The mathematical principles of natural philosophy by isaac newton pdf - Web Education

NEWTON

S

PRINCIPIA.

THE

MATHEMATICAL

PRINCIPLES

OF

NATURAL

_PHILOSOPHY,

BY

SIR

ISAAC

_NEWTON;

TRANSLATED

INTO

ENGLISH

BY

ANDREW

MOTTE.

TO

WHICH

IS ADDKTV

NEWTON

S

SYSTEM

OF

THE

WORLD

;

Witha Portraittaken fromthe Bustin the

Royal ObservatoryatGreenwich.

FIRST

AMERICAN

EDITION,

CAREFULLY

REVISED

AND

CORRECTED,

WITH

A LIFE OF

THE

AUTHOR, BY PI. W. _CHITTENDEN, M. A., &e.

NEW-YORK

p*-Kntered_accordingtoAct_{of Congress,}intheyear1846,by

DANIEL

ADEE.

3!Ltht ClerksOffice uttiieSouthernOisli:ctCourtofNew-York.

TWuey *Lockwoof,Stom

TO

THE

TEACHERS

OF

THE

NORMAL

SCHOOL

OF

THE

STATE OF

NEW-YORK.

GENTLEMEN

!

A

stirring freshness in the air,

and

ruddy

streaks

upon

the

horizon of the

moral

world betoken

the _grateful

_dawning

of a

new

ora.

The

_days

of_{a drivelling instruction} are _departing.

With

us is the

_{opening promise}

of a better _time,

_{wherein genuine}

man

hood

_doing

its noblest

work

shall

have

_adequate

reward.

TEACHER

is _{the highest}

and

most

_responsible office

man

can

fill.

Its _{dignity is,}

and

will _yet

be

held

commensurate

with

its

_duty

a

duty boundless

as

man

s intellectual _capacity,

and

_great as his

moral

need

a

_{duty from}

the

_{performance of}

which

shall

emanate

an

influence not limitedto the

now

and

the _here,

but

which

_surely

will, as

time

flows into eternity

and

space

into infinity, roll up, a

measureless

curse or a

measureless

_blessing, in inconceivable swellings

along

the infinite curve. It is

an

office that

should

be

esteemed

of

even

sacred

_import

inthis_country.

Ere

_long

a

hun

dred

_millions,

_extending

from

the Atlantic to the _Pacific,

from

Baffins

Bay

to that of

_Panama,

shall call

themselves

American

citizens.

What

a field for those

two

_{master-passions}

of

the

hu

man

soul the love of Rule,

and

the love of

Gain

!

How

shall

our

liberties continue to

_{be preserved from}

_{the graspings of}

Am

bition

and

the _corruptions

of

Gold

?

Not by

Bills of

_Rights

4

DEDICATION.

Constitutions,

and

Statute

Books

; but alone

by

the rightlyculti

vated

hearts

and heads of

the

PEOPLE.

_They

must

themselves

guard

the

Ark.

It is

yours

to tit

them

for the consecrated charge.

Look

well to it: for

you

appear

clothed in the

_majesty

of

_great

_power

! It is

yours

to fashion,

and

to inform, to save,

and

to_perpetuate.

You

are the

Educators

of the

_People

:

_you

are the

_prime

Conservators

of the _public weal.

_Betray

_your

trust,

and

the sacred fires

would go

out,

and

the altars

crumble

into dust:

_knowledge

become

lost in _tradition,

and

Christian

no

bleness a fable!

As

_{you, therefore,} are _multiplied in

number,

elevated in _{consideration, increased} in

_means,

and

_fulfill,well

and

faithfully, all the

requirements

of true

Teachers,

so shall

our

fa

voured

land lift

_up

her

head

_among

the nations

of

the _earth,

and

call herself blessed.

In _conclusion,

_Gentlemen,

to _you, as the

_conspicuous

leaders

in the vast

and honourable

labour

_{of Educational Helbrm, ana}

Popular Teaching,

the First

American

Edition

of the

PRINCIPIA

ol

Newton

_{the greatest}

w

r

ork

of the _greatest

Teacher

is

most

respectfully dedicated.

THAT

the

PRINCIPIA of

Newton

should

have

remained

so

_gen

erally

unknown

in this

country

to the present

day

is a

somewhat

remarkable

fact

;

because

the

name

of

the author, learned

with

the

_{very elements}

of _science, is

revered

at

_every

hearth-stone

where knowledge and

virtue are

of

_{chief esteem, while, abroad,}

in all the

_high

_places

of

the _land, the character

which

that

name

recalls is held

_up

as the noblest illustration

of

what

MAN

_may

be,

and

_may

do, in the possession

and

manifestation

of pre-eminent

intellectual

and moral

worth

;

because

the

work

is_{celebrated, not}

only

in the history

of

one

career

and

one mind, but

in the history

ofall

achievement and

human

reason _itself;

because of

the _spirit of_inquiry,

which

has

been

_aroused,

and

_which,

in

_pursuing

its

searchings, is not

_always

satisfied

_{with stopping}

short

of

thefoun tain-head of

_any

_given

truth ; and, finally,

because

of the earnest

endeavour

that has

been

and

is _constantly

_going

_on, in

_many

sections of the Republic, to elevate the

_{popular standard}

of

edu

cation

and

_give to scientific

and

other efforts a _higher

and

a

better aim.

True,

the

PRINCIPIA

has

been

hitherto inaccessible to

_popular

use.

A

few

_copies in Latin,

and

_occasionally

one

in

English

may

be

found

in

some

of our

_{larger libraries,} or in the _possession of

some

ardent _{disciple of the great}

Master.

