CON 
CON 
not only mark out the stars, but, that they 
may better bring them into order, they dis- 
tinguish them by their situation and position 
in respect to each other; and therefore they 
distribute them into asterisms, or constella- 
tions, allowing several stars to make up one 
constellation; and lor the better distinguish- 
ing and observing them, they reduce the 
constellations to the forms of animals, as men, 
bulls, bears, &c. or to the images of some 
things known, as of a crown, a harp, a ba- 
lance, & c. or give them the names of those 
whose memories, in consideration of some 
notable exploit, they had a mind to transmit 
to future ages. The division of the stars by 
images and figures is of great antiquity, and 
seems to be- as old as astronomy itself; for in 
the most antient book of Job, Orion, Arctu- 
rus, and the Pleiades, are mentioned: and we 
meet with the names of many of the constel- 
lations in the writings of the first poets, Ho- 
mer and Hesiod. .See Astronomy. 
Theantients, in their division of the firma- 
ment, took in only so much as came under 
their notice, distributing it into forty-eight. 
Modem astronomers divide the whole starry 
firmament into three regions: 1. The zodiac, 
or that portion of the heavens in which the 
planets would appear to move, to an eye 
placed in the sun. The breadth of this space 
depends on the inclination of the orbits in 
which the planets move, to one another; and 
includes twelve constellations, commonly 
called the signs of the zodiac, viz. aries, tau- 
rius, gem ini, cancer, leo, virgo, libra, Scor- 
pio, Sagittarius, capricornus, aquarius, and 
prices. 2. All that region of the heavens 
that lies on the north side of the zodiac, 
which contains 21 constellations, viz. the ursa 
minor and major, draco, cepheus, bootes, co- 
rona septentrionalis, hercules, lyra, cygnus, 
cassiopeia, perseus, andromeda, trianguhim, 
auriga, pegasus, equuleus, delphinus, sagitta, 
aquila, serpentarius, and serpens; to which 
were added afterwards two others, viz. that 
ofantinous, which was made of the stars not 
included in any image, near the eagle; and 
Berenice’s hair, consisting of stars which are 
near the lion’s tail. 3. That region on the 
southern side of the zodiac, which contains 
15 constellations, known to the antients, viz. 
cetus, theeridanus, lepus, orion, canis major, 
cams minor, argo, hydra, crater, corvus, 
centauiTis, lupus, ara, corona meridionalis, 
and piscis australis: to these are lately added 
twelve more constellations, which are not to 
be seen by us who inhabit the northern re- 
gions, because of the convexity of the earth, 
but in the southern parts they are very con- 
spicuous; these are the phoenix, grus, pavo, 
Indus, avis paradisi, triangulum australe, mus- 
ca, chameleon, piscis volans, toucan, hydrus, 
xiphias. The galaxy, or milky-way, is also 
to be reckoned among the constellations. 
.See each constellation, and the number of 
stars it contains, under its proper head ; and 
also the article. Astronomy. 
CONSTITUTION, an ordinance, decision, 
regulation, or law, made by authority of any 
superior, ecclesiastical or civil. The consti- 
tutions of the Boman emperors make apart 
of the civil law, and the constitutions of the 
church make a part of the canon law. 
Constitution, by way of eminence, is 
an appellation given to that hull of pope 
Clement XI. which begins with the word 
unigenitus. 
CON 
427 
the equations of the filth and sixth powers, 
and so on. For example: 
To construct a simple equation. This is done by 
resolving the given simple equation into a pro- 
portion, or finding a third or fourth propor- 
Thus, 1. If the equation be ax—bc\ 
be 
then a \ b \ \ c \ x — - , the fourth propor- 
a 
tional to a, b, c. 
b 2 
2 . If ax — b 2 ; then a \ b * * b \ x — , a 
a 
third proportional to a and b. 
3 - If ax — b 2 — c 2 ; then, since b 2 — c 2 = 
b -j- c x b — 
<+<X 
Constitution, apostolical, a collection j fho fourth power, because 2x2 = 4; and the 
of regulations attributed to the apostles, and | intersections of the circle or conic sections 
supposed to have been collected by St. Cle- with a line of the third order, will construct 
ment, whose name likewise they bear. It is " 
the general opinion, however, that they are 
spin ions, and that St. Clement had no concern 
in them. They appeared first in the 4th age, . 
but have been much changed and corrupted j 
since that time. They are divided into | tional, &c. 
eight books, consisting of a great number of 
rules and precepts, relating to the duties of 
Christians, and particularly the ceremonies 
and discipline of the church. Mr. Whiston, 
in opposition to the general opinion, asserts 
them to be a part of the sacred writings dic- 
tated by the apostles in their meetings, and 
written down Irom their own mouths by St. 
Clement ; and intended as a supplement to 
the New Testament, or rather as a system of 
Christian faith and polity. The reason why 
the constitutions are suspected by the ortho- 
dox, and perhaps the reason also why their 
genuineness is defended by Mr. Whiston, is, 
that they seem to favour Arianism. 
