643 Dr. Beddoes on Teaching Arithmetic and Mathematics. | [O&ober, 
will fix upon fomething foreign to the de- 
fign. : 
Give me leave to take, from the fecond 
rule in arithmetic, a more dificult and 
more interefting example. The pene 
who is taught to borrow in fubtragtion 
imitates his preceptor, and finds his fum 
right. But of the rationale he often either 
remains quite ignorant, or is puzzled by 
the attempts at elucidation. 
‘Fo explain the operation mechanically, ~ 
let a number of counters of the fize of a 
fixpence (or peafe or French-beans) be 
provided; let a portion of the counters 
be fixed together, in tens and hundreds, 
by a pes, pafling througha fmall hole in 
the centre of each (in the cafe of feeds a 
ftring nay be ufed).. Let it now be pro- 
pofed to take (or ‘ubtra&t) 136 from 24.55 
I fuppofe the pupil to Have been initiated 
in the rule of addition mechanically, I 
mean by counters; not by mere written 
figures: the 136 fhould fir be counted 
out of 245 detached picces, and the re- 
mainder afcertained; then iet the figures 
of the larzer fum be written down at fuch 
a diftance from one another, that two 
‘packs, of a hundred counters each, can 
be placed upon the left-hand figure, and 
four packs, of tea each, upon the middle 
figure, and five fingle counters upon the 
fight-hand figure: at thé fame time, the 
fum fhould be written down in the ufual 
manner ( ee ) on another part of the flate 
or paper. 
The method of ‘proceeding after this 
need fcarce be defcribed. Six cannot be 
taken from five; fo the learner muff be 
direSted to remove (borrow) one of the 4 
packs of ten from the fecond to the firit 
place of figures, detaching the counters. 
From: thefe fifteen counters he will take 
fix; he will next have three, ghat is, all 
the tens to take from the middle p 
and removing one pack from tne third 
place, there will be left one; and the fum 
compleated; and the management with 
ficures made perfectly intelligible. Of 
courfe, the teacher will propofe a concrete 
cafe; as, Mr. Wells borrowed of Mr. So- 
mers 245 pounds, and, at different times, 
paid back 135; he is come to difcharge the 
reft of his debt; and wants to know how 
much he fiill owes ? poe 
After borrowing in fabtraétion, our 
cuftom isto add an unit to the next figure 
in, the lower row: but it feems more per- 
Ipicuous at fir, and it is more conform- 
able to the theory of the procefs, to dimi- 
nifh one from the correfponding figure of 
the upper,* as Condorcet does. Boch 
aCe 
Gilg 

* ‘This had likewife been direCted in Prac. 
‘ical Education. z 
operations can afterwards be fhewn toe 
produce the faine effect. 
Some years ago, finding that the late 
Mr. B. Donne had mechanical demonftra- 
tions of the principal propofitions of Eu- 
clid; and that thefe demonfirations were 
fufficiently plain and ftriking, I procured 
him a number of fub{fcribers ; and fets of 
demonftrations were made, and an expla- 
natory. book printed. 
By help of thefe, young perfons foon 
and eafily learn many properties of plane, 
and fome of folid figures. Somewhat 
more than an hundred fets are difperfed 
through the kingdom; and it were to be 
wifhed, that more were in readinefs. But 
as the project was, 1 believe, never adver- 
tifed in any newfpaper, or noticed in any 
.literary journal, the knowledge of it was 
‘confined to ‘a few hundred families. 
Thofe who have ufed thefe models, have 
been fatisfied with them; though poffibly 
they could be greatly improved. I did 
not think the book well calculated for the - 
purpofe, fuppofing the whole had been to 
be put into the hands of young people. 
It does not want perfpicuity'; but many 
technical terms, as leswma, fcholium, are 
introduced. To thofe, however, who 
think with QuinGilian, that wivd voce 
inftruction is beft, and in the rudiments 
of knowledge it furely is particularly ad- 
vantageous, the defect of adaptation to 
the capacity of children in the book will | 
be a trifling obje@tion. ‘There is a work, 
entitled Cowdley’s Solid Geometry, fold by 
Jones, 135, Holborn, which would come 
in perfeCtly well atter Donne’s models. 
I am, Sir, your humble fervant, 
‘Tuomas BEDD@Es. 
Rodney-place, Clifton, 
Sept. 8,.1799- 
EEE 
To the Editor of the Monthly Magazine. 
SIR, Froffon, Aug. 17) 1799. 
IVE me leave to tell your angry _ 
correfpondent G. Y. (p. 538), that 
lefts hafte and paflion would probably have 
enabled him to do more juftice to himfelf, 
to Dipor, and to VirGIL. Criticifin is 
calm. 
I had fpoken very refpe&tfully of Didot, 
and of the neatnefs,, cheapneis, and conve- 
nience of his fimall ftereotype Vargil. 
There is no triumph where he fuppofes ; 
but a fimple ftatement. 
I continue to fay, that reperit, the. firft 
fyHable long, with a fingle £, is not agree- 
able to the fyftem of orthography puriued 
in this edition by Didot; in which Fupzter 
is printed with a.double ¢, and Kekgzo 
es with 
