Please see the [Transcriber’s Notes] at the end of this text.

SELF-HELP
MECHANICAL DRAWING
AN EDUCATIONAL TREATISE

“LEARN TO DO A THING BY DOING IT.”—OLD PROVERB

SELF-HELP
MECHANICAL DRAWING
AN EDUCATIONAL TREATISE

BY
N. HAWKINS, M. E.
Author of Handbook of Calculations, etc.

New York: THEO. AUDEL & CO., Publishers
1902

Copyrighted
by
Theo. Audel & Co.
New York
1902

This work
is
most kindly and
respectfully dedicated to
THE COMING MAN
who at the present time
is undoubtedly devoting
a goodly share of
his spare time to
the study of
drawing.

Preface.

It is because of a personal and practical experience of the advantage to be gained by the possession of a knowledge of drawing, that the author is prompted to undertake the rather pleasant task of producing a self-help book relating to the subject.

Since the days of youthful endeavor, the author has passed through an extended experience of mechanical life, and scarcely ever without chalk, pencil or instrument in hand, to illustrate by sketch or drawing, the tools to be employed, or to picture the finished product; accordingly, throughout this work, words of explanation and the drawings will go together to aid the diligent student.

It has been said by an eminent writer, that “one workman is superior to another—other circumstances being the same—directly in proportion to his knowledge in drawing, and those who are ignorant of it must in many respects be subservient to others who have obtained that knowledge.”

It has been also said that no man is fitted to be foreman of a shop who cannot draw, and it is generally true that no one will be appointed to that position, except temporarily, who does not possess some knowledge of the art, either “freehand” or instrumental.

It is a question how far a good working knowledge of drawing can be attained without a teacher; it is true that but few have become proficient without such aid, but it is equally true that “self-help” has been the key note to all advancement.

The author received personal instruction in several ways and times, at home, in school, in an architect’s office, and under an experienced mechanical engineer, but it was in the early morning hours of a bright summer time—lang syne—that he made his first serious attempt to master the art of mechanical drawing. It was a struggle and a battle to hold himself down to “the board” to the finish, but it was a victory—one, won over slothfulness and impatience, and of such a nature as to warrant the use of the term “self-help” to the encouragement of others.

In conclusion two sentiments may be added; if a good working knowledge of drawing is “worth the while” then, 1, the student should be thoroughly in earnest in acquiring it; 2, he should be willing to take sufficient time and give much hard study to gain the skill necessary for success.

This persistence is not irksome. It carries its own reward, and the results are definite and sure.

“One step and then another, and the longest walk is ended;
One stitch and then another, and the largest rent is mended.
One brick upon another, and the highest wall is made;
One flake upon another, and the deepest snow is laid.”

Introduction.

Drawing is one of the arts; art relates to something to be done, and art in the industrial and mechanical sense aims chiefly at utility, and is governed by exact rules; hence mechanical drawing—so-called—tends first to be useful and helpful, and second to accuracy in execution, including most minute details; it aspires to the perfection of nature in adaptability of the means to the end.

Drawing constitutes a universal language, to acquire which is a matter of importance, for by its use one is able to illustrate the form and dimensions of an object, device, or utility, in very much less time, and far more clearly, than by a verbal description.

To a person who may not be able perfectly to understand the language of a country, to be able to draw is an aid and a safeguard; to use the words of Sir Joshua Reynolds, “the pencil speaks the language of every land.”

In extensive iron works and metal-working establishments the designer and draughtsman is always in demand. His services are indispensable and his position is a highly responsible one. It becomes his pecial province to design improvements, to furnish sketches and to make finished drawings; to calculate strains, strength, power, motion, weight, friction and durability. All this and much more is the professional draughtsman’s work.

In “directory” classification, he who accomplishes such comprehensive results as above described is termed a “Draughtsman,” but the word has as wide a meaning as “Engineer,” which takes in civil, mechanical, naval, sanitary, steam and other engineering specialists. So, in drafting, it includes the office boy employed in making blue prints, it embraces the copyists, tracers and assistants, as well as the head draughtsman and chief engineer.

Consequently the range is wide, and the line hard to draw between draughtsmen who work with their hands, and those who work with their brains. It may be added that the best men are too frequently undervalued, owing to the unavoidable difficulty in distinguishing the difference in true worth, between the two widely separated classes.

