ALL 
ALL 
matician of the 16th century. He was born 
at Uttoxeter in Staffordshire, in 1542 ; was 
admitted a scholar of Trinity College, Ox- 
ford, in 1561 ; where he took his degree of 
master of arts in 1567. In 1570 he quitted 
his college and fellowship, and retired to 
Gloucester Hall, where he studied very 
closely, and became famous for his know- 
ledge in antiquities, philosophy, and mathe- 
matics. He received an invitation from 
Henry, Earl of Northumberland, a great 
friend and patron of the mathematicians, 
and he spent some time at the Earl's house ; 
where he became acquainted with those ce- 
lebrated mathematicians, Thomas Harriot, 
John Dee, Walter Warner, and Nathaniel 
Torporley. Robert, Earl of Leicester, too, 
had a great esteem for Alien, and would 
have conferred a bishopric upon him ; but 
liis love for solitude and retirement made 
him decline the offer. His great skill in the 
mathematics gave occasion to the ignorant 
and vulgar to look upon him as a magician 
or conjurer. Allen was very curious and 
indefatigable in collecting scattered manu- 
scripts relating to history, antiquity, astro- 
nomy, philosophy, and mathematics: which 
collections have been quoted by several 
learned authors, and mentioned as in the 
Bibliotheca Alleniana. He published in 
Latin the second and third books of Pto- 
lemy, “ Concerning the Judgment of the 
Stars, or, as it is usually called, of the qua- 
dripartite construction, with an exposition. 
He wrote also notes on many of Lilly’s 
books, and some on John Bale’s work, 
“ De Scriptoribus Mag. Britannia;.” He 
died at Gloucester Hall in 1632, being 90 
years of age. 
Mr. Burton, the author of his funeral 
oration, calls him “ the very soul and sun of 
all the mathematicians of his age.” And 
Selden mentions him as a person of the most 
extensive learning and consummate judg- 
ment, the brightest ornament of the univer- 
sity of Oxford. Also Camden says he was 
skilled in most of the best arts and sciences. 
A. Wood has also transcribed part of his 
character from a manuscript in the library 
of Trinity College, in these words : “ He 
studied polite literature with great applica- 
tion ; he was strictly tenacious of academic 
discipline, always highly esteemed both by 
foreigners and those of the university, and 
by all of the highest stations of the church 
of England, and the university of Oxford. 
He was a sagacious observer, an agreeable 
companion,” &c. 
ALLIGATION, in arithmetic, is the 
rule of mixture, which teaches to compound 
several species of ingredients or commodi- 
ties together, according to any intent or 
design proposed ; and is either medial or 
alternate. 
Alligation medial shews the rate or 
price of any mixtures, when the several 
quantities of the mixture, and their rates, 
are known. 
Rule : multiply each quantity given, by 
the price ; and then, by direct proportion, 
say, as the sum of the quantities given, to 
the sum of the products ; so is any part of 
the mixture, to the value of that part. 
Example : a goldsmith melts 3 ounces of 
gold, at 41. 6s. 8 d. per ounce, with 12 
ounces at 41. per ounce, and 8 ounces at 
41. 5s. per ounce : when they are all melted 
together, one ounce will be found to be 
worth 41. 2s. id. Thus, 
os. 1. s. d. 
3 at 4 6 81 
12 4 0 0 > 
8 4 5 0) 
multiplied toge- 
ther produce 
l. 
13 
48 
34 
23 Sum Sum 95 
oz. 1. oz. 1. s. d. 
Then as 23 : 95 : : 1 : 4 2 7i Ans. 
Alligation alternate teaches to mix 
goods, of different prices, in such propor- 
tion, that the mixture may be sold for any 
price proposed. 
Rule : set down the names of the things 
to be mixed, together with their prices ; 
then, finding the difference between each of 
these, and the proposed price of the mix- , 
ture, place these differences in an alternate 
order, and they will shew the proportion of 
the ingredients. 
ALLION IA, in botany, so called in ho- 
nour of Charles Allioni, professor of botany 
at Turin, a genus of the Tetrandria Mono- 
gynia class and order, of the natural order 
of Aggregatae ; the calyx is a perianthium 
common to three flowers ; and the perian- 
thium proper is obsolete superior ; the co- 
rollas proper, one-petalled, funnel-shaped, 
and erect : the stamina have setaceous fila- 
ments ; anthers roundish ; the pistillum has 
a germ inferior, oblong, style setaceous, 
longer than the stamens, stigma multifid and 
linear, no pericarpium ; seeds solitary, the 
receptacle naked. There are three species. 
ALLIOTH, a star in the tail of the Greater 
Bear, much used for finding the latitude at 
sea. 
ALLITERATION, in rhetoric, is a fi- 
gure or decoration in language, chiefly used 
in poetry, and consisting in the repetition 
