Copyright
Lincoln Phelps.

Lectures to young ladies, comprising outlines and applications of the different branches of female education, for the use of female schools, and private libraries online

. (page 21 of 27)
Online LibraryLincoln PhelpsLectures to young ladies, comprising outlines and applications of the different branches of female education, for the use of female schools, and private libraries → online text (page 21 of 27)
Font size
QR-code for this ebook


England, has, in those countries, received much attention.
' The most remarkable discovery,' says Bakewell, ' that
has been made respecting the tertiary deposites, is, that
many of them contain the remains of mammiferous*
quadrupeds, as perfect in their organization as any of the
existing species of land quadrupeds, but most of them
belonging to genera or species that are extinct. The
tertiary strata are further remarkable for presenting the
frequent alternation of beds containing the remains of
marine animals, with other beds that contain the bones
of land animals or fresh water shells. It appears that
tertiary strata were chiefly formed in detached inland
seas, or lakes.'

When commencing the science of geology, a pupil
may very naturally imagine that to be but a trifling
study, which directs the attention to a mere stone, such
as may at any time be seen in the street ; he may be ready
to say, ' It seems a very little thing, to know that this, a
piece of rock, is granite, and that granite is composed of
mica, quartz, and felspar.' If any of you have been led
to entertain thoughts of a similar kind, I trust you are
now convinced that it is well to suspend opinions, till
you have advanced beyond the mere elements of a study.
You find that geology presents a noble field for research ;
that it carries the mind from the consideration of rocks
and mountains, to the period of their creation, and to
Him who created them : you perceive them to be silent
and venerable historians, which, in a language that ad-
mits of no dispute, indicate changes that the globe has
undergone, many of which, but for these witnesses and

* Such four-footed animals as nourish their young with milk.
20*



234 GEOLOGY.

partakers, the inhabitants of the earth would have been
forever ignorant.

According to the discoveries of geologists, it appears
Jirst, that the whole surface of the earth was once
covered by a void and formless deep. Chemistry proves
that darkness and light, gasses, liquids, and solids, min-
gled in one universal chaos, might, according to the
laws of nature, have disengaged themselves, and formed
a uew arrangement.

Second, it appears from geology, that the waters were
gathered into their respective places, and that solids
were separated from liquids ; and gasses released from
their unnatural union, rose by their specific levity, into
higher regions.

Third, we learn from geology, that after the earth
had become fitted for the support of vegetation, plants
were created, their remains being found in older rocks
than those of animals.

Fourthly, we learn from geology, that after plants were
created, the ' waters brought forth abundantly,' the re-
mains of marine and fresh water animals being found in
older rocks than those of land animals.

Fifthly, we find by geology, that at this period land
animals were created, and that they ' multiplied greatly
upon the earth.'

Sixthly, we learn from geology, that after a long period
of time had elapsed from the creation of plants arid ani-
mals, the whole earth was again covered with water,
which swallowed up vast multitudes of animals arid vege-
tables, whose remains are daily becoming more and more
revealed to human observation. We know too that many
species and even genera of animals which existed pre-
vious to that catastrophe, are now extinct. We learn by
geology, from the fact of beds of shells being found upon
the highest ground at great distances from the sea, that
the * waters covered the tops of the highest mountains ; 7
and, from various other circumstances, it appears that they
gradually subsided. Now, compare these facts as revealed
by geology, with the events recorded in scripture, between
the 1st and 10th chapters of Genesis, and you will find
an entire corroboration of what is there recorded.



GEOLOGY. 235

Among all the diluvial and antediluvial relics, no hu-
man bones have yet been discovered. This, however, is
a fact which ought not to excite surprise, when we con-
sider how little is known of the fossil and other ancient
remains of Asia, which was the birth-place of the human
race. At the period of the deluge, mankind had not
probably extended far over the earth : at the approach of
this event, they would naturally collect in groups for mu-
tual assistance and protection, and in this condition prob-
ably met their fate. Seas may now cover their remains,
or it may rest for future geologists to discover and bring
forth the bones of those wretched arid miserable beings
who signally met with retribution, even in this life.