Constitution, in a physical sense, is 
that particular disposition of the human body, 
which results from the properties and mutual 
actions of the solids and fluids, and which 
renders them capable of exercising the func- 
tions proper and conformable to nature. 
CONSTRUCTION, in geometry, is the 
drawing such lines, such a figure, &c. as are 
previously necessary for the making any de- 
monstration appear more plain and unde- 
niable. 
Construction of equation'!, in algebra, 
is the finding the roots or unknown quanti- 
ties of an equation, by geometrical construc- 
tion of right lines or curves ; or the reducing 
- c, it will be a * b c \ * b — c * x 
h — c 
, a fourth proportional to a , 
b -{- c, and b — c. 
4. It ax — b 2 -j- c 2 ; then construct the right- 
angled triangle ABC, (See Plate Miscel. tig. 17 ,) 
whose base is b, and perpendicular is c, so shall 
the square of the hypothenuse be b 1 -j- c 1 , which 
call !r ; then the equation is ax — h 2 , and .v = 
b 2 
—, a third proportional to a and h. 
To construct a quadratic equation. 1 . If it he a 
simple quadratic, it maybe reduced to this form 
x 2 ~ ab ; and hence a * x ’ * x * b, or .v = 
\/ ab a mean proportional between a and b. 
Therefore upon a straight line (fig. 18 ) take AB 
— a, and BC = b ; then upon the diameter AC 
describe a semicircle, and raise the perpendi- 
cular BD to meet it in D ; so shall BD be = a- 
the mean proportional sought between AB an<b 
BC, or between a and b. 
2. If the quadratic be affected, let it first be 
d -f- 2 ax — b 2 ; then form the right-angled tri- 
giveil equations into geometrical figures^ I angle whose base AB (fig. 19 ) is a, and perpen- 
And this is effected by-lines or curves, ac- j dicular BC is i ; and with the centre A and ra- 
cording to the order or rank of the equation, i dius AC > d< * scribe the semicircle DCE ; so shall 
The roots of any equation may be deter- | and be tb f two roots tbe given qua- 
mined, that is, the equation.™, be co»- 1 2 „ = t „ cn 
stmeted, by the intersections of a straight line ! .^'construction will be the eery same as of the 
with another line or curve oithe same dimen- ; preceding one x 2 -f- 2 ax — b l . 
sions as the equation to be constructed ; for j 4. But if the form be 2 ax — a- 2 — b 2 ; form a 
the roots of the equation are the ordinates of right-angled triangle whose hypothenuse FG 
the curve at the points of intersection with is a, (fig 2 . 0 ,) and perpendicular GH is b ; then 
the right line, and it is well known that a with the radius FG and centre F describe a 
curve may be cut by a right line in as many j semicircle IGK ; so shall IH and HK be the 
points as its dimensions amount to. Thus, tw0 roots °f die given equation 2 ax — a 2 — b 2 * , 
then, a simple equation will be constructed or x \~ 2ax — See Maclaurin’s Algebra, 
by the intersection of one right line with an- P art 1U ’ ca P' and bim P son s Algebra, p. 267 . 
Other; a quadratic equation, or an affected ' 7 '° construct cubic and biquadratic equations. — 
equation of the 2d rank, by the intersection ! These a . re constructed by the intersections of 
of a right line with a circle, or any of the i * wo c B mc sections; for the equation will rise to 
conic sections; which are all lines of the 2d 1 ^ dimensions, by which are determined the 
order, and which may be cut by the right 
hue in two points, thereby giving the two 
roots of the quadratic equation. A cubic 
equation may be constructed by the intersec- 
tion of the right line with a line of the 3d or- 
der, and so on. 
But if, instead of the right line, some other 
line of a higher order be used, then the se- 
cond line, whose intersections with the former 
are to determine the roots of the equation, 
may be taken as many dimensions lower as 
the former is taken higher. And in general 
in equation of any height will be constructed 
by the intersections of two lines whose di- 
mensions, multiplied together, produce the 
dimension of the given equation. Thus, the 
intersections of a circle with the conic sec- 
tions, or of these with each other, will con- 
struct the biquadratic equations, or those of 
3 112 
ordinates from the four points in which these 
conic sections may cut one another; and the 
conic sections may be assumed in such a man- 
ner, as to make this equation coincide with any 
proposed biquadratic, so that the ordinates from 
these four intersections will be equal to the 
roots of the proposed biquadratic. When one of 
the intersections of the conic section falls upon 
the axis, then one of the ordinates vanishes; and 
the equation by which these ordinates arc de- 
termined, will then be of three dimensions only, 
or a cubic ; to which any proposed cubic equa- 
tion may be accommodated. So that the three 
remaining ordinates will be the root3 of that 
proposed cubic. The conic sections for this 
purpose should be such as are most easily de- 
scribed ; the circle may be one, and the parabola 
is usually assumed for the other. 
, CON SUBSTANTIATION, a tenet of the 
lulheran church with regard to the manner 
of the change made in the bread and v me 