It may be remarked that they only draw well who draw intelligently; aptness in this, as in many other virtues, is a matter of slow growth, “here a line and there a line”—it’s the proper direction, not the rate of progress, that counts in the end.

There are several methods of drawing—1, Free-hand; 2, Instrumental; 3, Geometrical; 4. Perspective. In the first the work, also termed sketching, is executed by pencil, pen, crayon, or even paint-brush; in the second the result is attained by the use of rule, tee-square, drawing pen, etc.; this method is also denominated mechanical drawing, and suggests the title of this volume.

The great usefulness, not to say necessity, of readiness in executing accurately, drawings “to scale,” is emphasized by the fact that now, more than ever, is all machinery designed, and it may almost be said, is “built,” in the draughting room—this is a valuable hint relating to “reading” drawings.

It is wise, as well as easy, to begin at the beginning of things; thus, it is altogether the good part to mount a ladder by the first and second rounds rather than to attempt it by taking the third, sixth, ninth, etc.—especially are first and second rounds the very best to start upon; “Chalk-work,” is the first subject introduced, next, that of “Free-hand.” These are the first steps leading upward in this most agreeable attainment—skill in illustrating and designing of objects, tools, and utilities.

A single word of advice before introducing the elementary work connected with mechanical drawing: if the student should experience difficulty in mastering the diagrams and curves abounding in this book, let him consult an experienced draughtsman or teacher, who, by a few strokes of a lead pencil, can easily make them plain; that knowledge—which cannot be printed or self-taught—termed the Craftsman’s Art, is communicated largely by personal telling and showing, from man to man; in drawing, this help should be thankfully availed of, when necessity arises.

Note.—Sketching is often in demand because there is no time for finished or careful drawings, and the one who can draw a few lines in a moment to let a sudden necessity be known, is the man of the hour. All candidates for First Class Engineer’s Certificates in marine service in the navy have to undergo an examination in rough drawing; this is intended not so much as a proof of the applicant possessing the capability of a draughtsman, but in the event of any injury to the engines in his charge, so that he may be able to send to his Superintendent a rough drawing of the particular part, properly dimensioned, so that it could be worked from, and time saved on the arrival of the ship at the port where the repairs are to be done.

“No matter how thorough our education may have been
at the first, rules and formulas will slip from the
memory, and every day’s experience gives additional
evidence of the truth of the old adage that ‘THE
KEY THAT RESTS, RUSTS.’”—Simpson Ballard.

The Plan of the Work.

The purpose or scope of this work may be briefly stated: It is to aid the aspiring student in making the first advance towards a thorough and useful knowledge of drawing in its several divisions, as elsewhere defined.

The method to be followed in presenting the subject will be the natural order clearly and simply defined, as “from the less to the greater.”

The first subject to be discussed comes under the heading of chalk-work, i. e., such drawings as can be executed on a blackboard, a floor, or even on more primitive surfaces, such as a smooth stone or board.

This is indeed a lowly beginning, but the author is quite confident it will awaken as much interest as any part of the book—even in the most experienced in the art of drawing, as to them it will revive the ambitions and first crude attempts made in the golden days of their youth.

Let it be clearly understood by all, and especially by those who wish to learn drawing, that the study of this delightful art does not require any special qualification. We need only ask one question: Have you learned to write? If so, be assured you may learn to draw, but to all the same rule applies, first the elements of the art, and afterwards the more advanced study.

It is not expected that all should exhibit a decided taste for drawing, for the possession of this is rather a gift of nature than the result of education; but a knowledge of principles and a certain amount of executive ability may be obtained by every one of average capacity, and whatever the natural power may be, it will be increased and developed by exercise; if the progress is steady and continuous and in the right direction, success is sure to crown the work.

The second division of the book will be free-hand drawing, i. e., that which is executed without instruments. Nothing to instruct has been spared in this important step in the path of advancement.

The illustrations accompanying the two opening sections have been made designedly elementary, for there are many who have a taste for drawing and who have a desire to learn, who from place of residence or other circumstances have not the opportunity of receiving the assistance of a master. To such this book presents itself as a friend directing to the right road, talking, reasoning, and explaining by the way.

The “chalk-work” and “free-hand” sections of the book relate to the foundations upon which all must rest who seek the aid to be derived from the art; hence, the following pages are written with a view to encourage all, and those who are prepared to follow the directions given in them may look forward to the possession of sufficient drawing power to add to their usefulness in after life.

