APQ 
earth in the centre of the system, was much 
taken up in ascertaining the apogee and pe- 
rigee ; which the moderns have changed for 
aphelium and perihelium. See the article 
Aphelium:, &c. 
APOLLONIUS, of Perga, a city in Para- 
philia, was a celebrated geometrician who 
flourished in the reign of Ptolemy Euerge- 
tes, about 240 years before Christ ; being 
about 60 years after Euclid, and 30 years 
later than Archimedes. He studied a long 
time in Alexandria under the disciples of 
Euclid ; and afterwards he composed seve- 
ral curious and ingenious geometrical works, 
of which only his books of Conic Sections 
are now extant, and even these not perfect. 
For it appears from the author’s dedicatory 
epistle to Eudemus, a geometrician m Per- 
gainus, that this work consisted of eight 
books ; only seven of which however have 
come down to us. 
From the Collections of Pappus, and the 
Commentaries of Eutocius, it appears that 
Apollonius was the author of various pieces 
in geometry, on account of which he ac- 
quired the title of the great geometrician. 
His Conics was the principal of them. Some 
have thought that Apollonius appropriated 
the writings and discoveries of Archimedes ; 
Heraclius, wiio wrote the life of Archime- 
des, affirms it ; though Eutocius endeavours 
to refute him. Although it should be al- 
lowed a groundless supposition, that Archi- 
medes was the first who wrote upon conics, 
notwithstanding his treatise on conics was 
greatly esteemed ; yet it is highly probable 
that Apollonius would avail himself of the 
writings of that author, as well as others 
Who had gone before him; and, upon the 
whole, he is allowed the honour of explaining 
a difficult subject better than had been done 
before ; having made several improvements 
both in Archimedes’s problems, and in Eu- 
clid, His work upon conics was doubtless 
the most perfect of the kind among the an- 
cients, and in some respects among the mo- 
derns also. Before Apollonius, it had been 
customary, as we are informed by Eutocius, 
for the writers on conics to require three 
different sorts of cones to cut. the three dif- 
ferent sections from ; viz. the parabola from 
a right-angled cone, the ellipse from an 
acute, and the hyperbola from an obtuse 
Cone ; because they always supposed the 
sections made by a plane cutting the cones 
to be perpendicular to the side of them ; 
but Apollonius cut his sections all from any 
one cone, by only varying the inclination 
Of position of the cutting plane; an improve- 
APO 
ment that has been followed by all other 
authors since hi3 time. But that Archi- 
medes was acquainted with the same man- 
ner of cutting any cone, is sufficiently 
proved, against Eutocius, Pappus, and 
others, by Guido Ubaldus, in the beginning 
of his Commentary on the 2d book of Ar- 
chimedes’s Equiponderantes, published at 
Pisa in 1588. See Conic Sections. 
The first four books of Apollonius’s co- 
nics only have come down to us in their ori- 
ginal Greek language ; but the next three, 
the 5th, 6th, and 7 th, in an Arabic version ; 
and the 8th not at all. These have been 
commented upon, translated, and published 
by various authors. Pappus, in his Mathe- 
matical Collections, has left some account of 
his various works, with notes and lemmas 
upon them, and particularly on the Conies. 
And Eutocius wrote a regular elaborate 
commentary on the propositions of several 
of the books of the Conics. 
A neat edition of the first four books in 
Latin was published by Dr. Barrow, in 4to. 
at London, in 1675. A magnificent edition 
of all the books was published in folio, by 
Dr. Halley, at Oxford, in 1710 ; together 
with the Lemmas of Pappus, and the Com- 
mentaries of Eutocius. The first four in 
Greek and Latin, but the latter four in La- 
tin only, the 8th book being restored by 
himself. 
APOLOGUE, in matters of literature, 
? n ingenious method of conveying instruc- 
tion by means of a feigned relation, called 
a moral fable. 
The only difference between a parable 
and an apologue is, that the former being 
drawn from what passes among mankind, 
requires probability in the narration : where- 
as the apologue being taken from the sup- 
posed actions of brutes, or even of things 
inanimate, is not tied down to the strict 
rules of probability. jEsop’s fables. are a 
model of this kind of writing. 
APONOGETON, in botany, a genus of 
the Dodecandria Tetragynia. Ament com- 
posed of scales ; no calyx, no corol ■ cap- 
sules four ; three seeded. There are four 
species. 
APOPHTHEGM, a short, sententious, 
and instructive remark, pronounced by a 
person of distinguished character. Such 
are the apophthegms of Plutarch, and those 
of the ancients collected by Lycosthenes. 
APOPHYSIS, in anatomy, an excres- 
cence from the body of a bone, of which it 
is a true continuous part, as a branch is of a 
tree. 
