By W. Abbott C.M.G., O.B.E., Ph.D., B.Sc., M.I..Mech.E., M.R.I. (auth.)
HIS booklet is meant to supply A path IN functional Geometry for engineering scholars who've already acquired a few guideline in basic airplane geometry, graph plotting, and the use T of vectors. It additionally covers the necessities of Secondary institution scholars taking sensible Geometry on the complicated point. The grouping followed, during which aircraft Geometry is handled partially I, and sturdy or Descriptive Geometry partially II, is man made, and it's the goal that the 2 components can be learn simultaneously. The logical therapy of the topic provides many problems and the series of the later chapters in either components is unavoidably a compromise; for instance, sure of the less difficult inter sections and advancements may possibly with virtue be taken at an prior level than that indicated. partially I massive area has been dedicated to Engineering snap shots, rather to the functions of graphical integration. using graphical tools of computation is absolutely justified in such a lot engineering difficulties of a realistic nature-especially the place analytical tools might turn out exhausting -the effects received being as actual because the information warrant.
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Extra resources for Practical Geometry and Engineering Graphics: A Textbook for Engineering and Other Students
The centre of curvature at any point P on a conic. except when P coincides with the vertex. may be determined as follows : Refer to Fill. 2. Join p. to the focus F . At P draw the normal PNO cutting the axis in N . At N draw NE perp. to NP to intersect in E the line PF produced. At E draw EO perp . to PE to intersect the normal in O. o is the centre of curvature of the conic at the point P. As P approaches the vertex. the points N. 0 and E move towards one another; the student should test this by taking P in several positions approaching V.
Take any Exercise 3, Fi~. -Let C coin- external point P and draw tangents cide with B and draw the line BD, PB and PC. Join BF and CF and which is now a tangent to the conic. show that the angles PFB and PFC Join DF and BF. This is the limiting are equal. Hence: tangents drawn from case of fig. 3, and DF is perp. to any point to a conic subtend equal BF, because BF and FE now coincide. angles at the focus . At B draw the Hence: the angle subtended at the focus normal BG meeting the axis at G. by that part of the tangent intercepted between the conic and the directrix is a Show that ;~ = the eccentricity of right angle.
E. draw tangents at Band C. duce CF to an y point E . Measure the Show that these meet in D 1 on the angles BFD, EFD-they should be directrix, and that D 1F is perp. to BC. equal. Hence : if a straight lin e cut the Hence: tangents at the extremities of directrix in D and the conic in Band a fo cal chord intersect on the directrix. C, and if D, B and C be joined to the Draw other pairs of tangents from focus, then DF bisects the exterior angle points on the directrix (dotted ), and between BF and CF.