From what has been observed, you will readily see
the vast importance of the discoveries of geologists and
anatomists respecting organic remains ; especially when
taken in connexion with established facts relative to the
comparative ages of the different strata or layers of rocks.
If a certain tribe of plants or animals are found imbedded
in a certain rock formation, while the rocks of more re-
cent origin are never found to contain such remains, we
must believe they were of more ancient date than the
species found in newer rocks.

'If it had been predicted a century ago, that a volume
would be discovered, containing the natural history of
the earliest inhabitants of the globe, which flourished
and perished before the creation of man, with the dis-
tinct impressions of the forms of animals no longer exist-
ing on earth, what curiosity would have been excited
to see this wonderful volume ; how anxiously would Phi-
losophers have waited for the discovery ! But this volume
is now discovered ; it is the volume of nature, rich with
the spoils of primeval ages, unfolded to the view of the
attentive observer in the strata that compose the crust of
the globe.' *

This interesting branch of Natural History has hither-
to been little introduced into female seminaries; the rea-
son of this is, undoubtedly, the want of popular, elemen-
tary treatises on the subject; as this want shall be sup-
plied, it is to be hoped that a study which so powerfully

* Bakewell.




236



MATHEMATICS.



confirms the truth of revelation, and which so evidently
tends to elevate and enlarge the rnind, will no longer be
considered unnecessary, or unimportant.* All who study
nature, must, with the poet Montgomery, feel that

* There is a voiceless eloquence on earth
Telling of Him who gave her wonders birth ; '

And all such will be ready to exclaim with him,

' And long may I remain the adoring child

Of Nature's majesty, sublime or wild ;

Hill, flood and forest, mountain, rock and sea,

All take these terrors and their charms from Thee.

From Thee, whose hidden but supreme control,

Moves through the world, a Universal Soul.'



LECTURE XIX.

Mathematics Arithmetic Algebra Geometry.

IN commencing my remarks on the study of Mathe-
matics as a branch of female education, I shall intro-
duce a passage from Hannah More's Strictures, which
will show you the state of our sex as to intellectual
improvement at the beginning of the present century,
with the opinions of one deserving of deference and
respect, as to the proper means by which the existing
evils might be remedied. ' Women, 3 says Mrs. More,
' are little accustomed to close reasoning on any subject;
still less do they inure their minds to consider par-
ticular parts of a subject : they are not habituated
to turn a truth round, and view it in all its varied
aspects and positions : and this is one cause of the too
great confidence they are disposed to place in their own

* Since this lecture was delivered, the author has been engaged
in making some additions to a small work written by the author of
the Child's Botany, and entitled the Child's Geology. This will
soon be given to the public. Should the author of these lec-
tures be enabled to fulfil her present intentions, a work on Geolo-
gy, adapted to female seminaries, for which she has six years been
collecting materials, will be soon prepared for publication.



MATHEMATICS. 237

opinions. Though their imagination is already too live-
ly, and their judgment naturally incorrect; in educating
them, we go on to stimulate the imagination, while we
neglect the regulation of the judgrnent. They already
want ballast, arid we make their education consist in
continually crowding more sail than they can carry.
Their intellectual powers being so little strengthened by
exercise, makes every little business appear a hardship
to them : whereas serious study would be useful, were it
only that it leads the mind to the habit of conquering
difficulties/ t

In another part of her work, Mrs. More says, ' The
chief end to be proposed in cultivating the understand-
ing of women is to qualify them for the practical pur-
poses of life. The great use of study with them is to
regulate their minds and render them capable of fulfil-
ling the duties of life. To woman therefore 1 would recom-
mend a predominance of sober studies, those which will
teach her to elicit truth ; will give precision to her ideas ;
will make an exact mind, which instead of stimulating
her sensibility, will chasten it; which will give her
definite notions; will bring her imagination under
dominion ; will lead her to think, to compare, to metho-
dize. Economy is the exercise of a sound judgment,
exerted in the comprehensive outline of ordor and
arrangement. She who has the best regulated mind
will, all other things being equal, have the best regulat-
ed family.'

