1802. ] A Sketch. of the Eliflory of Bure Mathematics. 
change.’ This fentence requires no com- 
ment. 
If fuch are the notions of ecclefiattical 
authority and religious benefit, prevalent 
in the minds of thofe who prefide over our 
principal feats of education, it is prelumed, 
that the friends of liberty and rational 
piety will {carcely defire that their acti- 
vity in promoting theological inftruction 
fhould be quickened. ~ 
To conclude ; there is much reafon for 
the invitation given -by the writer of the 
retrofpe&t, to unite in rallying round the 
ftandard of free enquiry, and guarding. 1t 
with jealous vigilance. And as the pa- 
trons of authority have confented for a 
time to fufpend their mutual animolities, 
in order to aid each other in their. impo- 
fitions upon mankind ; fo the votaries of 
reafon fhiould forbear reciprocal holtilities, 
while they concur in maintaining the prin- 
ciples common to them all. Especially 
they fhould withold thofe imputations up- 
on the defigns and intentions of thofe who 
philofophize ina manner fomewhat different 
from their-own, which have been ‘too fre- 
quent and have given too much advantage 
to their common adverfaries. | Ib reality, 
the fincere purfuers after truth are all of © 
one party, and their efforts cannot but in 
the end affift each other, how widely fo- 
ever they may feem to deviate in their pre- 
fent concluhons. MOniToOR. 
a ae 
To the Editor of the Monthly Magazine. 
SIR, 
N reply to the enquiries of Mr. Sin- 
gleton, page 29 of your laft Number, 
it may be briefly obferved, that repavras 
in Hom. Il. 16. v. 207, is the fingular - 
‘number ; -webappeot, wepavoat, wepevTat. 
With refpe€t to expeevos apaduy vepernv, the 
fact feems to be this; ew, as a verb of 
cloathing, is conftrued with two accufa~ 
tives; but, after the paflive voice, it ad- 
mits the dative of the part, ftill retaining 
the accufative of the thing worn or puton. 
Thus Od.z.v.7 2. nana de ypis eyata ees, 
Ut wvineta egomet cadam mea, 1 feel 
difpofed to retraét the change of i/ere 
into I fere, in Virgil, Ec. r. Vv. 74. as the 
irony implied in J mune feems too fevere 
for the occafion. : 
I was fomewhat gratified, a few days 
ago, in looking into Heyne’s zew edition 
of Virgil, to find the punctuation which I 
propofed in your Jatt of Virg. /&n. v. 
370, Vidlorem Buten, &c. confirmed by 
the judgment of this admirabie {cholar. 
Walthamfiow, Iam, Sir, 
Feb. 3, 18026 Your’s, &c. 
E. Cocan, 
107 
For ihe Monthly Magazine. 
A SKETCH of the HisTORY of PURE MA-~ 
THEMATICS, tranflated from “ Trauné 
Elementaire de Mathematiques Pures, 
par Lemoine, Profefeur de Mathema- 
tiques et de Phyfique, &c. 
(Continued from|Page 21, of No. 83 ) 
GEOMETRY. 
13. LL writers agree in referring to 
. A Egypt the origin.of geometry. 
Herodotus fixes it at the period when Se-. 
foftris interfeted that country with nume- 
rous canals. The Egyptian priefts, poffefs- 
ing leifure for ftudy, brought to perfection 
that {pecies of geometry which nature has 
made common to all men. But they ap- 
pear to have made little progrefs in that 
icience. If we-may judge of their knew- 
dedge by their communications to the 
Greek Philofophers who travelled into 
their country, they were in poffeffion of 
nothing more than the moft elementary 
truths. of Geometry. 
14. It feemed neceflary that Geome- 
try fhould be tranfplanted into Greece, in 
order to make a rapid progrefs. Thales* 
repaired to Egypt, and profited fo much 
by the inftruétions of the priefts of that 
country, that he foon foared to a height 
unattained by his preceptors. He de- 
termined the altitude of the pyramids by 
means of their fhadows, a method founde 
on the theory of fimilar triangles, On 
his return home he communicated to his 
countrymen the knowledge which he had 
acquired. tis true, that before his time 
the Greeks had fome idea .of Geometry. 
They knew the ule of ‘the ruler and com- 
pafs, the invention of which they. attribu- 
ted to Talaus, the nephew of Daedalus ; 
and of the fquare and level, which they’ 
owed to Theodorus of Samos, one of the 
architects of the temple at Ephefus. But 
thofe inventions were only the effe&ts of 
natural Geometry, and it was Thales who 
fir gave the Greeks a tafte for the Sci- 
ence truly fo called, which is conduéted 
by reafoning, and the light of evidence. 
He pointed out the ufe of the circle, as 
* Thales was born at Miletus, in Ionia, 
about 640 years before Chrift. That philofo- 
pher, being the firft of the feven wife men 
of Greece, was the founder of the Ionian 
fe&. He was chiefly admired for his know- 
ledge of Aftronomy. He foretold an eclipfe 
of the fun, and the event verified his pre- 
diftion. He affigned the true caufes of 
eclipfes, and fhowed that the earth was fphe- 
rical. That juftly celebrated man died at 
the age of ninety, 550 years before the Chrif- 
tian era. He advifed his difciples to live in 
harmonious union. 
. P 2 ameae . 
