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remains one entire epiftle, and confiderable fragments of 
others in Eufebius, fome of them objects of curiofity, 
and others truly valuable. He wrote alfo againft the 
doctrine of Sabcllius refpefling the trinity, who main¬ 
tained that the terms Father, Son, and Spirit, were only 
names and offices of the fame perfon ; and againft Paul 
of . Samofata, whofe opinions refpedting Chrift appear to 
have been nearly fnnilar with thofe of modern Unitarians. 
Dionyfius’s own fentiments refpefting the trinity, differed 
little, if at all, from thofe of Arius. 
DIONY'SIUS, pope, or bifltop, of Rome, in the third 
century, was appointed a prefbyter of Rome, the duties 
of which office he difeharged while Stephen and Sixtus 
II. prefided over the church in that city. After the mar¬ 
tyrdom of Sixtus, in 258, he was elected his fucceffor, 
in the middle of the following year, and filled the fee of 
Rome until his death, in 269. He is fpokenof as a very 
learned and admirable man, and is particularly praifed 
for his extenfive benevolence, which he fignally difplayed 
towards the Chriftians at Casfarea. Balil lays, that he 
was illuftrious for his orthodoxy, as well as every other 
virtue. And -Athanalius informs us, that he wrote at 
once againft the followers of Sabellius, and againft thofe 
opinions for which Arius had been expelled the church. 
The only fragment of his writings which remains is pre- 
ferved in the works of Athanalius, and is chiefly of im¬ 
portance, as it ffiews the concurrence of Dionyfius with 
the other Chriftians of his time in acknowledging the 
feriptures to be the rule of faith by which all dodtrines 
were to be tried. 
DIONY'SIUS, furnamed Exigmts, or the Little, from 
the fhortnefs of his ftature, was born in Scythia, and be¬ 
came a monk and an abbot at Rome, where he flourilhed 
about the middle of the fifth century. Caffiodorus, with 
whom he lived on terms of great intimacy, has bellowed 
high encomiums on his learning and character. At the 
requeft of Stephen, bifltop of Salonae, he drew up a bo¬ 
dy of canons, intitled, CollcSlio five Codex Canonum Ecclcfwf- 
ticorum, &c. mandated from the Greek, containing the 
firft fifty apoftolical canons, as they are called, and thofe 
of the councils of Nice, Conllantinople, Chalcedon, Sar¬ 
dis, and of 138 canons of certain African councils; which 
is to be met with in all the collections of the councils, and 
is inferted in the firft volume of Juftell’s Bibliotheca Juris 
Canonici veteris. He afterwards drew up ColleBio Dccrctorum 
Pontificum Romanorum a Sincio ad Anafafnan, which is to be 
found in the fame work of Juftell. He w'as alfo the author 
of feveral tranflations from the Greek, which are ftill pre¬ 
ferred. To this Dionyfius fomew'riters aferibe the inven¬ 
tion of the chronological period, by others attributed toVic- 
torius, or Victorinus, who lived in the time of pope Hilary, 
and which is more commonly called the Vidtorian period. 
DIONY'SIUS’s EAR, a celebrated grotto of Syracufe, 
in Sicily, confifting'of chambers and galleries which are 
hewn out in the folid rock, very wide and capacious at 
the bottom, but rudely arched, as it were at top, from 
which arifes a winding paflage, that becomes narrower 
upwards until it terminates in a fmall orifice at the fur- 
face. Ancient tradition fays that this was a prifon, which 
the tyrant Dionyfius catifed to be hewn out for ftate pri- 
foners, that in an apartment of his palace, which ftood 
over the narrow end of the paflage, lie might hear every 
thing the prifoners faid, or what plots they wiftied to 
form againft him. This grotto, therefore, is called Ore - 
ckio di DionyfiO) or la grotta della favella ; auris Dionyfii , the 
ear of Dionyfius. Many travellers and others formerly 
imagined, that this paflage was an ingenious imitation of 
that part of the human ear called the helix, which was 
firft remarked by Alcmaon the Pythagorean, and confi- 
dered as one of the greateft wonders of antiquity. This 
is the account given by Kircher, who examined it in 163S. 