At this point of attainment there arises a need to know the meaning of many words and phrases used by draughtsmen; these are grouped alphabetically from A to Z under the heading of,——

Useful Terms and Definitions: Memorizing these few pages will be of benefit, as an intimate knowledge of the language of the drawing office stamps a man as worthy of a hearing, and assures attention to anything which he may write or say pertaining to the art.

After the Definitions the subject explained will be the Instruments and Materials used in mechanical drawings; following in due course appear Geometrical and Mechanical Drawing, Gearing, Linear Perspective, Projection, Shading, Tracing, Lettering, Drawing Office Rules, Reading Drawings, Useful Tables and a General Index, to which the student is referred. A careful reading is requested to the following helpful note.

Grateful acknowledgment is made to George Perrott, Esq., M. E., for practical and technical assistance throughout the work, and to Theo. Lucas, Engineer, for text and illustrations in the portions of the book relating to Linear Perspective and Projection.

Note.—In Machinery Prof. Chas. H. Benjamin says, referring to drawing, under heading “How and what to study,” “... I have so far said nothing about drawing, for I do not think it of much use to learn that, until you know what you want of it. All this time that you have been studying mechanism you should have had a sketch book or pad of note paper, and made free hand sketches of mechanical movements which interested you and of various machine details. You should accustom yourself to use drawing as a means of expressing ideas, just as you use written words, so that it becomes a second nature to you to sketch anything you wish to remember or describe. If you work from blue-prints in the shop, or if you can borrow some to study, this will help you to understand how a drawing is made. You can get some drawing instruments at any time and begin to practice on drawing straight lines and circles, so as to become familiar with the instruments. And here it will be of great benefit to you if you can attend an evening drawing school for one night in the week at least.

“When you have become sufficiently familiar with the principles of drawing, a book on mechanism will tell you how to draw gear teeth and cams, and how to design various link motions. Make up your own problems from what you see in the shop and make your drawing a means to an end and not the principal thing; it is of little use to be able to make a nice drawing unless you know what to draw and why.

“Drawing is a convenient tool as an aid in expressing to others the ideas which you wish to convey; in all cases take the problems and the ideas from your every-day work and that which is around you; your success will depend upon the close connection which you keep at all times between your acquired knowledge and your practical work.”

General List of Contents.

Chalk Work.

The blackboard has been well called the great weapon of the modern educator; this is especially true in reference to instruction in an art dealing with lines, curves and figures.

Fig. 6.

Many a man can chalk out on a blackboard, or on a piece of sheet-iron, or on the floor, just what he wants to show, and make his meaning very plain; hence, in every workshop, and many other places, a blackboard is more than useful, and it has been said that no draughting office is complete without one.

[Fig. 6] represents a chalk-crayon.

Fig. 7.

Fig. 8.

[Figs. 7 and 8] need no explanation, as they represent two forms of the well-known blackboard.

Chalk lines have this advantage—they are easily altered or rubbed out when not needed any longer. The work executed upon a blackboard is mostly done by hand, without aid from instruments; a few tools, however, are useful—such as, 1, large wooden blackboard compasses holding a crayon, which are made and sold by the trade in size twelve inches to thirty inches in length; 2, a straight-edge; and 3, some crayons. With the compasses circles and part of the circle can be made, and with the straight-edge the larger lines can be drawn.

These instruments are shown on [page 29], and are, 1, compasses, for holding chalk for making circles; 2, a tee-square; 3, a straight-edge; 4, a protractor for measuring angles; 5, a triangle 60° and 30°; 6, a brass holder for crayons.

Blackboard Drawing.—The use of a blackboard comes principally and properly under the head of free-hand drawing, but its importance is such that a separate division of the volume is assigned to it.

Thus, chalk-work may be considered the first lesson in “free-hand,” as all the examples can also be most profitably practiced with pencil and paper.

Very rapid drawing upon the board should not be encouraged, as it is likely not to be accurate enough; again, the board should be entirely free from grease. Cloths, sponges or chamois skin rubbers may be used to erase or change the chalk marks. Vertical lines should be drawn from above downward; short lines should be drawn with the fingers alone, those somewhat longer with the hand, using the wrist-joint; the still longer lines with the forearm, using the elbow-joint; those longer yet with the whole arm, using the shoulder-joint; lines should always be drawn with a uniform motion, slow enough for the eye to follow.

