Richmond enquirer. [volume] (Richmond, Va.) 1815-1867, 1828-05-09


| ~ Juiges, among Others OF the late Preside,
'.lisrson, who had seen other things of me b. ior
ana VINO, when informed him of my intentioa
l1'lOiish 1t, wrote To me: . have no doubt c i
: *alue Tor our schools in general, and that, "a
elementary WORK for their use, il win be ciea
" and easy, a every thing il which comes lrou,
- you, sc. shall gladly for myself request you
F" 10 give my name place on your subscription
/ " iist, Sc. This, however, being less than
mouth before his death, he never the book it
| ed, and no subscription list was ever communica
! el 10 the public, perhaps mistake; ii il had been
tn aim 10 act upon the public, by acces>oi ~
means, which Is not my habit The favorable
opinion OF the writer in the American Quarterly
neei not to refer 10, rs it has drawn upon thi
attack, nor need say any thing in favor # the ar
ucle; II speas for t-elf 10 all who understand the
subject; and these men of the opinion
wiih INN. may, therefore, be grateful to him ios
its publication.
| state in my preface, that | intend to proceed
from Principles the most general, yet at the same
time the mast simple; TO found upon thema system
the result oil which may be- fitted for MurerSa
! application The ). Reviewers in admitting IN
nFst part, are completely silent upon the second
because IN general they do enter upon the
book, itself; the introduction furnishes them the
desired theme OF sOphis;icdi discussion, upon the
words OF Synthetic analytic, geOmletricai, cdlcu-
t,tS, tduSceRddHf, and even ina gilary, &c SC.
! sc. more than half of which considered IN ysell
a authorised TO dispense with 10 bring the subject
SIMPLE and clear before my scholars, instead OF
raising difficulties shall not even here clear up
the darkness in the ideas of the Southern Reviewers
upon these words, because it would require dispo
ston TO listen TO true simple principles, which
dare NOT suppose, when | see them so nightly
tonSh;d at seeing the egg stand easily upon the
broken end,as they do by finding in my Trigono-
meuy nothing, but what can be deduced from the
hrst principles OF Geometry, With some application
OF Algebra. AS -dtdlytic Irig0a0metIy always is
con ideIed TO be, by It's place in the course of Ma
themaca studies, and as stated il, by saying, that
IT was dP'O6iem Of algebra applied 10 Geometry,
(con>idering the terms fully understood, mathe-
ma icians know what that means.) So in fact, we
meet upon this point; only il appears that the
side from which the Southern Reviewers look at il
they see that subject tfrou gh mist, and am
not disposed TO analyse their atmosphere chemical
iy
The ). Reviewers arc displeased al the very
nrSt phrase OF my introduction, where say ,hi,
The nseoi irigonometry is in the form (calle onaiy
icdf, ana stat, in few words the outline OF the
history oil this branch OF mathematics; however a
this is too ell known and established TO need
defence or rctraction, and my mode OF exc cutting
this notwithstanding il is ne has ON account of
It's JutneSs and simplicity, received the dpproba
Ton OF all those men, whose opinion upon the sub
Ject have. reason 10 consider competent; if the
name dlspleases the Southern Reviewers will leave
10 ihem the honor OF invt nhg new one; 10 treat
IriSonomery in th- useful form, is adapted to the
STATE Of me science, hence, duty, not choice of
teacher; that Is well acknowledged, where mathe-
mates are known. 1t would not he proper for me
TO entertain the public upon the other little difficult
ties oil the Southern Reviewers upon the introtluc-
ton
begin the subject itself with the ratios the sides
oi the rightangled triangle, y am blamed by the s.
reviewers Tor the want OF a Radius, which they
ind likely bright thought TO write by placing a
row of seven eight cyphers after an unit; |
gladly leave these round quantities TO them, as
they appear TO lit their mathematics, land every
man making actual use of mathematics will equal
ly supply them without an. loss TO himsef) they
can therefore have much they NAV ever
wish; have given the type OF the calculation of
every Kind OF practical formula, that solve every
case oil single trIanges plane and spherical, with
out single such row of 000000O0, and so every
'nan would do who ever calculated more than one
triangle for actual use. Until vcrr lately the
:. OPtH platinum de fiang,tiis' of Rhetic,ss has
been the groundwork from which all the triporu-
metric tables have been constructed: in thai the
southern reviewers (as they likely have larg. Ii
brary OF rare books will find the whole of the re
qnisre numbers given, base, perpendicular
hYp0uenuSe, and the favorite Radius j.. no, To be
found though the book is old as TO have prece-
ded the use OF logs SineS, cosmos, SC. in Europe il
these old people could do without it, the young
ones certainly can.
Although the first propositions of elementary
geometry clearly show, that lines and angles are
different in their nature, the Southern Reviewers
ilnd me blancable for saying so. / am sorry that
this will not alter the Case, because tn .ir mathe-
lnaicai comparison would have been much easier
l-'A"''N'I"uCS 'dhc as tncy are, Wnen III
cannot be altered, as III this ease, enquire upon
Their nature accoT ing 10 sOaIsd principieS-the
inatheuidliciin pursues them with clear ideas and
utstHct steps by so doing able, without
introducing any imaginary quantities, to deduce
the whole OF the most useful formula of plane and
Sphcnc trigononeiry, aud Tor higher analysis even
without objections on the part OF the Southern Re-
Viswer- Tor they pass il unnotced, until they meet
my series Tor the tangent OF multiple arcs TO which
! they refuse the appellaOn of Re,C, which the A.
nerican Quarterly gave it. This, however, is
really So as lar as publications go, and confess
t'nk The American Quarterly showed, by his
quoting II as such, more knowledge of what IS or
is not, (ior also this latter is rrquise for man to
Nnow,) than the South reviewers, by their blum
dcrs upon the Subjec for they quote Prong ana
| Cdgn0H, who directly condemn their stalenent-
irony, III giving account OF the construction OF the
tables du cddaSfre," states, that for the tangens
means are not yet obtained to avoid the division ia
very irksome thing in series, and long rows OF de-
nalS,)-and Cagnoli, i'll the three last lines of
page 63, says, that he does not know to help him
sell better, IN that case, but by The diUision-
BeTn0tH hrst investigated this subject from i'm
| possible Quantities; Euler gave the series of the
tangent, by the division oil the two series of sim,
ana cosine; from him CagnoIi and many others CO.
| pied 1t; whether The s. Reviewers have not seen
! the division sign O. at the end oil the line, between
the TWO series In Cagnoi, page Ill, us he has O.
CROOKED the passage on page 63, or how he came
| to Ind my series, which has dicIsion, TO be Tn
same, leave 10 him for future enquiries. After
having deduced the series OF sines aId co,ines 10
nc divided, without, however, passing through l.
! imaginary Quantities. Cagno does, but by clear
INA elementary steps, obtained my series by an
appropriated substitution for the binomial co Ell
GENTS, which made it free frOm diUisiOH, las had
'ecn desired, and was my aim,) it shows a simpl.
law, a. Is well known TO be the aim in all such in
'estigation', il is the series W. No. 8, page H.
dUd believe il i'm good audlvfical priucinle 40