In later times, however, this grotto has been furveyed 
with more fkill and acutenefs by people lefs fubjedt to 
prejudice, and fince that period the fuppofed wonder has 
Yol. V. No. 319. 
D I O 
been leffened. The rock confifts of lime-ftone, according 
to Brydone, who found it every where full of cracks and 
fifftrres. The (tones of which Syracufe was built were 
hewn from the rock ; and hence have been formed thefe 
chambers or openings, like thole found in the neighbour¬ 
hood of other ancient and modern cities, fuch as Rome, 
Naples, and Maeftricht. Many of thefe places, in the 
courfe of time, have been employed as prifons, or ufed 
as burying-vaults. The above-mentioned paflage, which 
has excited fo much w'onder, is not a true fpiral, and is 
of fuch a figure that it may have been produced either 
by accident, or through the whim of the workmen em¬ 
ployed to hew out the (tones. The double echo, which 
Kircher affures us he heard in the grotto, was not re¬ 
marked by Schott, who was there in 1646. Yet in the 
accounts (till remaining of Dionyfius, we find mention 
of an aftoniftiing prifon, which is w r ell deferibed by Ci¬ 
cero, in His fifth oration againft Verres : “You have all 
heard of,” fays he, “and mod of you know, the prifon 
(lautumias) of Syracufe. It is an immenfe and magni¬ 
ficent work, executed by kings and tyrants ; the whole is 
funk to a wonderful depth in the rock, and has been entire¬ 
ly cut out by the labour of many hands. No place fo le- 
cured againft an efcape ; no place fo inclofed on all fides; 
no place fo fafe for confining prifoners can be either plan¬ 
ned out or conftru£ted.” At prefent, the upper end of 
the winding paflage is clofed up ; and it is fo narrow, 
that, fome years ago, the captain of an Englifh veflel 
found great difficulty to clamber up it. It cannot, how¬ 
ever, be denied that this grotto may have been ufed for 
the fervice aferibed to it; and, from the form and con- 
ftrudfion of the fpiral or winding paflage, Kircher affures 
us he was led to the invention of the ear-trumpet. 
DIOPHAN'TINE Problems, in algebra, are certain 
queftions relating to fquare and cubic numbers, and to 
right-angled triangles, &c. the nature of which were firft 
treated of by Diophantus; and hence their name. In thefe 
queftions, it is chiefly intended to find commenfurable 
numbers to anfwer indeterminate problems ; which often 
bring out an infinite number of incommenfurable quan¬ 
tities. For example, let it be propofed to find a right- 
angled triangle, whofe three fides x, y, z are expreffed by 
rational numbers ; from the nature of the figure it is 
known that x 2 + y‘‘ — z 2 , where z denotes the hypothe- 
nufe. Now it is plain that x andj may alfo be fo taken, 
that z dial 1 be irrational; for if x—i, andj)'=:2, then 
is z= f 5. The art of refolving fuch problems confifts 
in ordering the unknown quantity or quantities, in fuch a 
manner, that the fquare or higher power may vanifli out 
of the equation, and then by means of the unknown quan¬ 
tity in its firft dimenfion, the equation may be refolved 
without having recourfe to incommenfurables. See the 
article Algebra. 
DIOPHAN'TUS, a celebrated Greek mathematician, 
and author of the oldeft treatife on algebra which has 
come down to 11s, on which account he has been reputed 
to have been the inventor of that fcience. It is not cer¬ 
tain at what period he lived ; fome authors placing him 
before Chrift, and others about the middle of the fourth 
century. If he was the fame Diophantus who wrote the 
Canon Afronomicus, on which Suidas informs us the learned 
female philofopher Hypatia commented, lie mod probably 
lived before the fifth century. From the few circum- 
ftances of his life which are recorded we learn, that his 
reputation was fo high among the ancients, that they 
ranked him with Pythagoras and Euclid in mathematical 
learning, and that he lived to the great age of eighty-four 
years. He wrote thirteen books of arithmetic, or algebra, 
which Regiomontanus, in his preface to Alfraganus, 
written in the fifteenth century, tells us w'ere at that time 
preferved in manufeript in the Vatican library. Of thele 
thirteen books no more than fix, and part of a feventh, 
have been publiflied ; and Bombelli, in the preface to 
his algebra, written in 1372, fays, that there were but fix 
jo E of 