Practice in chalk-work should alternate with sketching in a sketchbook and with geometrical drawing—to be hereafter described. The student should practice a short time on the board, at least once a week; large sizes are the most profitable for the representations to be made; when drawing in different directions the hand should be turned, not the paper or board; the hand should never be allowed to obstruct the sight, hence the hand and fingers should be held in a position of freedom—with fingers not nearer than 1¹⁄₂ or 2 inches from the board.

Note.—The first lesson of any kind the author received in drawing was to make a straight line; this was effected by holding the pencil nearly erect and guiding it along by the aid of the little finger held pressed against the edge of a board; this was a useful item of knowledge, as proved by passing years.

A well-known artist, in telling his early experience, said: “The first thing I was taught was to draw a line, divide it, erect a perpendicular from its center, and afterwards to divide the angle made by the perpendicular.” In answer to a question asking how long he was kept at the lines, he replied, “about two months—or a month or two,” indicating that even the longer time would have been well spent in learning to draw a straight line.

PREPARATORY PRACTICE IN DRAWING.

Every visible object is bounded by lines which enable the observer to determine its shape. If these lines are straight or curved, the shape of the object is regular; if broken, the shape of the object is irregular.

The elements, then, of form are lines, straight, curved, or broken, and these, therefore, furnish the beginning of all instruction in free-hand or mechanical drawing.

PERPENDICULAR LINES.

[Fig. 15] shows six lines—upright and perpendicular, with points or “dots” indicated at the top and bottom of each line; to draw these, proceed thus:

Fig. 15.

Fig. 16.

The learner should stand with his right shoulder opposite the board, and the weight of the hand and the arm should be allowed to fall naturally; now, make on the board two points, one being six inches above the other, these being merely “dots,” shown at the ends of the lines, [figs. 15], etc., and made with two motions; the line between the points should now be drawn not too quickly from the upper to the lower point; three movements of the hand and arm complete the line; to draw the other five lines the movements have simply to be repeated.

If the student pronounces to himself “one,” “two,” “three,” at each motion, it will be helpful; in this exercise, [fig. 15], the aim is to make six lines, each line being parallel to the first. Again, in the example, it is intended that the lower point should be made first, next the upper, and lastly the line drawn from the upper to the lower point, but the order may be reversed; at one the upper point, at two the lower, at three the stroke upwards to complete the line.

HORIZONTAL LINES.

To make these as shown in [fig. 16], proceed as follows: With the word one make a point, with two another point six inches at the left, with three draw a straight line from the left point to the right. All added lines should be parallel: for practice, reverse the process thus, one, make a “point,” at two another point at the right, at three draw line to the left.

The student will note that the two motions—at the words one and two—are to fix the positions of the ends of the lines; this practice will be found useful in the most advanced examples and an item of elementary practice never to be forgotten—like the help to be derived by the first round of a ladder.

Fig. 17.

Fig. 18.

OBLIQUE LINES.

In drawing oblique straight lines as shown in [fig. 17], at the word one let the student make the lower point; at the word two the upper, a little to the right of the lower; at the word three draw a line quickly from the upper to the lower point. In pronouncing the words one, two, three, let the student make the additional parallel lines.

As shown in [fig. 18], at the word one make the lower point; at the word two the upper point, a little to the left; at the word three draw a line rapidly from the upper to the lower point, and “timing” the process by repeating one, two, three, make the additional parallel lines.

Fig. 19.

BROKEN LINES.

A broken line is composed of two or more straight lines at angles to each other (see [fig. 19]). To draw them begin (saying) one, make a point; two a point below at the left; three, a point above at the left; four, draw a line from the left hand point to the lower point; at the word five, from the lower point to the upper right hand point. For practice draw numerous lines in the same way, keeping them parallel to each other, as shown in [fig. 20].

Fig. 20.

Fig. 21.

Fig. 22.

Fig. 24.

Fig. 23.

Fig. 25.

In example, [fig. 21], the arrangement of the points is changed—let the student draw at the words, as follows: One, a point; two, a point above at the left; three, a point below at the left; four, draw from the point at the left to the upper point; five, from the upper point to the lower right hand point; continue to add parallel lines to complete the figure as shown.

[Figs. 22] and [23] are given as examples to practice, making first the points and then the connecting lines and afterward the parallel lines to complete the figures.

