Several figures, 83 to 96, representing more or less familiar parts of
machines, utilities, etc., are introduced for practice in free-hand,
but--
It must be noted that even in free-hand the wise student will
occasionally use the straight edge and compasses, so as to make his
first attempts fairly creditable. Many good draughtsmen have begun by
simply copying such figures and illustrations as are used throughout
this volume and other similar sources; perhaps there is nothing better
for practice or training than the copying and reproducing of samples of
good mechanical drawings, yet it must always be remembered that
advancement in free-hand must be made in the line of less to greater
efforts, and that the why and wherefore will be constantly asked by the
aspiring student; that good and correct drawings are to be aimed for at
all times in every line and dimension--never forgetting the law of
proportion in the smallest outlines of objects to be represented.
[Illustration: Fig. 78.]
[Illustration: Fig. 79.]
[Illustration: Fig. 80.]
[Illustration: Fig. 81.]
Fig. 83 is a section, or end view of a bar of angle iron; the student
will find helpful practice in attempting this figure; he may be allowed
to use a straight-edge in drawing the lines, but no measurements; the
work should be tested on completion by a rule, or better by penciling
from the original on tracing paper, and comparing the free-hand with the
copy, when the defective proportions, if any, will be clearly exhibited.
Fig. 84 is a section of tee iron, and fig. 85 is a section of channel
iron. These three figures on page 75 should be practiced alternately,
although seeming similar in shape.
Fig. 86 is a side and end view of an angle plate shaded. Fig. 87 is a
wrench shaded.
Examples of bolt ends are shown in the two next numbers; fig. 88
exhibits the common square-head bolt, and fig. 89 the hexagon or
six-sided bolt-head; these are also examples of _straight-line shading_.
Fig. 90 is a lathe-dog, and shows an example of _curved shading_; fig.
92 is an engine crank, and an example of _straight and curved shading_;
fig. 91 is a screw clamp.
Fig. 93 is a section of boiler plates riveted together; a caulking tool
is also shown.
In the example, fig. 94--a hand-wheel--the principal difficulty, even
for the most advanced student in free-hand, will be in drawing the
circles; a coin, if convenient, can be used to scribe about, in drawing
these; the other parts can afterwards be filled in around the circle.
Fig. 96 is introduced for practice in penciling and shading; the figure
represents a water-wheel on a stone pier.
The familiar oil can is shown in fig. 95. These all are excellent
objects for practice.
[Illustration: Fig. 83.--Fig. 84.--Fig. 85.]
[Illustration: Fig. 86.]
[Illustration: Fig. 87.]
[Illustration: Fig. 88.--Fig. 89.--Fig. 90.--Fig. 91.]
[Illustration: Fig. 92.]
[Illustration: Fig. 93.]
[Illustration: Fig. 94.]
[Illustration: Fig. 95.]
[Illustration: Fig. 96.]
[Illustration: GEOMETRICAL DRAWING]
[Illustration]
Geometrical Drawing.
Geometry is the science of measurement; it has been known for more than
three thousand years; many lives have been devoted to its development,
and it exists to-day as the foundation of all mathematics.
Geometrical drawing is the art of representing, to the eye, the problems
“worked out” by geometricians, and the importance of a knowledge of
geometrical drawing is paramount. The student will find that the figures
delineated and explained in the next few pages constantly occur in
mechanical drawing. Says Walter Smith, State Director of Art Education
in Massachusetts, “I have never known a case where a student did not
progress more satisfactorily in his studies after a course of practical
geometry.”
The elementary conceptions of geometry are few:
1.--A point.
2.--A line.
3.--A surface.
4.--A solid, and
5.--An angle.
All of which elements are used in mechanical drawings.
From these, as data, a vast number of mathematical problems have been
deduced; of which a few of the most elementary will be illustrated in
this work; but these few will repay the attention of the student.
In “freehand” drawing the crayon and pencil are used; in geometrical
drawings the dividers, as shown in illustration, fig. 97, together with
a rule, are all that is necessary to accomplish the work.
A problem is something to be done, and geometry has been defined as the
science of measurement; the relation between geometry and mechanical
drawing is very close, hence the term “geometrical problem.”
[Illustration: Fig. 97.]
[Illustration: Fig. 98.]
Before proceeding with the examples, a few elementary statements
belonging to the science of geometry are presented; these will be useful
to the student, not only while “doing” the problems, but in many cases
of every-day--future--experience.
Geometry is one of the oldest and simplest of sciences; it may be
defined as _the science of measurement_; geometry is _the root_ from
which all regular mathematical calculations issue. It has claimed the
best thought of practical men from the times of the Greeks and Romans
two thousand years ago; they derived their knowledge of the science from
the Egyptians, who in turn were indebted to the Chaldeans and Hindoos in
times beyond any authentic history; hence it was under the operations of
the laws explained in geometry, that the pyramids of Egypt and the
temples of Greece were constructed, as well as the engines of war and
appliances of peace of ancient times.
_A point_ is mere position, and has no magnitude.
_A line_ is that which has extension in length only. The extremities of
lines are points.
_A surface_ is that which has extension in length and breadth only.
_A solid_ is that which has extension in length, breadth and thickness.
_An angle_ is the difference in the direction of two lines proceeding
from the same point.
[Illustration]
Lines, Surfaces, Angles and Solids constitute the different kinds of
quantity called _geometrical_ magnitudes.
_Parallel lines_ are lines which have the same direction; hence parallel
lines can never meet, however far they may be produced; for two lines
taking the same direction cannot approach or recede from each other.
[Illustration]
An _Axiom_ is a self-evident truth, not only too simple to require, _but
too simple to admit of demonstration_.
A _Proposition_ is something which is either proposed to be done, or to
be demonstrated, and is either a problem or a theorem.
A _Problem_ is something proposed to be done.
A _Theorem_ is something proposed to be demonstrated.
A _Hypothesis_ is a supposition made with a view to draw from it some
consequence which establishes the truth or falsehood of a proposition,
or solves a problem.
A _Lemma_ is something which is premised, or demonstrated, in order to
render what follows more easy.
A _Corollary_ is a consequent truth derived immediately from some
preceding truth or demonstration.
A _Scholium_ is a remark or observation made upon something going before
it.
A _Postulate_ is a problem, the solution of which is self-evident.