But

a

d^ad

_language

in the

one

_case,

and

an

enormous

_price in _{both, particularly} in

that

of

the

_English

_edition,

have

thus far

_opposed

_very

sufficient

obstacles to the

wide

circulation of the

work.

It is

_now,

how

ever,

placed

within the

reach of

all.

And

in

_performing

this la

bour, the

utmost

care has

been

taken,

by

collation, revision,

and

otherwise,to

render

the First

American

Edition

the

most

accurate

and

beautiful in

our

_language. u

Le

_plus

beau

monument

_que

l

?

on

_{puisse clever}

a

la _gloire

de

_Newton,

cest

une

bonne

edition

V:

_{INTRODUCTION TO}

set up.

The

PRINCIPIA,

above

all,

glows

with

the

immortality

of

a transcendant

mind.

Marble and

brass dissolve

and

_pass

_away

;

but

the true creations

of

_{genius endure,} in

time

and

_beyond

_time,

forever :

_high

upon

the

adamant

of the indestructible,

_{they send}

forth afar

and

_near,

over

the troublous

waters of

life, a pure,

un

wavering, quenchless

light

whereby

the

_myriad

_myriads

_{of barques,}

richly laden

with

reason, intelligence

and

various faculty, are

guided through

the _night

and

the _storm,

_by

the _{beetling shore}

and

the

hidden

_{rock, the}

breaker

and

the _{shoal, safely into}

havens

calm and

secure.

To

the teacher

and

_{the taught, the scholar}

and

the_{student, the}

devotee

of

Science and

the

_{worshipper of Truth,}

the

PRINCIPIA

must

ever

continue to

be

of

inestimable value. If to

educate

means,

not so

much

to store the

_memory

with

_{symbols and}

facts,

as to _bring forth the facultiesof the soul

_{and develope}

them

tothe

full

_by

_{healthy nurture}

and

a

_hardy

discipline, then,

what

so effec

tive to the

_{accomplishment}

of that

end

as the

_study

of

Geometri

cal _Synthesis ?

The

_Calculus, in

some

_shape

or other,is,indeed,

necessary

to the successful prosecution of researchesin_{the higher}

branches of

_philosophy.

But

_{has not the Analytical}

encroached

upon

the Synthetical,

and

Algorithmic

Formulae

been

employed

when

not _requisite, either for the evolution of truth, or

even

its

apter illustration?

To

each

method

belongs,

undoubtedly,

an

appropriate use.

Newton,

himself

the inventor

of

Fluxions,

censured

the

_handling

of

Geometrical

_subjects

_by

_Algebraical

calculations;

and

the

maturest

opinions

which

he expressed

were

additionally in favour

of

the

Geometrical

Method.

His

prefer ence, so strongly

marked,

is not to

be

reckoned

a

mere

matter

oi

taste

;

and

his authority

should bear with preponderating weight

upon

the decision of

_every

instructor in

_adopting

what

_may

be

deemed

_{the best plan} to insure the

_completes!

mental

_develop

ment.

_Geometry,

the

_{vigorous product}

of

remote time

;

blended

with

the _{earliest aspirations} of

Science

and

the earliest _applica tions of

Art

; as well in the

measures

of

music

as in the

move

ment

_{of spheres}; as

wholly

inthe structure of the

atom

as in that

of

the

_world;

_directing

MOTION

and

_shaping

_APPEARANCE;

in a

view, the

outward

form of

that

Inner

_Harmony

of

which and

in

which

all _things are. _{Plainly, therefore, this}

noble

_study

has

other

and

_infinitely

_higher

uses than to increase the

_power

of ab

straction.

A

more

_general

and

_thorough

cultivation

of

it should

oe strenuously insisted on.

_{Passing from}

the

_{pages of Euclid}

or

Legendre,

might

not the student

be

led, at the suitable time, to

those

of

the

PRINCIPIA wherein

_Geometry

_may

be found

in varied use

from

the familiar to the

sublime

?

The

_profoundest

and

the happiest results,it is _believed,

would

attend

_upon

this

_enlargement

of

_{our Educational System.}

Let

the PRINCIPIA, then,

be

gladly

welcomed

into

every Hall

where

a

TRUE TEACHER

_presides.

And

_they

who

are

_guided

to

the diligent

study

of

this

incomparable

work,

who

become

strengthened

by

its _reason,

assured

_by

its _evidence,

and

_enlight

ened

_by

its_truths,

and

who

rise into _loving

communion

with

the great

and

pure

spirit

of

its author, will

go

forth

from

the scenes

of

their _pupilage,

and

take their _places in the

world

as

strong-minded,

right-hearted

men

such

men

as the

Theory

of our

Government

_contemplates

and

its _{practical operation}

absolutely

SIE

ISAAC

NEWTON.

Necfasest_{proprius mortal? attingere}Divos. HALLEY.

FROM

the thick

darkness of

the

_{middle ages}

man

s _struggling

spirit

emerged

as in

new

birth ;

breaking

out

of

the iron control

of

that

_period

;

growing

strong

and

confident in the

tug

and

din

of succeeding

conflict

and

_revolution, it

bounded

forwards

and

upwards

with

resistless

_vigour

to_{the investigation of physical}

and

moral

truth

;

ascending

height after height ;

sweeping

afar

over

the earth, penetrating afar

up

into the

heavens

; increasing in

en

deavour, enlarging in

endowment

;

every

where

boldly, earnestly

out-stretching, till, in the

AUTHOR

of

the PRINCIPIA,

one

arose,

who,

grasping

the

master-key of

the universe

and

treading its

celestial paths,

opened up

to the

human

intellect the

_stupendous

realities

of

_{the material world, and,} in _{the unrolling}

of

its

harmo

nies,

gave

to the

human

heart a

new

_song

to the

_{goodness, wis}

dom, and

majesty

of

the all-creating, all-sustaining, all-perfect

God.