CURVED LINES.

To draw curved lines, as shown in [fig. 24]. At the word one, point; at the word two, point three inches directly above; three, at the same distance above again make a point; now draw a curve as shown, joining the middle point and the upper point; now draw the curve as shown below it; finally complete figure as shown.

Fig. 26.

Fig. 27.

Fig. 28.

Fig. 29.

Fig. 30.

[Figs. 25] to [30] are to be practiced, making first the points and then connecting them by the curves to complete the figures.

When two or more students are working together, with each having a blackboard, the counting may be in concert—or a teacher could count for a class. In these line examples care should be used in making them of uniform length. There is a difference to be noted between a crooked line and a broken line, the latter being a straight line and the former deviating from it.

Square chalk crayons are the best for hand work, as lines of an even or uniform width can be drawn with them.

A very fine effect is produced by using two thicknesses of chalk, one being double the thickness of the other; the heavy lines being used on the shade side of objects will produce a good effect, giving thickness and body to the object.

Round chalk crayons are used in the compasses to draw circles, but hand lines drawn with them are not so neat as those produced with the square-shaped chalk.

To obliterate or remove the construction, or false lines made on the blackboard, a wooden handle two inches in diameter with a cone end 3 or 4 inches long, covered with chamois skin or soft cloth tightly wrapped round the cone and fastened with a tack or drawing pin, makes the best implement to erase lines not required, the point of the cone will remove these without destroying the lines or curves which meet them.

Sponges, chamois skin or cloth rubbers are used to rub out the chalk drawings and clean the blackboard.

The best height for a diagram on the blackboard is not higher than the head, nor lower than the elbow.

Horizontal lines should be made from the left to the right; the body and arm being moved with the hand, and kept in the same relative position with it, will steady the hand.

Curved lines to the left should be drawn first, enabling the eye to take in not only the curve in process of formation but that already made.

Passing the crayon in the hand, over the intended curve previous to marking it, will guide the eye and give confidence to the hand in chalking the curve.

A proper distance from the blackboard is essential, the face being about two feet away from it.

Draw with the whole arm extended from the shoulder-joint, not from the elbow or wrist.

Fig. 31.

ELECTRA.

Preliminary Terms and Definitions.

Like all the arts, drawing has a nomenclature of its own, and nothing can be more helpful to the beginner than to know the name of things relating to the art of drawing. This is a language almost peculiar to itself, and used daily and hourly by many thousands of superintendents, foremen and master mechanics, as well as by owners, designers and draughtsmen, hence its introduction at this early stage.

ALTITUDE.—This is the elevation of an object above its base, or the perpendicular distance between the top and bottom of a figure.

Fig. 33.

Fig. 34.

Fig. 35.

Fig. 36.

Fig. 37.

ANGLE is the difference in the direction of two lines which meet or tend to meet. The lines are called the sides and the point of meeting, the vertex of the lines.

To make an angle apparent, the two lines must meet in a point, as A B and A C, which meet in the point A, as shown in [fig. 33].

Angles are measured by degrees.

A Degree is one of the three hundred and sixty equal parts of the space about a point in a plane.

Angles are distinguished in respect to magnitude by the terms Right, Acute and Obtuse Angles.

A Right Angle is that formed by one line meeting another, so as to make equal angles with that other.

The lines forming a right angle are perpendicular to each other.

An Acute Angle is less than a right angle. See [Fig. 35].

An Obtuse Angle is greater than a right angle. See [Fig. 36].

Obtuse and acute angles are also called oblique angles; and lines which are neither parallel nor perpendicular to each other are called oblique lines.

The Vertex or Apex of an angle is the point in which the including lines meet.

An angle is commonly designated by a letter at its vertex; but when two or more angles have their vertices at the same point, they cannot be thus distinguished.

For example, when the three lines A B, A C, and A D in [fig. 37] meet in the common point A, we designate either of the angles formed, by three letters, placing that at the vertex between those at the opposite extremities of the including lines. Thus, we say, the angle B A C, etc.

APEX.—The summit or highest point of an object.

ARC.—See [circle].

AXIS OF A SOLID.—An imaginary straight line passing through its center.

AXIS OF A FIGURE.—A straight line passing through the center of a figure, and dividing it into two equal parts.

BASE.—The base of a solid figure is that on which it stands—the lowest part.

BISECT.—To divide into two equal parts.

