Elementary Pure Geometry With Mensuration a Complete Course of Geometry for Sc
Elementary Pure Geometry With Mensuration a Complete Course of Geometry for Sc
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BB'D, CCD) ; then CD bisects ang. BDC. If now B'C turns about C to coincidence with BC, D moves to P, point of contact of BC with envelope, and CD to CP, perp. To tangt. BP. Hence the point of contact of a moving line in any position Avith its envelope is the foot of perpendicular on the line fi'om the centre of rotation. CH. V. ] ENVELOPES INSTANTANEOUS CENTRE. 147 This centre of rotation is not in general fixed, but varies with the position of the line ; it is therefore called the instantaneo...us centre of rotation for the particular position of the moving line. In fig. 3, last page, if E is the point of the side BA of the right angle, which momentarily coincides with A ; then as B begins to move on circle O, E moves at first along direction AB ; . *. Inst. Centre O' is intersection of BO', AO', perp. To BT, AB. And O'P, perp. To BC, determines pt. Of contact P. The method is useful for a figure given in magnitude and form. By the aid of Theorem 109 we can show that ' The envelope of one side of an angle whose vertex describes a fixed circle, and whose other side traverses a fixed point, is an ellipse or hyperbola.
What to read after Elementary Pure Geometry With Mensuration a Complete Course of Geometry for Sc?
You can find similar books in the "Read Also" column, or choose other free books by Edwin Budden to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
BB'D, CCD) ; then CD bisects ang. BDC. If now B'C turns about C to coincidence with BC, D moves to P, point of contact of BC with envelope, and CD to CP, perp. To tangt. BP. Hence the point of contact of a moving line in any position Avith its envelope is the foot of perpendicular on the line fi'om the centre of rotation. CH. V. ] ENVELOPES INSTANTANEOUS CENTRE. 147 This centre of rotation is not in general fixed, but varies with the position of the line ; it is therefore called the instantaneo...us centre of rotation for the particular position of the moving line. In fig. 3, last page, if E is the point of the side BA of the right angle, which momentarily coincides with A ; then as B begins to move on circle O, E moves at first along direction AB ; . *. Inst. Centre O' is intersection of BO', AO', perp. To BT, AB. And O'P, perp. To BC, determines pt. Of contact P. The method is useful for a figure given in magnitude and form. By the aid of Theorem 109 we can show that ' The envelope of one side of an angle whose vertex describes a fixed circle, and whose other side traverses a fixed point, is an ellipse or hyperbola.
What to read after Elementary Pure Geometry With Mensuration a Complete Course of Geometry for Sc?
You can find similar books in the "Read Also" column, or choose other free books by Edwin Budden to read onlineMoreLess
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