Sir Isaac

_Newton,

in

whom

the _{rising intellect}

seemed

to_attain, as it

_were,

to its

_culminating

point,

was

born

on

the

25th

of

De

cember, O.

S.

1642

Christmas

_day

at

_Woolsthorpe,

in the parish of

Colsterworth,

in Lincolnshire.

His

_father,

John

New

ton, died at the

age of

thirty-six,

and

only

a

few months

after his

marriage

to

Harriet

Ayscough,

daughter

of

James

Ayscough,

oi

Rutlandshire.

Mrs.

_Newton,

_probably

_wrought

_upon

_by

the early loss of

her husband,

gave premature

birth to

_{her only and}

posthumous

child,

of which,

too,

from

its

extreme

diminutiveness,

she

_appeared

likely to

be

soon

bereft.

Happily,

it

was

otherwise

decreed

!

The

tiny infant,

on

whose

little

10

LIFE

OF

SIR ISAAC

NEWTON.

so

_doubtingly

hovered, lived ; lived to a

vigorous

maturity,to a

hale old

_age

; lived to

become

the boast of

his_{country, the}

won

der

of

his time,

and

the "ornament ofhis srjecies."

Beyond

the grandfather,

Robert Newton,

the

descent

of

Sir Isaac

cannot with

_certainty

be

traced.

Two

traditions

were

held

in the _family: _one, that

they

were

of

Scotch

extraction ; the

other, that

_they

came

originally

from

Newton,

in Lancashire, dwelling, for a time,

however,

at

_Westby,

_county

of Lincoln,

be

forethe

removal

to

_{and purchase}

of

_Woolsthorpe

about

a

hundred

years

before this

memorable

birth.

The widow

Newton

was

left

with

_{the simple}

means

of a

com

fortable subsistence.

The

_Woolsthorpe

estate _together

with

small

one

which

she

_possessed

at

_Sewstern,

in_{Leicestershire, yield}

ed her an

income

of

some

_eighty

_pounds

;

and upon

thislimited

sum,

she

had

to _{rely chiefly} for the

_{support of}

_herself,

and

the

educa

tion of

her

child.

She

continued

his

nurture

for three _years,

when,

marrying

again,she confided the

tender charge

to the care

of

her

own

mother.

Great

_genius is

seldom

marked

_by

_precocious

_development

;

and

_young

Isaac, sent, at the usual age, to

two

day

schools at

Skillington

and

Stoke, exhibited

no

unusual

traits of character. In his twelfth _year,

he

was

_placed

at _{the public school} at

Gran-tham,

and

boarded

at the

house

of

Mr.

Clark,

an

apothecary.

But

even

in this excellent _seminary, his

mental

_acquisitions

con

tinued fora

_{while unpromising}

_enough

:

_{study apparentlv}

had

no

charms

for

him

;

he

was

very

inattentive,

and ranked low

in the

school.

One

_day,

_however,

the

_boy

_immediately

above

our

seem

ingly dull student

gave

him

a severe

kick

in the

stomach

; Isaac,

deeply

affected,

but

with

no

outburst

of

passion,

betook

himself,

with

_quiet, incessant toil, to his

books

;

he quickly passed above

the offending classmate ; yet there

he

stopped

not ; the strong

spirit was, for

once

and

forever,

awakened,

and, yielding to itb

noble impulse,

he

_speedily

took

_up

his _position at the

head

ofall.

His

_peculiar character

_began

now

_rapidly to unfold itself.

Close

_application

_grew

to

be

habitual.

Observation

alternated

with

reflection. "

A

sober, silent, thinking lad," yet, the wisest

Gener-osity,

modesty, and

a love oftruth distinguished

him

then asever afterwards.

He

did not often_join his classmates in _play

; but

he

would

contrive for

them

various

amusements

of a scientific kind.

Paper

kites

he introduced

; carefully

determining

their best

form

and

_proportions,

and

the _position

and

number

_{of points}

_whereby

to attach the _string.

He

also

invented

_paper

lanterns ; these

served

_ordinarily to

_guide

the

_way

to school in

_{winter mornings,}

but

_occasionally for_quite

_{another purpose}

;

they

were

attached to

thetails ofkitesina

dark

_{night, to}the

_dismay

of the

_{country people}

dreading portentous comets,

and

to the

immeasureable

delight ol

his

_companions.

To

_him,

_however,

_young

as

he

was, life

seemed

to

have

become

an

earnest _thing.

When

not

_occupied

with

his studies, his

mind

would

_{be engrossed with mechanical}

contrivances;

now

_imitating,

now

_inventing.

He

became

_singularlyskilful in the use of his little _{saws, hatchets,}

_{hammers, and}

other tools.

A

windmill

was

erected

near

Grantham

;

during

the operations ol

the

_workmen,

he

was

_{frequently present} ; in a short time,

he

had

completed

a _perfect

_{working model}

of it,

which

elicited general

admiration.

Not

_content,

however, with

this

exact

imitation,

he

conceived

the ideaof

_employing,

in_{the place}

of

sails,

animal

power

,

and,

adapting

the construction ofhismillaccordingly,

he

enclosed

in it a

_mouse,

called the _miller,

and

which by

_acting

on

a sort ot

treadvvheel,

gave

motion

to the

machine.