It had not probably entered into the mind of the excel-
lent woman whose judicious observations have just been
quoted, that her sex, in thirty years from the time
in which she advanced these ideas, would be admitted
by general consent to share in those pursuits, which
have the most undoubted tendency to produce the effects
which she desired a tendency to sober the imagination,
develope the reasoning powers, and strengthen the under-
standing, so apt in the female character to be biassed by
prejudice or borne on the gossamer wing of a lively fan-
cy into the regions of error and folly. Mrs. More recom-
mended the reading of Watts on the Mind, Butler's
Analogy, and other writings of a grave and metaphysical



238 MATHEMATICS.

character ; but she did not, (if indeed she was aware of
their superior importance as aids to mental discipline)
dare to speak of the higher branches of mathematics.

Watts observes that ' Mathematics have a strange influ-
ence toward fixing the attention of the mind, and giving a
steadiness to a wandering disposition, because they deal
much in lines, figures and numbers, which affect and
please the sense and imagination.' The same writer, in
speaking of the tendency of the mind to * narrow and low
conceptions,' remarks that * this defect may be remedied
by beginning wiih the first principles in geometry, and
proceeding to the doctrine of quantities, which are
infinite and innumerable. A little acquaintance with
true philosophy and mathematical learning, would soon
teach the mind that there are no limits either to the ex-
tension of space, or the division of body, and would lead
it to believe that there are bodies amazingly great or
small beyond their present imagination.' The same
writer further observes, ' It is owing to the narrowness of
our minds, that we are exposed to the same peril in the
matters of human prudence and duty. In many things
which we do, we ought not only to consider the mere
naked action itself, but the persons who act, the persons
towards whom, the time when, the place where, the
manner how, the end to which the action is done,
together with the effects that must, or that may follow,
and all other surrounding circumstances ; these things
must necessarily be taken into view, in order to deter-
mine whether the action, which is indifferent in itself,
be either lawful or unlawful, good or evil, wise or foolish,
decent or indecent, proper or improper.'

Females have been said, and not without reason, to
be fluctuating in purpose, desultory in action, aijd un-
settled in principle. Possessing vast power over the
destinies of the world, by their influence as wives and
mothers, they have often been the cause of contention
and misery among nations, and of agitation and disquiet
in the more limited domestic sphere. Of how much
importance to the well-being of mankind is it, that
this fickle, restless, yet powerful being should become
consistent and reflecting, and learn to exercise her



MATHEMATICS. 239

influence for the good of society. And how shall this
be done? The question is answered by Watts, Locke,
Stewart, and all other judicious writers on the power of
education upon human character ; for all have united in
giving their testimony to mathematical studies, as one
of the most important aids to mental discipline.

But it may be said, that these writers did not intend to
apply their remarks to female education ; that it was
for the other sex for whom they wrote. Strange indeed,
if the nearer the mind of man resembles in its organi-
zation that of woman, the more he should be required to
follow investigations calculated to fix the attention and
strengthen reason, while for woman herself, this should
be considered unnecessary and improper.

Women are often reproached for their limited views,
their low and narrow conceptions ; true it is, that their
sphere of action tends to such results. The minute
objects towards which . their attention is necessarily
directed, the routine of their domestic duties and occu-
pations have a tendency to contract their minds. How
shall this be remedied 1 Let the direction of Watts on
this subject be our answer. Although in his day he
could not have anticipated this application of his re-
marks, yet had the appeal even then been made to his
judgment in behalf of women, I am persuaded the jus-
tice of his character and the benevolence of his heart
would have secured a verdict in their favor.

Again, with respect to 'our conduct in matters of pru-
dence and duty/ as Watts expresses it; 'it is owing to
the narrowness of our minds, that we are exposed to peril
here.' What human being more needs a sure guide in
matters of prudence and duty than woman ? Caressed
and flattered, and yet watched with jealousy and suspi-
cion thrown off her guard by the most tender indulgence,
while the slightest shadow of imprudence renders her lia-
ble to misconstruction and reproach, does she not need
an unerring standard of rectitude in her own bosom, a
clear arid acute sense of her own actual condition ; pru-
dence to direct her in the path of duty, and fortitude to sus-
tain her under various trials ? The mode of discipline by
which the human mind maybe brought to a calm, ration-



240 MATHEMATICS.

al and dignified state, is pointed out in the passage of
Watts to which we have referred. An enlarged and ex-
tended view of our various duties and relations towards
ourselves, our friends, society, and especially towards our
Maker, accompanied with virtuous principles and disci-
plined minds, cannot fail to secure respectability in this
world, and happiness in a future state.

