## Construction Of Triangles Perimeter Altitude Vertical Angle Given

Preface to the second odition iii

Acknowledgment* iv

PART I GEOMETRIC DRAWING

Chepter

1 Scale» 3 The representative fraction; plain scales; diagonal scales; proportional scales

Exercises t 8

2 The construction of geometric figures from given data 10

Construction of the following tnanglea: Equilateral. given one of the sides Isosceles, given the perimeter and altitude Scalene, given base angles and altitude Scalene, given base, altitude end vertical angle Scalene, given penmeter and ratio of sides Scalene, given perimeter, altitude and vertical angle

Similar triangles with different penmeter Construction of the following quadrilaterals: Square, given one side Square, given the diagonal Rectangle, given the diagonal end one side Parallelogram, given two sides and an angle Rhombus, given the diagonal and length of sides Trapezium, given the parallel sides, the perpendicular distance between them and one angle

Construction of the following polygons: Regular hexagon, given the length of side Regular hexagon, given the diameter Regular octagon, given the diagonal (within a circle)

Regular octagon, given the diameter (within e square)

Reguter polygon, given tho length of side (three methods)

Reguler polygon, given the diagonal (within a circle)

Regular polygon, given the diameter

Exercises 2 19

page

3 Isometric projection 20 Conventionel isometric projection (isometric drawing); circles and curves in isometric;

true isometric projection, isometric scales. Exercises 3 26

4 The construction of circles to satisfy given conditions 29

To construct the circumference, given the diameter

To construct the diameter, given the circumference

To find the centre of a circle

To construct circles, given the following conditions:

To pass through three given points Inscribed circle of a regular polygon Circumscribed circle of a regular polygon Escribed circle to a regular polygon To pass through a fixed point and touch a line at a given point

To pass through two given points and touch a given line

To touch two given lines and pass through a given point

To touch another given circle and a given line To touch another circle and two tangents of that circle

To touch another circle and two given lines To pass through two given points and touch a given circle

Three circles which touch, given the position of their centres

Two circles within a third circle, ell three circles to louch

Any number of circles within a given orcle. all circles to touch

A number of equal circles within a given regular polygon

Equal circles around a given regular polygon Exercises 4 37

Tangency 39

Tangent from a point on the circumference w

Tangent from a point outside the circle Common tangent to two equal circle« (exterior)

Common tangent to two equal circle« (interior)

Common tangent to two unequal circle« (exterior)

Common tangent to two unequal circles (interior)

Exercises 5 42

6 Oblique projection 44 Oblique (aces at 30°. 45*. 60s. oblique scale

(1- J- I): Cavalier and Cabinet protections; circles and curves in oblique projection Exarcises 6 47

7 Enlarging and reducing plane figure*

and equivelent areas 50

Linear reductions m size; reduction of s<des by different proportions; reductions in area. Equivalent areas:

Rectangle equal in area to a given triangle Square equal in area to a given rectangle Square equal in area to a given triangle Triangle equal in area to a given polygon Circle which has the same area as two smaller circles added together To divide a triangle into three parts of equal area

To divide a polygon into a number of equal areas

Exercises 7 58

8 The blending of lines end curves 60 To blend a radius with two straight lines at nght angles

To bland a radius with two straight lines meeting at any angle To find the centre of an arc which passes through a given point and blends with a given line

To find the centre of an arc which blends with a line and a circle To find the centre of an arc which blends, externally and internally, with two circles To join two parallel lines with two equal radii, the sum of which equals the distance between the lines

To join two parallel lines with two equal radii

To join two parallel lines with two unequal radii

Exercises 8 66

9 loci 68 Loci of mechanisms, trammels, some other problems in loci

Extremes 9 76

page

10 Orthographic projection 78 Third Angle projection. First Angle projection: elevation and plan; front elevation, end elevation and plan, auxiliary elevations and auxiliary plans; prisms and pyramids;

cylinders and cones: sections.

Exercises 10 98

11 Conic sections—The Ellipse, the Parebola. the Hyperbola 102 The ellipse as a conic section; as a locus;

three constructions for the ellipse; the focus.

the normal and the tangent

The parabola as a conic section: as a locus;

within a rectangle; the focus and tangent

The hyperbola as a conic section; as a locus.

