By W. Abbott C.M.G., O.B.E., Ph.D., B.Sc., M.I..Mech.E., M.R.I. (auth.)

HIS ebook is meant to supply A direction IN sensible Geometry for engineering scholars who've already acquired a few guideline in trouble-free aircraft geometry, graph plotting, and the use T of vectors. It additionally covers the necessities of Secondary institution students taking useful Geometry on the complicated point. The grouping followed, within which aircraft Geometry is handled partly I, and good or Descriptive Geometry partially II, is synthetic, and it's the purpose that the 2 components could 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, convinced of the easier interĀ sections and advancements may with virtue be taken at an previous degree than that indicated. partly I enormous area has been dedicated to Engineering pictures, quite to the functions of graphical integration. using graphical equipment of computation is totally justified in so much engineering difficulties of a realistic nature-especially the place analytical tools could turn out arduous -the effects bought being as exact because the info warrant.

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**Example text**

Pascal's Theorem states that P, Q and R lie in a straight line. The hexagon can be taken as abfedca ; and then another straight line such as PQR results. A useful construction, used in Problem 54b on the next page, is that for a conic required to pass through a given point and to touch two tangents at given points. This construction will be approached by considering first the construction for extra points on (a) a conic defined by five points; and (b) a conic defined by a tangent point and three points.

Exercise 5, Fi~. -Suppose the Exercise I, Fi~. -Draw a line points G and H, fig. 5, to move tointersecting the directrix in D and the wards Band C until they coincide conic in Band C, Band C being well with Band C respectively. Repeat apart. Join each point to F and pro- Ex. 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.

Join PF and on PF as diam . deTo determine Q, a point of contact, scribe a circle cutting the tangent at produce the tangent CP to meet the the vertex in Band C. Join PB and directrix in D. Join DF, and draw PC, and produce them ; these are the FQ at rt. L s to F D . The normal may required tangents. then be drawn at Q perp. to QP. Problem 38 . To construct a Parabola, using measured Absclssee. " a property of the in which the double ordinate is divided by 10 equall y spaced diameters, and the curve is that the abscissa is proporti onal to the produ ct of th e parts into which it abs cissse are made equal, to scale.