We are far from considering mathematics as the only
instrument of that mental discipline which we feel to be
so necessary for our sex ; every branch of education,
which has a tendency to fix the attention, to impress
truth upon the mind, and to produce the habit cf reasoning
closely and consecutively, is of importance in this view.
We have already spoken of the studies of grammar, lan-
guages, geography and history, as auxiliaries in this
great work. The studies of natural science, mental
and moral philosophy, are all of great utility in the form-
ation of character: but the study of mathematics has, by
philosophers, been considered the most direct way of
controlling the imagination, perfecting reason and judg-
ment, and inducing a habit of method and love of order.

The term mathematics is derived from the Greek verb
matkeo, to learn. This science treats of quantity or
whatever can be measured, as in geometry, or numbered,
as in arithmetic and algebra. Mathematics is divided
into pure and mixed; pure mathematics is the abstract
consideration of quantity, without any reference to mat-
ter; mixed mathematics treats of magnitude as subsist-
ing in material bodies, which are subject to certain laws,
a knowledge of which constitutes natural philosophy.
Mathematics here becomes united to natural philosophy,
and hence arises tho term, mixed mathematics. The
reasoning in mathematics is of that kind called demon-
strative, or that which admits of positive proof. Thus the
truths developed in the reasoning of the first proposition
of Euclid admit of no more dispute than the axiom that
things equal to the same, are equal to one another ; the
latter is self-evident, or apparent without any reasoning;
but the truth of the former is not evident without the in-
termediate steps used in the reasoning.

Moral reasoning is of a different kind, and cannot be



MATHEMATICS. 241

rendered thus positive. Dr. Paley asserts that 'virtue
is the doing good, in obedience to the will of God, and
for the sake of everlasting happiness' Now if he could
have proved this by a train of reasoning founded upon a
self-evident proposition, no one would distrust the as-
sertion ; yet many do dispute it, which shows that it is
not proved to complete demonstration, for the human
mind cannot dispute such evidence. Some moral truths
do however seem to admit a proof equal to demon-
stration. Thus the existence of God is demonstrated,
from the existence of matter, which could not have crea-
ted itself. Taking then for an axiom or first truth, what
seems self-evident, we would say that matter must have
been made it cannot have made itself, therefore since it
does exist, it must have had a maker ; this maker we call
God. Yet an atheist might object to what we called a self-
evident truth he might say, we are not certain that mat-
ter has not existed from eternity. He may of course object
to our reasoning, if he does not consent to our premises
or the foundation of our arguments. Yet demonstrative
reasoning is not to render us unbelieving on moral sub-
jects ; but the rather, tends by accustoming the mind to
deliberate investigation and careful comparison of proofs,
to detect the true from the false, even in moral reasoning.
Mathematics is peculiarly a science of comparisons ;
these comparisons are always exact and may be made
manifest to the senses. When it is said there are fifty
yards of ribbon in a piece, there is an exact and sensible
comparison between the ribbon in the piece, and the
length of the yard measure, fifty times repeated.

A French writer* says, c is it not certain that a young
person accustomed to the justness and accuracy of math-
ematical demonstrations, habituated to exercise his intel-
lect in discovering the connexion of ideas in a train of rea-
soning in order to prove a truth, is it not certain that such
an one will carry into the world a penetrating and observ-
ing mind ; that he will pursue other studies with greater
facility, when his judgment and all his intellectual facul-

* Delpierre du Tremblay , author of Lettres sur les Etude, et sur
leur Rapport Jlvec L' Entendement Humain.