He

invented, too, a

mechanical

_carriage

_having

four wheels,

and

_put

in

motion with

a

handle

_{worked by}

the

_person

_sitting inside.

The

measurement

of

time

_early

drew

his attention.

He

hrst

constructed

a

water

clock, in _proportions

somewhat

like an old-fashioned

house

clock.

The

index

of the dial _plate

was

turned

_by

_{a piece of}

wood

acted

upon by

dropping

water.

This

instrument,

though

long used

by

himself,

and

_by

Mr.

Clark

s _family, did not _satisfy his _inquiring

mind.

His

_thoughts

rose to the

sun

; and,

by

careful

and

oft-re

peated

observations

of

the solar

movements,

he

subsequently

formed

_many

dials.

One

of

these,

named

Isaac

s dial,

was

the

accurate result

_{of years}

_labour,

and

was

_{frequently referred} to

for the

hour of

the

_day

_by

the

_country

_people.

May

we

not discern in these continualefforts the _{diligent re}

12

LIFE

OF

SIR

ISAAC

NEWTON.

of

discovery

the stirring

elements

of

that

wondrous

spirit,

which,

clear, calm,

and

great,

moved,

in after years,

through

deep

onward

through

deep

of

Nature

s _mysteries,

_{unlocking her}

strongholds, dispelling darkness,

educing order

everywhere

si

lently conquering.

Newton

had

an

_early

and

decided

taste for

_drawing.

_Pictures,

taken

sometimes

from

_copies,

but

often

from

life,

and

drawn,

coloured

and framed

_by

himself,

ornamented

his apartment.

He

was

skilled _also, in _{poetical composition,} "

excelled in

_making

verses

;"

some

of

these

were

borne

in

remembrance

and

_repeated,

seventy years

afterward,

by

Mrs.

Vincent,

for

_whom,

in _early

youth, as

Miss

Storey,

he

formed

an

ardent attachment.

She

was

the sister

of

a _physician resident

near

_Woolsthorpe

;

but

Newton

s intimate

_acquaintance

with

her

_began

at

Grantham.

where

_they

were

both

_{numbered among}

the

inmates

of the

same

house.

Two

or three

_years

_younger

than _himself, of _great

per

sonal _beauty,

and

unusual

_talent,

her

_{society afforded}

him

the greatest pleasure ;

and

their youthful friendship, it is believed,

gradually rose to a

higher

passion;

but

inadequacy

of fortune

prevented

their union.

Miss

Storey

was

afterwards

twice

mar

ried

;

Newton,

never;

his

esteem

for

her

continued

unabated

during

life,

accompanied

by

numerous

acts

of

attention

and

kindness.

In

_1656,

Newton

s

mother

was

_again left a

widow

r

,

and

took

up

her

abode

once

more

at

Woolsthorpe.

He

was

now

fifteen

years

ofage,

and

had

made

great progressinhisstudies

;

but

she,

desirous of_{his help,}

and from

motives

of

_economy,

recalled

him

from

school.

Business

_occupations,

however, and

the

_manage

ment

of

_{the farm,}

_proved

_utterly distastefultohim.

When

sentto

Grantham Market

on

_Saturdays,

he

would

betake himself

to his

former

_lodgings in the

_apothecary

s _garret,

where

some

of

Mr.

Clark

s old

_{books employed}

his

_thoughts

till the

_{aged and}

trust

worthy

servant

had

executed

the family

commissions

and

announced

the necessity of return : _or,at other_times,

our

_young

_philosopher

would

seat

himself under

_{a hedge,}

_by

the

_{wayside, and}

continue

his studies till the

same

faithful

_personage

_proceeding

alone to

re-turned.

The

more

immediate

affairs of the

farm

received

no

better attention. In fact, his passion for

study

grew

daily

more

absorbing,

and

his dislike for

every

other

occupation

more

in

tense.

_{His mother,}

_therefore,

_wisely

resolved to _give

him

allthe

advantages

which

an education could

confer.

He

was

sent

back

to

Grantham

_school,

where

he

remained

for

some

months

in

_busy

preparation for his

academical

studies.

At

the

recommendation

of

one

of_{his uncles,}

who

had

himself studied at _{Trinity College,}

Cambridge,

Newton

proceeded

thither,

and

was

duly

admitted.

on

the

5th

_day

of

June

1660,

in the

_{eighteenth year of}

_{his age.}

The

_eager

student

had

now

entered

_upon

a

new

and

wider

field;

and

we

find

him

devoting himself

to the pursuit

of

know

ledge with

amazing

ardour and

perseverance.

Among

other

sub

jects, his attention

was

soon

drawn

to that

of

Judicial

Astrology

He

_exposed

the _folly of this

_{pseudo-science}

_by

_{erecting a figure}

with the aid

of

one

or

two

of the

_problems

of

Euclid

;

and

thus

began

his

_{study of}

the

Mathematics.

His

researches into this

science

were

_prosecuted

with

_{unparallelled}

_{vigour and}

success.

Regarding

the propositions

contained

in

Euclid

as self-evident

truths,

he passed

rapidly

over

this ancient

system

a step

which

he afterward

much

_regretted

and

_mastered,

without

further

_pre

paratory

study, the Analytical

Geometry

of

Descartes.

Wallis

s

Arithmetic

of _Infinites,

Saunderson

s

_{Logic, and}

the

_Optics

of

Kepler,

he

also studied

with

great care ; writing

upon

them

many

comments

; and,

in these notes

on

Walliss

work was

un

doubtedly

the

germ

ofhis_fluxionary calculus.

