POS 
armoury, &e. proper for the hanging on of 
cloaks, hats, &c. 
PORTRAIT, PouRTRAiT, or PouR- 
TRAiTURE, in painting, the representation 
of a person, and especially of a face done 
from the life. In this sense we use the 
term portrait-painting, in contradistinction 
to history-painting, where a resemblance 
of person is usually disregarded. Portraits, 
when as large as tlie life, are usually painted 
in oil-colours ; sometimes they are painted 
in miniature with water-colours, crayons, 
pastils, &c. See Painting. 
PORTUL.ACA,in botany, purslauc, a ge- 
nus of the Dodecandria Monogynia class 
and order. Natural order of .Succiilentae. 
PortulaccEE, Jussieu. Essential character : 
calyx bifid ; corolla tive-petalled ; capsule 
one-celled, cut round, or tlnec-valved. 
There are twelve species ; of which P. ole- 
facea, garden purslane, is an annual her- 
baceous plant, with a round, procumbent, 
succulent stem ; diffused branches, often 
throwing out fibres at the joints ; leaves 
wedge-shaped, oblong, blunt, fleshy, ses- 
sile, clustered, especially at the ends of the 
branches: flowers sessile, corollas yelloiv, 
spreading ; it is a native of both Indies, 
Xlhina, and Japan. 
PORTULACARIA, in botany, a genus 
of the Pentandria Trigynia class and order. 
Essential character : calyx two-leaved ; pe- 
tals five; seed one, tlu-ee-sided and winged. 
There is but one species, viz. P. afra, a na- 
tive of Africa. 
POSITION, or the rule of false Posi- 
tion, otherwise called the rule of Fals- 
HOOD, in arithmetic, is a lule so called, 
because in calculating on several false num- 
bers taken at random, as if they were the 
true ones, and from the differences found 
therein, the number sought is determined. 
This rule is either single or double. Single 
position is when there happens in tlie pro- 
position some partition of numbers into 
parts proportional, in which case the ques- 
tion may be resolved, at one operation, by 
this rule. Imagine a number at pleasure, 
and work therewith according to the tenor 
of the question, as if it were the true num- 
ber : and what proportion there is between 
the false conclusion and the false propor- 
tion, such proportion the given number has 
to the number sought. Therefore the num- 
ber found by argumentation shall be the 
first term of the rule of three ; the second 
number supposed, the second term ; and 
the given number, tlie third. Or the result 
is to be regulated by this proportion, vis. 
POS 
As the total arising from the error to the 
true total, so is the supposed part to' the 
true one. Example, A, B, and C, design- 
ing to buy a quantity of lead to the value 
of 1401. agree that B shall pay as much 
again as A, and C as much again as B ; 
what then must each pay ? 
Now suppose A to pay 101. then B must 
pay 201. and C 401. the, total of which is 
701. but should be 1401. Therefore, if 701. 
should be 1401. what should 101. be ? 
Answer, 201. for A’s share, wdiicli dou- 
bled makes 401. for B’s share, and that 
again doubled gives 801. for C’s share, the 
total of which is 1401. Double position is 
when there can be no partition in the num- 
bers to make a proportion. In this case, 
tlieiefore, you must make a supposition 
twice, proceeding therein according to the 
tenor of the question. If neither of the 
supposed numbers solve the proportion, ob- 
serve the errors, and whether they he 
greater or less than the supposition requires, 
and mark the errors accordingly with the 
sign X and — . 
Then multiply contrarywise Ihe one po^ 
sition by the other error, and if the errors 
he both too great, or both too little, sub- 
tract the one product from the other, and 
divide the difference of the products by the 
difference of the errors. If the errors he 
unlike, as the one -j- and tiie other — , add 
the products, and divide the sum thereof 
by the sum of the errors added together : 
for the proportion of the errors is the same 
with the proportion of the excesses or de- 
fects of the numbers supposed to be the ' 
numbers sought ; or tlie suppositions and 
their errors being placed as before, work 
by this proportion as a general rule, viz. 
as tjie difference of the errors if alike ; or 
their sum, if unlike, to the difference of 
the suppositions, so eitiier error to a fourth 
number, which accordingly, added to or 
subtracted from the supposition against it, 
will answer the question. 
Position, in geometry, is a term some- 
times used in contradistinction to magni- 
tude ; tlius a line is said to be given in po- 
sition, positione data, when its situation, 
bearing, or direction, wdth regard to some 
other line, is given ; on the contrary, a line 
is given in magnitude, when its length is 
given, but not its situation. 
POSITIVE, a term of relation some- 
times opposed to negative ; hence a posi- 
tive quantity, in algebra, is a real or af- 
firmative quantity, or a quantity greater 
than nothing ; thus called in opposition to 