21



242 ARITHMETIC AND ALGEBRA.

ties have been exercised and strengthened by mathematical
investigations. Many persons who have not sufficiently
reflected upon the manner in which our faculties can be
exercised to the greatest advantage, and upon the assist-
ance which the sciences mutually render to each other,
say that the mind can pursue any science to which it
gives attention, that it is but lost time to occupy it with
mathematics instead of the profession which is to be the
business of life. But has the mind always the capacity
for the study of any kind of science ? Is it not necessa-
ry to form the judgment by preliminary studies? And
are not the mathematics the best means of accomplish-
ing this, and the method of reasoning and investigation
acquired in this science a most important aid in all
others ? ' Suppose of two young persons of equal talents,
and who have devoted equal time to study, the one is a
geometrician, and the other has given her time more to
other branches of knowledge suppose these two com-
mencing together some new science, botany, chemistry, or
mental philosophy, we shall soon perceive the great
advantage which the knowledge and practice of mathe-
matical reasoning gives the one, over the other, in the
mode of arranging facts, of developing truth, and per-
forming such mental analyses as are necessary to disen-
tangle, and bring to light the most complicated subjects.
For the greatest discoveries, which have enlightened the
world we are indebted chiefly to those powerful minds
which have first strengthened and invigorated them-
selves at the fountains of mathematical knowledge:
Descartes, Mallebranche, Gallileo, Kepler, Bacon, Locke,
Newton, and Fontenelle. Plato wrote over the entrance
into his school, ' He who has not studied the Elements
of Geometry cannot enter here.'

Arithmetic and Algebra.

Arithmetic is the lowest and most simple branch of
mathematics. The word is derived from the Greek
arithmos, signifying number. It is the science of num-
bers. Arithmetical calculation signifies operations per-
forme'l by various modes of adding, subtracting, multi*



ARITHMETIC AND ALGEBRA. 243

plying or dividing. The word calculation, (ha French
called calcul,) is derived from a Latin word signifying
little stones, because the ancients used such, instead of
figures in their arithmetical computations. All our
numbers are expressed by different arrangements of the
cipher and the nine figures, called digits. These were
learned from the Arabians, who are said to have
derived their knowledge from countries still farther
east. The Greeks and Romans used the letters of their
alphabet to express numbers. Thus, instead of the
Arabic character for I they used the letter I ; for 2 they
used II ; for 3, II [; for 4," IV, &c.

Of all the sciences, arithmetic is perhaps the most
ancient, it having been taught by the Egyptians 600
years before Christ. It is said they attempted to ex-
plain everything by numbers, and even thought that an
accurate knowledge of these would conduct them to the
fountain of divinity, to God himself.

It is unnecessary to urge the importance of this study
as a branch of 'female education, since this is universally
admitted ; but it cannot be unnecessary to recommend
a more practical use of it than is generally made. I
should blush for any pupil of this institution, who, after
having studied arithmetic even but a short time, should
be found ignorant of the proper method of keeping an ac-
count, or of making out a bill. The practical object of
arithmetic is to teach you to do those things. It should
also have a moral influence on the conduct by teaching
you to regulate your expenses according to your income.
Many a man has been ruined because his wife and daugh-
ters have not practised arithmetic ; and there are those, who
resorting to dishonest methods for procuring wealth, have
dragged out in a state's prison a miserable existence, which
economy in their family might have rendered virtuous and
happy. Suppose that a man in business earns a thousand
dollars a year ; which is probably as large an income, as,
upon an average, is received by clergymen, lawyers, physi-
cians and merchants in this country ; in many cases, from
this income, house-rent is to be paid, fuel and provisions
furnished, children to be educated, and a family cloth-
ed. What, in siich a situation, should be the manage-



244 ARITHMETIC AND ALGEBRA.

ment of a wife and daughters? Perhaps some may
reason something in this way, my husband or father has
an income of a thousand dollars; now, I want this shawl
which costs only thirty dollars, or this bonnet which
costs only twenty, and this will be but a very little part
of the yearly income. I am sure it can be easily spared.
But if the calculation was first made, how much of
this sum must be expended in necessaries, it would be
at once seen that very little could be afforded for
superfluities.

Arithmetic teaches only the properties of numbers
which are known ; its calculations are carried on by the
use of figures ; but in Algebra, letters are made to rep-
resent quantities that are unknown. It takes for grant-
ed the unknown quantity sought, and by means of one
or more given quantities, proceeds, until the supposed
quantity is discovered by some other known quantity to
which it is equal. The first letters of the alphabet, a, b,


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 21 23 24 25 26 27

Online LibraryLincoln PhelpsLectures to young ladies, comprising outlines and applications of the different branches of female education, for the use of female schools, and private libraries → online text (page 21 of 27)