His

_progress

was

so_greatthat

he found himself

more

_{profoundly versed}

thanhistutor

in

_many

branches

of _learning.

Yet

his _acquisitions

were

not gotten

with

the rapidity ofintuition;

but

they

were

thoroughly

made

and

_firmly secured.

_Quickness

_{of apprehension, or} Intel

lectual

nimbleness

did not

_belong

to him.

He

saw

too far: _his,

insight

was

too deep.

He

dwelt

fully, cautiously

upon

the least

subject;

while

to the consideration

of

the greatest,

he brought

a

massive

_{strength joined}

with

a

matchless

_{clearness, that,}

_regard

less of the

_merely

trivial or

_{unimportant, bore with}

_unerring sa

gacity

upon

the

prominences

of the subject, and,

grappling

with

14

LIFE

OF

SIR ISAAC

NEWTON

His

_early

and

fast _friend,

Dr.

Barrow

in

_compass

of

inven

tion

_only

inferior to

Newton

who

had been

elected Professor of

Greek

in the _University, in

_1660,

was

made

Lucasian Profes

sor

of

Mathematics

in

_{1663, and}

soon

afterward

delivered his

Optical

Lectures

: the

manuscripts

of these

were

revised

by

New

ton,

and

several oversights corrected,

and

_many

important

sug

gestions

made by

him

;

but they

were

not

published

till

1669.

In the

_{year 1665, he}

received the

_degree

of

Bachelor

of

Arts

;

and, in

_{1666, he entered}

_upon

those brilliant

and

_imposing

dis

coveries

which

have

_{conferred inappreciable}benefits

_upon

_science,

and

_immortality

_upon

his

own

name.

Newton,

himself, states that

he

was

in_possession

of

his

Method

of Fluxions, "

in the

_year

_1666,

or before." Infinite _quantities

had

_long

been

_{a subject of}

_profound

_{investigation}

;

among

the

ancients

_by

_{Archimedes, and}

_Pappus

of

Alexandria

;

among

the

moderns

_by

_{Kepler, Cavaleri,}

_Roberval,

Fermat

and

Wallis.

With consummate

_ability

Dr. Wallis

_{had improved upon}

the

la-hours

ofhis

_predecessors

:

with

a

_higher

power,

Newton

moved

forwards

from

where

Wallis

_stopped.

Our

author

first invented

his celebrated

BINOMIAL

THEOREM.

And

then,

applying

this

Theorem

to the rectification _{of curves,}

and

to the

determination

of the surfaces

and

contents

of

_solids,

and

the _position of their

centres

of

gravity,

he discovered

the general principle of

deducing

the areas of

curves

from

the _ordinate,

_by

_{considering the area} as a

nascent

_{quantity, increasing}

_by

continual fluxion in the

_propor

tion

of

the _{length of the ordinate,}

and

_supposing

the abscissa

to increase

_uniformly

in

_proportion

to the time.

_Regarding

lines as

_generated

_by

the

motion of

_points, surfaces

_by

the

motion

of

lines,

and

solids

by

the

motion

of surfaces,

and

considering that

the _{ordinates, abscissae, &c.,}

of curves

thus

_{formed, vary accord}

ing to a regular

law

depending

on

the equation of the curve,

he

deduced from

this

_equation

the velocities

with

which

these

quantities are generated,

and

obtained

by

the rules

of

infinite

series, the ultimate value required.

To

the velocities

with

which

every

line or quantity is generated,

he

gave

the

name

of

FLUX

IONS,

and

to the lines or quantities themselves, that

of

FLUENTS.

intellects: _{that, variously modified,}

has

_proved

of incalculable

service in _aidingto

_develope

the

most

abstruse

and

the _highest ruths in

Mathematics

and

_Astronomy

:

and

that

was

of itself

enough

to

render

_any

name

illustrious in the

crowded

Annals

of

Science.

At

this_{period, the}

most

_{distinguished philosophers}

were

direct

ing all their energies to the subject

of

light

and

the

improvement

of

_{the refracting telescope.}

_Newton,

_having

_applied himself to the grinding

of

_{"opticglasses}

of

other_figures

than

spherical,"

ex

perienced

the impracticability

of executing such

lenses;

and con

jectured that their defects,

and consequently

those of refracting telescopes,

might

arise

from

some

other

cause than

the imperfect

convergency

of rays toasingle point.

He

accordingly

"procured

a _{triangular glass}

_prism

to _try

therewith

the celebrated

_phenom

ena

of colours."

His

_{experiments, entered}

_upon

with

_zeal,

and

conducted with

that _{industry, accuracy,}

and

_{patient thought,} for

which

he

was

so

_remarkable,

resulted in the

_grand

_conclusion,

that

LIGHT WAS

NOT

_{HOMOGENEOUS, BUT CONSISTED OF}

_RAYS,

SOME OF

WHICH

WERE

MORE

REFRANGIBLE

THAN

OTHERS.

This

profound

and

beautiful

discovery

opened up

a

new

era in the

History of

Optics.

As

bearing,

however,

directly

upon

theconstruc

tion of_telescopes,

he

saw

that a lens_{refracting exactly}likea

_prism

would

_necessarily

_bring

the different _rays to different _foci, at

different distances

from

the _{glass, confusing}

and

_rendering

the

vision indistinct.

_Taking

for

_granted

that all

bodies

_produced

spectra of^ jtial length,

he

dismissed all further consideration of the refracting instrument,

and

took

_up

_{the principle}

of

reflection.

