The daily Madisonian. [volume] (Washington City [i.e. Washington, D.C.]) 1841-1845, 1842-01-15
Mean Of 4 years, 1882
From The United States Gas

Ne"H Va yCaifj ii'oS
From the United States Gas.Ae
UNwILLINGNEss OF MAN TO INVESTIGATE, AND HIS
WILLINGNESS TO COPY.
By Oliver Byrne, Professor of Mathematics College
for Civil Engineers London.
1t Is difficult to make men think for themselves;
most of would rather take what we hear for granted
than be troubled with the investigation, when
private ends are MT concerned and against that
again, we find men opposing the most reasonable, and
uphoding the most absurd doctrines support par
y to fill their purses, to gatify pride in order to be
thought singular, or to as'onsh that it may please
the mass OF mankind for they are fond Of the won
derful.
Again in thngs that are really useful " some are
too indolen to read thing ill its reputation es-
ablished; Others, too envious 10 promote that fame
which gives them pain by increase. What is new is
opposed because most unwilling be taught what
is known is rejected because it is not sufficiently
sidered that men more frequently require to be
minded than informed" This article is written TO
show the willingness Of man to copy and his unWil-
lingness to investigate and nothing can show this
clearly than the which are promulgated
and transmitted from age to age by these who
called learned" In mathe NAUTICAL investigations
investigation in which The mathematician is will
ling to occupy the most unfavorabe position, he re-
qures from you the exercise of no prejudice in his
favor but, on the contrary, would invite you in
dulge in the most scrupuous frame of mind to uso
the utmost penetration to discover flaw ay to put the
spite of all your opposition he will engage
you of the truths he proposes to establish
In this science, the sanctuary and strong hold OF
absolute certainty, which claims exception from the
inGrmilies that attached to all other branches of
human knowledge and although what we thus esta-
blish is real truth subject to abatement-no nodi-
misunderstanding upon no hypo hess of man, -
upon the authority of no great name mat hematca
truths will be the thousand years hence as
they at the present day. standing nmuabIe
amidst all the changes of systems and the fluctuations
Of; opinions.
And yet, either from Gas have before mentioned
an unwlllingness to investigate, or from an inclina
ton to copy, find oversghts mistakes, logical alb
surdities, and errors, of the numerous Investigators
and copiers. We shall here give few instances
Simpson, the great mathematician, in his Elements Of
Geometry, which work passed through eight editions
and was translated into almost all the languages Of
Europe, and must have been read by thousands for
upwards Of eighty years, we find the following
neous proposition:
1.-TWO triangles that have two sides ofthe one pro-
portona to two sides after other, and angle in one
equal Ia an angle IN the other, opposite homologous
sides are similar"
Sir David Brewster, in his translation of Legon-
dre's Geometry, falls into notable error, insomuch
that he makes assertions which not at all true
In speaking of Legendre, he says ''the author has
provided for the application OF proportion to incom-
measurable quantities, and demonstrates every case
as 1t occurred, 10y means of The reductio ad absr-
dunn"
Professor Lese's Elements Of Geometry is re-
markabe for false demonstrations; and in his fifth
book he demonstrates the propositions or proportion
to be true, when the magntudes are commensurate
The fact that those demonstrations do not hold good
when the magnitudes are incommensurable seems
well known to Mr. Leslie; but that those magntudes
should also be homogeneous is altogether neglected
by him.
Bonnycaste, in two of the principal propositions
of his fifth book, gives demonstrations undoubtedly
intended for general ones which only apply to cases
where all the magntudes are of the same kind, That
those demonstrations were intended for general ones
there can be no doubt, for in his notes, page 25I
Bonnycastle finds fault with Euclid's method Of com
position and division of ratios not being sufficiently
general respecting these points.
DR. Austin, in his g Examination of Euclid )" com
mits the error Mr. Keith, who being des-
rous Of applying new demonstration to Proposition
XVII, Of his edition of Euclid he employs altena-
ton to quantities whose anecedents might be hete
rogencous.
Professor Young, of Belfast, who ably criticised
many ofour modern writers on Geometry, in cultivat
ing the ideas of NJ. de Cunha on the doctrine OF ra-
lios falls himself if not into error, into great
nconsisten cythat of discardlng Euclds doctrine Of
ratios om his fifth Book. He undoubtedly treats
proportion without using the term "ra-
no, but he gives other Terms OF more heightened
nature, which precisely convey the same meaning
Now TO do away with the term ratio" here is to do
away with ii in every subject that follows or through
whole course of mathematics, and any such attempt
should not be entertained for it very difficult
10 define what Is intended TO be expressed by the
ratio" 1t is different thing to havea clear concep-
ion of what the technical term ratio" is meant 10
convey, from knowing that What is intended by The
term cannot be expressed in many cases by numbers.
Babbege, in speaking OF his table of Logarthms,
says the proofs The present tables read three
lines LIST, with the marked copy of Callet's loga
rhm-; 2dly with copy of Huttons logcri'hms,
tourth edition. 1904 3dy, with copy OF Negars 10
,ariihns folio 1874. They received from
he printer, and were again compared with the loga-
-hms OF Vega; 5thly, they were read with those of
he Tli,ono metra Attic "a j. of Briggs.
They were next returned to the printer and stereo
yped and the proofs from the plates were read
;thly with the logarbms Of Vega 7thly with the
whole of the ogarithms Of Gardiner ethly with the
ogarthms of Taylor; and, 9thly by different sci
# readers they were again read with the logarhm.
# Taylor. After all this care and investigation
ound an error in MIR. Babbage's work not long since
Bowditch copies the ovcrsights of Laplace. Most
{ our English mathematical works are TRANSACTIONS
rom the French and in the higher branches Lard
er and others not only copy the works but also their
rrors, and in many typographical ones.
The 18th lemma of Newton's Principal, edit l,7l3
wrong
In conclusion, will ask those who are willing TO
lvestigate, where did rredgold get the number i59,
D often used by him in bis work on the Steam En-
inc, &C. See Woodhouses edition, page "a, where
is first introduced,