The essential of perspective

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VPL RESEARCH LIBRARIES

3 3433 081 912 9 2

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THE ESSENTIALS OF PERSPECTIVE
IVITH ILLUSTRATIONS

DRAIVN BY THE AUTHOR.

BY

M,

W. MILLER
Art of
the Pennsylvania

Principal of the School of Industrial

Museum, Philadelphia

6^

DISCARD^ tJ.
1887

NEW YORK

CHARLES SCRIBNER'S SONS

ItHE

new YORK

[PUBLIC LIBRARY

475873
LtViO'i. »HtTtLCEV Fi-NDATi;**.

A8TDR,

Copyright, 1887, by Charles Scribner's Sons

TROW'8

NO BOOKBINOrNQ COMPAN". NEW TORK.

(V\6l4-

PREFACE.
book
"

CALL

this little

The Essentials

of Perspective," because
it

it

seems to

me

that

it

contains as

much

I
I

information about the science of which

treats as the artist or the

draughtsman ever hasoccasion to

make

use

of,

except under the most unusual conditions.
in the principles or possible applications of per-

do not claim to have discovered any new thing, either

spective science.

But

it

has occurred to me, as I

know

it

has occurred to

many

others with a similar ex-

perience in teaching drawing, that a book on perspective, which should beexhaustive enough to redeem the

study from the contempt with which
extent, justified

it is

too often treated
it

by

artists

—an

estimate which

is,

to a considerable

by such presentations
as far as possible,

of

as

ai-e

usually found in the " hand-" and " text-books " in
difficulties

common

use

— and yet
If,

fi'ee,

from the technical
might beof
use.

which the

unscientific

mind

is

pretty sure

to encounter in the profounder treatises,

on glaucing through the book, some things are found to have been

left

out which are usually intro-

duced into a work of
this

this kind, I ask the reader to look twice before he finds fault

with the omission, as
I

weeding out of what have seemed, to me, unessentialthings has been the means on which

have mainly

relied in the efEoit to

make

clear the really important truths.

I

have aimed,

too, to

make

the illustrations such

as should seem to connect the study with the

work of the

artist rather

than to use them as diagrams by

which to demonstrate
of letters of reference.
It

abstractions,, and such also as might,for the

most

part, be understood

without the help

may be

of interest to teachers of drawing to

know

that these illustrations are of precisely the aame
;

character as those which I have used for

many

years in teaching perspective from the black-board

and while

vi

PREFACE.

pupils do not always

make
and

as

good transcripts of them
the

in theirnote-books as one would like to
is

see,

they make
infi-

them
nitely

quite good enough to

fix in

mind the

lesson which each

intended to convey, and find them

more

interesting

jjractical

than the pure theory to which they are so often treated in counettion

with

this

branch of study.
^vho cares to go farther in the scientific study of perspectivethan I have attempted to lead

The reader
him
will find
"

Modern

Persi^ective,"

by Professor W. E. Ware, of Columbia

College, the best

book for
and I

his

purpose.

Mr.
sure his

Ware was my

teacher,

and

I

have to thank him for the most that I know about the subject
of
it

;

am

work remains the most masterly and thorough presentation

which hasyet been made.
L.

W. M.

Philadelphia, March, 1887.

CONTENTS.
FAO£

CHAPTER CHAPTER CHAPTER
CHAPTER

I.

FIRST PRINCIPLES

1

n.
HI.
IV.
V.
VI.

THE HORIZON
MEASUREIVIENT BY IMEANS OF PARALLELS

11

21

MEASUREMENT BY MEANS OF DIAGONALS MEASUREMENT BY MEANS OF TRIANGLES

33

CHAPTER CHAPTER
CHAPTER

43
59 63
74

THE PERSPECTIVE OF CURVES
A QUESTION...
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