BISECTOR.—A line which bisects.

Fig. 38.

CIRCLE.—A Circle is a plane figure bounded by one uniformly curved line, all of the points in which are at the same distance from a certain point within, called the Center.

The Circumference of a circle is the curved line that bounds it.

The Diameter of a circle is a line passing through its center, and terminating at both ends in the circumference, as A C B.

The Radius of a circle is a line extending from its center to any point in the circumference. It is one-half of the diameter. All the diameters of a circle are equal, as are also all the radii C D, C B and C A.

An Arc of a circle is any portion of the circumference, as B D and A D.

Semi-Circle.—Half a circle formed by bisecting it with a diameter, as A C B. [Fig. 38].

An angle having its vertex at the center of a circle is measured by the arc intercepted by its sides. Thus, the arc A D measures the angle A C D, and in general, to compare different angles, we have but to compare the arcs, included by their sides, of the equal circles having their centers at the vertices of the angles.

CIRCUMSCRIBE.—To draw a line of figures about or outside, such as a circle drawn around a square touching its corners or angles.

Inscribe.—To draw a line or figure inside or on the interior, such as a circle drawn within a square touching its sides.

CONCAVE.—Curving inwardly.

CONE.—A solid body or figure having a circle for its base, and its top terminated in a point or vertex.

CONSTRUCTION.—The making of any object.

CONTOUR.—The outline of the general appearance of an object.

CONVERGENCE.—Lines extending towards a common point.

CONVEX.—Rising or swelling into a round form—the opposite to concave.

CORNER.—The point of meeting of the edges of a solid, or the two sides of a plane figure.

CROSS-HATCHES.—In free-hand drawing the use of lines crossing each other to produce light and shade effects.

CURVE.—A line of which no part is straight.

Reversed Curve.—One whose curvature is first in one direction and then in the opposite direction.

Spiral Curve.—A plain curve which winds about and recedes, according to some law, from its point of beginning, which is called its center.

CYLINDER.—A solid bounded by a curved surface and by two opposite faces called bases; the bases may be any curved figures and give the name to the cylinder; thus a circular cylinder is one whose bases are circles.

CYLINDRICAL.—Having the general form of a cylinder.

DEGREE.—The 360th part of a circle.

DESCRIBE.—To make or draw a curved line; to draw a plan.

DESIGN.—Any arrangement or combination to produce desired results in industry or art. To delineate a form or figure by drawing the outline—a sketch.

DEVELOP.—To unroll or lay out.

DIAGONAL.—A right line drawn from angle to angle of a quadrilateral or many angled figure and dividing it into two parts.

DIAMETER.—A right line passing through the center of a circle or other round figure terminated by the curve and dividing the figure symmetrically into two equal parts.

EDGE.—The intersection of any two surfaces.

ELEVATION.—The term elevation, vertical projection and front view—applied to drawings—all have the same meaning.

FACE.—One of the plane surfaces of a solid; it may be bounded by straight or curved edges.

FINISHING.—Completing a drawing whose lines have been determined by erasing unnecessary lines and strengthening and accentuating where this is needed.

FORESHORTENING.—Apparent decrease in length, owing to objects being viewed obliquely; thus a wheel, when seen obliquely, instead of appearing round, presents the appearance of an ellipse.

FREE-HAND.—Executed by the hand unaided by instruments.

GENERATED.—Produced by.

GEOMETRIC.—According to geometry.

HALF-TINT.—The shading produced by means of parallel equidistant lines.

HEMISPHERE.—Half a sphere obtained by bisecting a sphere by a plane.

HORIZONTAL.—Parallel to the surface of smooth water. In drawing, a line drawn parallel to the top and bottom of the sheet is called horizontal.

INSCRIBE.—See [circumscribe]—its opposite.

INSTRUMENTAL.—By the use of instruments.

LINE.—A line has length, only, as A C; a right line is a straight line, the shortest line that can be drawn between two points, A——C.

Straight. One which has the same direction throughout its entire length.

Curved. One no part of which is straight.

Broken. One composed of different successive straight lines.

Mixed. One of straight and curved lines.

Center. A line used to indicate the center of an object.

Construction. A working line used to obtain required lines.

Dotted. A line composed of short dashes. - - - - - -

Dash. A line composed of long dashes. — — —

Dot and Dash. A line composed of dots and dashes alternating. — · — · —

Dimension. A line upon which a dimension is placed.