Rays

of

all _colours,

he

_found,

were

_{reflected regularly,} sothatthe angle ofreflection

was

_equal

to _{the angle}

of

_incidence,

and hence

he concluded

that _ojitical

instruments

_might

be

_brought

to

_any

degree of perfection

imaginable,

provided

reflecting

specula

of

the _{requisite figure}

and

finish

could

be

obtained.

At

this _stage

of_{his optical researches,}

he

was

forced to leave

_Cambridge

on

account of

the

_plague

which

was

then

_desolating

England.

He

retired to

_Woolsthorpe.

The

old

_manor-house,

in

which

he

was

_born,

was

situated in a beautifullittle_valley,

on

the

west

side

of

the river

Witham

;

and

here

in _{the quiet}

home

ofhis

_boyhood,

16

LIFE

OF

SIR ISAAC

NEWTON.

he passed

his

days

in serene contemplation,

while

the stalking

pestilence

was

hurrying

its tens

of

thousands

into _{undistinguisha} ble _graves.

Towards

the close

of

a _pleasant

_day

in the _early

autumn

of

1666, he

was

seated alone

beneath

a _{tree, in}his_garden,

absorbed

inmeditation.

He

was

a _slight

_young

man

; in the

twenty-fourth

year of

his

age

; his

countenance mild

and

full _{of thought.}

For

a

_century

_{previous, the science}

of

_Astronomy

had advanced

with

rapid strides.

The human

mind had

risen

from

the

gloom

and

bondage

of

the

middle

ages, in unparalleled vigour, to unfold the

system, to investigate the

phenomena, and

to establish the

laws

of

the

_heavenly

bodies.

_Copernicus,

_Tycho

_Brahe,

_Kepler,

Galileo,

and

others

had

prepared

and

lighted the

way

for

him

who

was

ta

_give to their

labour

its_{just value,}

and

to their_genius

its true lustre.

At

his

_bidding

isolated facts

were

to

take order

as _{parts of}

one

harmonious

_whole,

and

_{sagacious conjectures}

_grow

luminous

in the certain

_splendour

of

demonstrated

truth.

And

this ablest

man

had

come

was

here.

His

mind,

familiar

with

the

_knowledge

of

_past effort,

and

its

unequalled

faculties

develop

ed

in

transcendant

_strength,

was

now

_moving

on

to the

_very

threshold

of

Its

_{grandest achievement.}

_Step

_by

_{step the}

untrod

den

_path

was

measured,

till, at length,

the

entrance

seemed

dis closed,

and

the tireless

_explorer

to stand

amid

the first

_opening

wonders

of

the universe.

The

nature of

_gravity that

_mysterious

_power

which

causes

all bodies to

descend

towards

the centre

of

the earth _had, in

deed,

dawned

upon

him.

And

reason

busily united link to link

of

that chain

which

was

_yet

to

be

_{traced joining the} least to the

vastest, the

most remote

to the nearest, in

one

harmonious

bond.

From

the

bottoms

of

the

_deepest

caverns

to the

summits

of

the

highest mountains, this

power

suffers

no

sensible

_change

:

may

not

its action,then,

extend

tothe

moon

?

_Undoubtedly

:

and

furthei

reflection

convinced

him

that

such

a

_power

_{might be}

.sufficientfor

retaining that

luminary

in

her

orbit

round

theearth. But,

though

this

_power

suffers

no

sensible variation, in the little

_change

of

distance

from

the earths centre, at

which

_{we may}

place

our-.

more

or less

diminution

?

The

_conjecture

appeared

most

proba

ble : _and, in

order

to estimate

what

the

_degree

of diminution

might

be,

he considered

that ifthe

moon

be

retained in

her

orbit

by

the force of_gravity, the

_primary

_planets

must

also

be

carried

round

the

sun

_by

the like

_power;

_and,

_by

_comparing

_{the periods}

of the several planets

with

their distances

from

the _sun,

he found

that, if

_they

were

held in their courses

_by

_any

_power

like_gravity,

its _strength

must

decrease

in _{the duplicate}

_proportion

of

the in

crease ofdistance. In

_forming

this _conclusion,

he

_supposed

the planets to

move

in perfect circles, concentric to the sun.

Now

was

this the

law

of the

moon

s

motion

?

Was

such

a _force,

em

anating

from

the earth

and

directed to the

moon,

sufficient,

when

diminished

as the

_square

of the _{distance, to} retain

her

in her

orbit ?

To

ascertain this _master-fact,

he

_compared

the

_space

through

which heavy

bodies

fall, in a

second

of time,at a

_given

distance

from

the centre

of

the earth,

_namely,

at its _surface,

with

the

_{space through}

which

the

moon

falls, as it _were, to the _earth,

in the

same

time,

while

revolving in a circular orbit.

He

was

absent

from

books

; and, therefore, adopted, in

computing

the

earths _{diameter, the}

common

estimate of_{sixty miles} to a

_degree

of latitude as

then

in use

_among

_geographers

and

_navigators.

The

result of his calculations did _{not, ot course,}

answer

his

ex

pectations; hence,

he

concluded

that

some

other cause,

beyond

the

reach

of observation _{analogous, perhaps,} to the vortices

of

Des

cartes _joined its action to that

of

the

_power

of

_gravity

_upon

the

rnooil.

_{Though by}

no

means

satisfied,

he

yet

abandoned

awhile

further _inquiry,

and

remained

_totally silent

_upon

the _subject.

These

_rapid

marches

in the career _{of discovery,}

combined

with

the

_youth

of

_Newton,

seem

to evince a _penetration the

most

lively,

and an

invention the

most

exuberant.

But

in

him

there

was

a _conjunction

of

influences as

extraordinary

as fortunate.