Exercises 11 110

12 Intersection of regular solids 112 Intersection of the following solids:

Two dissimilar square prisms at right angles Two dissimilar square prisms at an angle A hexagonal pnsm and a square prism at right angles

Two dissimilar hexagonal prisms at an angle A hexagonal prism and an octagonal pnsm at an angle

A square prism and a square pyramid at right angles

A square pyramid and a hexagonal prism at an angle

Dissimilar cylinders at right angles Dissimilar cylinders at an angle Dissimilar cylinders in different planes at an angle

Cylinder and square pyramid at right angles Cylinder and square pyramid at an angle Cylinder and hexagonal pyramid at an angle Cylinder and cone with cone enveloping the cylinder

Cylinder and cone, neither enveloping the other

Cylinder and cone with cylinder enveloping the cone

Cylinder and cone in different planes Cylinder and hemisphere Fillet curves

Exercises 12 129

13 Further orthographic projection Rabatment. traces. The straight line:

Projection of a line which is not parallel to any of the principal planes True length of a straight line and true angle between a straight line and vertical and horizontal planes

To find traces of a straight line given the plan and elevation

To draw the elevation and plan of a straight lint given the true length and the distances of the and* of the line from the principe! pianos

To construct the plan of a straight line given the distance of one end of the line from the XY line in the pian, the true length of the line and the elevation

To construct the elevation of a straight line given the distance of one end of the line from the XY line in the elevation, the true length of the line and the plan To construct the elevation of a straight line given the plan and the angle that the line makes with the horizontal plane To draw the plan of a line given the elevation and the angle that the line makes with the vertical plane The inclined plane:

Projection; traces; angles between planes; true shape of an inclined plane; true shapes of the sides of an oblique, truncated pyramid

The oblique plane: Projection ; traces.

To find the true angle between the oblique plane and the horizontal plana

To find the true angle between the oblique plane and the vertical plane

To find the true angle between the traces of an oblique plane

Exercises 13 141

14 Developments

Development of prisms: Square prism

Square prism with an oblique top Hexagonal prism with oblique ends Intersecting square and hexagonal prisms Intersecting hexagonal and octagonal prisms Development of cylinders: Cylinder

Cylinder with oblique top Cylinder cut obliquely at both ends Cylinder with circular cut-out An intersecting cylinder Both intersecting cylinders Development of pyramids Pyramid

Frustum of a square pyramid Hexagonal pyramid with top cut obliquely Hexagonal pyramid penetreted by a squere prism

Oblique hexagonal pyramid Development of cones: Cone

Frustum of e cone

Frustum of e cone cut obliquely

Cone with a cylindrical hole

Oblique cone

Exercises 14 156

16 Further problem« in loci 159

The cycloid; tangent and normal to the cycloid; epi- and hypo-cycloids; tangent and normal to the epi- and hypo-cycloids; inferior and superior trochoids; the involute; normal and tangent to the involute; the Archimedean spiral; the helix; round and square section coiled springs; square section threads.

Exercises 15 167

16 Freehand sketching 169 Pictorial sketching; sketching in Orthographic Projection; sketching as an aid to design

17 Some more problems solved by drawing 176 Areas of irregular shapes; the mid-ordinate rule Resolution of forces; a couple, calculation of some forces acting on a beam; forces acting at a point; equilibrant and resultant forces

Simple cam design; cam followers Exercises 17 190

PART II ENGINEERING DRAWING

18 Introduction 194 Type of projection

Sections Screw threads Nuts and bolts

Designation of ISO screw threads Types of bolts and screws

### Dimensioning

Conventional representees Machining symbols Surface roughness Abbreviations Framing and title blocks Assembly drewings Some engineering festerings: The stud and set bolt Locking devices Rivets and riveted joints Keys, keyweys end splines Conered loints Worked examples

Exercises 18 230

Appendix A 258

Sizes of ISO metric hexagon nuts, bolts and washers

Appendix B 260

Sizes of sloned and castle nuts with metnc threeds

Index 261

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### Responses

• Otto
How to draw the common tangent to two unequal circles?
9 years ago
• vanna
How to construct a similar triangle given perimeter?
8 years ago
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How to draw the isometric projection of a regular pentagon on a cylinder?
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How to construct an isosceles triangle given the perimeter and altitude?
4 years ago
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