CON 
equal to the effect ; hence it has been in- 
ferred that fluidity is the consequence of 
caloric. See Fluidity. Evei’y particular 
kind of substance requires a different de- 
gree of temperature for its congelation, 
which affords an obvious reason why p£u-ti- 
cular substances remain always fluid, while 
others remain always solid, in the common 
temperature of the atmosphere, and why 
others are sometimes fluid, and at others 
solid, according to the vicissitudes of the 
seasons, and the vai'iety of climates. See 
Cold, Freezing. 
CONGREGATION, an assembly of 
several ecclesiastics united, so as to consti- 
tute one body ; as an assembly of cardinals, 
in the constitution of the pope’s court, met 
for the dispatch of some particular business. 
Congregation is likewise used for as- 
semblies of pious persons, in manner of fra- 
ternities. 
CONGREGATION ALISTS, in church 
history, a sect ofprotestants who reject all 
church government, except that of a single 
congregation. In other matters, they agree 
with the Presbyterians. See Presbyte- 
rians. 
CONGRESS, in political affairs, an as- 
sembly of commissioners, envoys, deputies, 
&c. from several courts meeting to concert 
matters for their common good. 
CONGRUITY, in geometry, is applied 
to figures, lines, &c. which being laid upon 
each other, exactly agree in all their parts, 
as having the very same dimensions. 
CONIC sections, as the name imports, are 
such curve-lines as are produced by tiie mu- 
tual intersection of a plane and the surface 
of a solid cone. The nature and properties 
of these figures were the subject of an ex- 
tensive branch of the ancient geometry, and 
formed a speculation well suited to the sub- 
tle genius of the Greeks. In modern times 
the conic geometiy is intimately comiected 
with every part of the higher mathematics 
and natural philosophy. A knowledge of 
fliose discoveries that do the greatest ho- 
nour to the last and the present centuries 
cannot be attained without a familiar ac- 
quaintance with the figures that are now to 
engage our attention. 
We are chiefly indebted to the preserva- 
tion of the writings of Apollonius for a 
knowledge of the theory of tlie ancient 
geometricians concerning the conic sections. 
Apollonius was born at Perga, a town of 
Paraphylia, and he is said to have lived un- 
der Ptolemy Philopater, about forty years 
posterior to Archimedes. Resides his great 
CON 
work on the conic sections, he published 
many smaller treatises, relating chiefly to 
the geometrical analysis, which have all 
perislied. The treatise of Apollonius on the 
conic sections is written in eight books, and 
it was esteemed a work of so much merit 
by his contemporaries as to procure for its 
author the title of the great geometrician. 
Only the four first books have come down 
to us in the original Greek. On the revival 
of learning the lovers of the mathematics 
had long to regret the original of the four 
last books. In the year 1668, Borelli, pass- 
ing tlirough F’lorence, found an Arabic 
manuscript in the library of the Medici 
family, which he judged to be a translation 
of all the eight books of the conics of 
Apollonius : but, on examination, it was 
found to contain the first seven books only. 
Two other Arabic translations of the conics 
of Apollonius have been discovered by the 
industry of learned men : and as they all 
agree in the want of the eighth book, we may 
now regard that part of the treatise as irre- 
coverably lost. The work of Apollonius 
contains a very extensive, if not a complete, 
theory of the conic sections. The best edi- 
tion of it, is that published by Dr. Halley in 
1710 : to which the learned author has add- 
ed a restoration of the eighth book, execut- 
ed with so much ability as to leave little 
room to regret the original. 
Since the revival of leaming the theory of 
the conic sections has been much cultivated, 
and is the subject of a great variety of in- 
genious writings. Dr. Wallis, in his treatise 
“ De Sectionibus Conicis,” published at 
Oxford in 1656, deduced the properties of 
the curves from a description of them on a 
plane. Since this time authors have been 
much divided as to the best way of defining 
the curves, and demonstrating their elemen- 
taiy properties ; many, in imitation of the 
ancient geometriciims, making the cone the 
groundwork of their theories ; while others 
have followed the example of Dr. Wallis. 
OF the cone and its sections. 
Di^nitions. 
Let ADR be a circle (Fig. 1. Plate I. 
Conic Sections) and V a fixed point without 
the plane of the circle ; tlien, if a right line, 
passing continually through the point V, be 
carried round the whole periphery of the 
circle ADR, thatrightline, beingextended 
indefinitely on tlie same side of V as the 
circle, will describe a conic surface ; and, if 
it be likewise extended indefinitely on the 
other side of V it will describe two opposite 
conic surfaces. 