Study,

unbroken,

persevering

and profound

carried

on

its

inform

ing

and

disciplining

work

upon

a genius, natively the greatest,

and rendered

freest in its

_movements,

and

clearest in its vision,

through

the

untrammelling

and

enlig}tenirig

power

of

_religion.

And,

in this

_happy

concurrence, areto

_{be sought}

the

elements

of

18

LIFE

OF

SIR ISAAC

NEWTON.

minute

and

the _stupendous,

_brought

_{these successively} to _light,

and caused

science to

make them

her own.

In

_1667,

Newton

was

made

a

Junior

Fellow

; and,

in the

_year

following,

he took

his

degree

of

Master

of Arts,

and

was

appoint

ed

to a

Senior

_Fellowship.

On

his return to

_Cambridge,

in

_{1668, he}

resumed

his _optical labours.

_Having

_{thought of}

a delicate

method

_{of polishing metal,}

he proceeded

to the construction of his

_newly

_projected reflect

ing telescope ; a small

specimen of

which

he

actually

made

with

his

own

hands, It

was

six inches

_long

;

and

magnified

about

forty

times

; a

power

greater

than

a refracting

instrument of

six

feet

tube

could

exert

with

distinctness. _Jupiter,

with

his four

satellites,

and

the horns, or

moon-like

phases

of

Venus

were

plainly visible

through

it.

THIS

WAS

THE

FIRST

REFLECTING

TELESCOPE

EVER

EXECUTED

AND

DIRECTED

TO

THE

HEAVENS.

He

_{gave an account}

ofit, inalettertoafriend,

dated

February

23d,

1668-9

a letter

which

is also

remarkable

for _{containing the}firs

allusion to his discoveries "

concerning

thenature oflight."

En

couraged

by

the success ofhis first

_{experiment, he}

_again

executed

with

his

own

_hands,

not

_long

afterward, a

second

and

superior

instrument

of the

same

kind.

The

existence

of

this

_having

come

to the

_knowledge

of the

_Royal

_{Society of}

_London,

in

_{1671, they}

requested

it of

Newton

for examination.

He

_accordingly

sent it

to

them,

It

excited

_great

_admiration;

it

was shown

to _{the king*}

a

_drawing

and

_{description of}it

was

sent to Paris

;

and

the

tele-scope

itself

was

carefully

preserved

inthe

_Library

of the _Society.

Newton

lived to see his invention in _{public use,}

and

of

eminent

service inthe

cause

ofscience.

In the _spring of

_{1669, he}

wrote

to his friend

_{Francis Aston,}

Esq.,

then about

setting out

on

his travels, a letter

of

advice

and

directions, it

was

dated

_May

_18th,

and

is

interesting as exhibit ing

some

of the

prominent

features in

Newton

s character.

Thus

:

"

Since

in

_your

letter

_you

_give

me

so

much

_libertyof

_spending

my

judgment

about

what

may

be

to

_your

_advantage

in_travelling,

1 shall

do

it

more

_freely

than perhaps otherwise

would

have

been

decent, Fir,c

which, I bolieAe,

you

have

considered

already

; but if

any

of

them

be

new

to _you,

_they

_may

excuse

the rest

; if

none

at all,

yet is

_my

_punishment

more

in _writing

_{than yours}

in _reading.

"When

_you

come

into

_any

fresh

_company.

1.

Observe

their

humours.

2. Suit

_your

own

_{carriage thereto,}

_by

which

insinua

tion

_you

will

make

their

converse

more

free

and

_open. 3.

Let

your

discourse

be

more

in _queries

_{and doubtings}

than

_peremptory

assertions or _disputings, it

_being

the design of_{travellers to learn,}

not to teach. Besides, it will

_persuade

_your

_acquaintance

that

you

have

the greater

esteem

of

them, and

so

make them more

ready

to

communicate

what

they

know

to

you

;

whereas

nothing

sooner

occasions _disrespect

and

_quarrels

than

_{peremptoriness.}

You

will find little or

_{no advantage}

in

_seeming

wiser

or

much

more

_ignorant

than

_your

_company.

4.

Seldom

discommend

any

thing

though

never

so bad, or

do

it

_{but moderately,}

lest

_you

be

unexpectedly

forced to an

unhandsome

retraction. It is safer to

commend

_any

_thing

more

than it _deserves,

than

to

discommend

a _{thing so}

much

as it _deserves; for

commendations

meet

not

so often

with

_oppositions, or, at least, are not _usually so ill re

sented

_by

men

that think _otherwise, as

discommendations

;

and

you

will insinuate into

men

s favour

_by

_{nothing sooner than}

seem

ing to

approve

and

commend

what

they

like

;

but

beware

o

doing

it

_by

_comparison.

5. If

_you

be

affronted, it is _better, in c

foreign country, to pass it

_by

in _silence,

and

with

a _jest,

_though

with

some

dishonour,

than

to

_{endeavour revenge}

; for,

in the first

case,

your

credits

ne

er the

worse

when

_you

return into

_England,

or

come

into other

_company

that

have

not

heard

of the _quarrel. But, in the

second

_case,

_you

_may

bear

the

marks

of the _quarrel

while

_you

_live, if

_you

outlive it at all. _But, if

_you

find _yoursell

unavoidably engaged,

tis _best, I think, if

_you

can

command

_your

passion

and

language, to

keep them

pretty

evenly

at

some

certain

moderate

_pitch, not

much

_heightening

them

to

_exasperate

_your

adversary, or

provoke

his friends,

nor

letting

them

grow

overmuch

dejected to

make

him

insult. In a

word,

if

_you

can

_keep

reason

above

_passion, that

and watchfulness

will

be

_your

bestdefendants.

