On a curious Property of vulgar Fractions. 335 
is true, but known in France by the name of Pylones, and which 
the Greeks also called Propylee. There are here also two 
truncated pyramids 66 feet high, which contain between them the 
principal gate and grand entrance. ‘This gate leads into a spa- 
cious court surrounded by galleries, formed on one side by eight 
columns, on the other by pilasters, on which are affixed as 
caryatides, but without bearing any thing, some colossal statues 
of Osiris. The aspect of the whole inspires, accor ding to the 
report of eye-witnesses, a sentiment of ineffable veneration. 
Opposite to the principal entrance rises a second pylone of a 
smaller size. It leads into a second peristyle, also formed of 
caryatides, pilasters, and columns. 
[ fo be continued. | 
ae 
LXXIX. Ona curious Property of vulgar Fractions. By 
Mr. J. Farry, Sen. 
To Mr. Tilloch. 
Sin, — a3 examining lately, some very curious and ePita 
Tables of “ Complete decimal Quotients,” calculated hy Henry 
Goodwyn, Esq. of Blackheath, of which he has printed a copious 
specimen, for private circulation among curious and practical 
calculators, preparatory to the printing of the whole of these 
useful Tables, if sufficient encouragement, either public or indi- 
vidual, should appear to warrant such a step: | was fortunate 
while so doing, to deduce from them the following general pro- 
perty 5 viz. 
If all the possible vulgar fractions of different values, whose 
greatest denominator (when in their lowest terms) does not exceed 
any given number, be arranged in the order of their values, or 
quotients; then if both the numerator and the denominator of any 
fraction therein, be added to the numerator andthe denominator, 
respectively, of the fraction next but one to it (on either side), 
the sums will give the fraction next to it; although, perhaps, 
not in its lowest terms. 
For example, if 5 be the greatest denominator given; then are all 
the possible Be pe: when arranged, = 33 - = = os 
as the given fraction, we have 
4 baw 
> =» and 3 taking = 
4 1 
the next smaller fraction then ss 
=> the next larger fraction to + Again, if 99 be 
€ 
ol. 47. ". 217. May 1816.' Bb the 