Full. An unbroken line, usually representing a visible edge. ———

Shadow. A line about twice as wide as the ordinary full line.

A straight line is often called simply a line, and a curved line a curve.

LONGITUDINAL.—In the direction of the length of an object.

MODEL.—A form used for study.

OBLIQUE.—Neither horizontal nor vertical.

OBLONG.—A rectangle with unequal sides.

OVAL.—A plane figure resembling the longitudinal section of an egg; or elliptical in shape.

OVERALL.—The entire length.

PARALLEL.—Having the same direction and everywhere equally distant.

PATTERN.—That which is used as a guide or copy in making things.

Flat. One made of paper or other thin material.

Solid. One which reproduces the form and size of the object to be made.

PERIMETER.—The boundary of a closed plane figure.

PERPENDICULAR.—At an angle of 90°.

PERSPECTIVE.—View; drawing objects as they appear to the eye from any given distance and situation, real or imaginary.

PLAN.—Plan, horizontal projection and top view have the same meaning.

PLANE FIGURE.—A part of a plane surface bounded by straight or curved lines, or by both combined.

Fig. 39.

POLYGON.—A plane figure bounded by straight lines called the sides of the polygon. The least number of sides that can bound a polygon is three. Polygons bounded by a greater number of sides than four are denominated only by the number of sides.

A polygon of five sides is called a Pentagon; of six, a Hexagon; of seven, a Heptagon; of eight, an Octagon; of nine, a Nonagon, etc.

Diagonals of a polygon are lines joining the vertices of angles not adjacent.

The Perimeter of a polygon is its boundary considered as a whole.

The Base of a polygon is the side upon which the polygon is supposed to stand.

The Altitude of a polygon is the perpendicular distance between the base and a side or angle opposite the base.

Fig. 40.

A Quadrilateral is a polygon having four sides and four angles.

A Parallelogram is a quadrilateral which has its opposite sides parallel.

The side upon which a parallelogram stands and the opposite side are called respectively its lower and upper bases.

A Rectangle is a parallelogram having its angles right angles.

A Square is an equilateral rectangle, [fig. 41].

Fig. 41.

Fig. 42.

Fig. 43.

Fig. 44.

Figs. 45-49.

A Rhomboid is an oblique-angled parallelogram.

A Rhombus is an equilateral rhomboid, [fig. 42].

A Trapezium is a quadrilateral having no two sides parallel, [fig. 43].

A Trapezoid is a quadrilateral in which two opposite sides are parallel, and the other two oblique, [fig. 44].

A POLYHEDRON is a solid bounded by planes. There are five regular solids which are shown in [figs. 45, 46, 47, 48 and 49]. A regular solid is bounded by similar and regular plane figures.

[Fig. 45].—The tetrahedron, bounded by four equilateral triangles.

[Fig. 46].—The hexahedron, or cube, bounded by six squares.

[Fig. 47].—The octahedron, bounded by eight equilateral triangles.

[Fig. 48].—The dodecahedron, bounded by twelve pentagons.

[Fig. 49].—The icosahedron, bounded by twenty equilateral triangles.

PRISM.—A solid whose bases or ends are very similar plane figures, and whose sides are parallelograms; prisms are called triangular, square, etc., according as the bases are triangles, squares, etc.

PRODUCE.—To continue or extend.

PROFILE.—An outline or contour.

PROJECTION.—The view of an object obtained upon a plane by projecting lines perpendicular to the plane.

QUADRANT.—The fourth part; a quarter; the quarter of a circle.

QUADRISECT.—To divide into four equal parts.

SECTION.—A projection upon a plane parallel to a cutting plane which intersects any object. The section generally represents the part behind the cutting plane, and represents the cut surfaces by diagonal lines.

SECTIONAL.—Showing the section made by a plane.

SHADOW.—Shade and shadow have about the same meaning.

SOLID.—A solid has three dimensions—length, breadth and thickness.

SPHERE.—A solid bounded by a curved surface every point of which is equally distant from a point within called the center.

SURFACE.—The boundary of a solid. It has but two dimensions—length and breadth. Surfaces are plane or curved.

A Plane Surface is one upon which a straight line can be drawn in any direction.

A Curved Surface is one no part of which is plane.

The surface of the sphere is curved in every direction, while the curved surfaces of the cylinder and cone are straight in one direction.