To

which

_purpose

_you

_may

consider, that,

though

such

excuses

20

LIFE

OF

SIR ISAAC

NEWTON.

among

friends,

_yet

amongst

strangers

they

are insignificant,

ina

only

argue

a travellers

weakness.

"

To

these I

_may

add

some

_general

heads

for _inquiries or

ob

servations,

such

as at present I

can

think on. As, 1.

To

observe

the _policies, wealth,

and

state affairs of _nations, so far as a

soli-f

ary

traveller

may

conveniently

do. 2.

Their

impositions

upon

all sorts

of

_people, trades, or

commodities,

that are

remarkable.

3.

Their

laws

and

customs,

how

far

_they

differ

from

ours. 4.

Their

trades

and

arts

wherein

_{they excel}

or

come

short of us in

England.

5.

Such

fortifications as

_you

shall

meet

with, their fashion, strength,

and

advantages

for _defence,

and

other

such

mili

tary affairs as are considerable. 6.

The

power

and

respect

be

longing to their

degrees of

nobility or magistracy. 7. It will not

be

_{time misspent}

to

make

a

_{catalogue of}

the

names and

excellen

cies of those

men

that are

most

_{wise, learned, or}

esteemed

in

_any

nation. 8.

Observe

the

mechanism and

manner

_{of guiding}

_ships.

9.

Observe

the

_products

of

Nature

in several_{places,especially} in

mines,

with

the

circumstances of mining

and

of

extracting metals or minerals out

of

their _ore,

and

of

_refining

them

;

and

if

you

meet

with

_any

transmutations out

of

their

own

_species into

another

_(as out of iron into _{copper, out}

of

_any

metal

into

quick

silver, out of

one

salt into another, or into

an

insipid

body,

&c.),

those,

above

all, will

be

worth your

noting,

being

the

most

lucif-erous,

and

many

times

lucriferous

_experiments,

too, in _philosophy.

10.

The

_prices of diet

and

other _things. 11.

And

the _staple

commodities

of_places.

"

These

generals

(such

as at present I

could

think of), if

they

will serve for

_nothing

else, yet

they

may

assist

you

in

_{drawing up}

a

model

to_regulate

_your

travels_by.

As

_{for particulars,}thesethat

follow are all that 1

can

now

think of, viz. ;

whether

at

Schem-nitium, in

_Hungary

_(where

there are

mines of

_{gold, copper, iron,}

vitriol,

antimony,

&c.).

they

change

iron into

copper

by

dissolving

t in a vitriolate water,

which

they

find in cavities

of

rocks

in the

mines,

and then melting

the

slimy

solution in a stroiig fire,

which

in _{the cooling}

_proves

_copper.

The

like issaid to

be

done

inother

places,

which

I

cannot

now

remember

; perhaps, too, it

may

be

a certain vitriol

came

from thence

_(called

Roman

_vitriol), but of a

nobler

virtue

than

that

which

is

now

called

_by

that

name

;

which

vitriol is not

now

to

be

_{gotten, because, perhaps,}

_they

make

a _{greater gain}

_{by some}

such

trick as _turning iron into

_copper

with

it

than

_by

_selling it. 2.

_Whether,

in

Hungary,

Sclavonia,

Bohemia,

near

the

town

Eila, or at the

mountains

of

Bohemia

near _Silesia, there

be

rivers

whose

waters

are

_{impregnated with}

gold ; perhaps, the

gold being

dissolved

by

some

corrosive

water

like

_aqua

_regis,

and

the solution carried

_{along with}

the _stream,

that runs

_through

the mines.

And

whether

_{the practice of laying}

mercury

in the _rivers, till it

be

_tinged

with

_gold,

and

then

strain

ing the

mercury

through

leather, that the

gold

may

stay behind,

be

a secret _yet, or

_openly

_practised. 3.

There

is

_newly

con

trived, in Holland, a mill to

_grind

_{glasses plane withal,}

and

I

think polishing

them

too;

perhaps

itwill

be

worth

the

while

to see

it. 4.

There

is in

Holland

one

_Borry,

who

some

_years

since

was

_imprisoned

_by

the

_Pope,

to

have extorted

from

him

secrets

(as I

am

told) of great

worth, both

as to

medicine

and

profit,

but

he escaped

into

_Holland,

where

_{they have granted}

him

a _guard.

I think

he

_usually

_goes

clothed in _green.

_Pray

_inquire

_{what you}

can of

him,

and whether

his ingenuity

be

any

profit tothe

Dutch.

You may

inform

_yourself

whether

the

Dutch

have

_any

tricks to

keep

their _ships

from

_being

all

worm-eaten

in their

voyages

to

the Indies.

Whether

_pendulum

clocks

_{do any}

service in _finding

out the longitude,

&c.

"

I

am

_{very weary, and}

shall not _stay to _part

with

a _long

compliment, only

I

wish

you

a

_good

_journey,

and

God

be with

you."

It

was

not till the

month

of

_June,

_1669,

that

our author

made

known

his

Method

of Fluxions.

He

then

communicated

the

work

which

he

had

_composed

_upon

the _subject,

and

_entitled,

ANALYSIS PER

EQUATIONES NUMERO TERMINORUM

INFINITAS,

to his friend

Dr. Barrow.

The

latter, ina letter

dated

20th

of

the

same

month,

mentioned

it to

Mr.

Collins,

and

transmitted it to

him,

on

the

31st

of

July

thereafter.

Mr.

Collins greatlyapprov>

ed

of the

work

;

took

a

_copy

of it

;

and

sent the original

back