (in.
Side 125 - The problem therefore is reduced to finding the centre of a circle to touch externally two given circles (DG, EG) and pass through a given point (Q), which is always possible since the circles must cut each other and Q lie outside both, ie the problem reduces to Prob. 32. [Draw a common tangent EDM to the two circles meeting fP in M.
Side 358 - SOLID GEOMETRY AND CONIC SECTIONS. With Appendices on Transversals and Harmonic Division. For the Use of Schools. By JM WILSON, MA New Edition. Extra fcap. 8vo. 3-r. 6d. WILSON— GRADUATED EXERCISES IN PLANE TRIGONOMETRY.
Side xi - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Side 30 - 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 97 - 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.