ISO 
TSO'LA SA'CRA, a fmall ifland at the mouth of the 
Tibet, near Oftia. 
ISO'LA della SCA'LA, a town of the Veronefe : 
thirteen miles fouth of Verona. 
ISOLAC'CIO, a town of the ifland of Corfica, thirty- 
eight miles of Porto Vecchio, and thirty-nine fouth-fouth- 
eaft of Corte. 
ISOLET'TA, a town of Italy, in the department of 
the Mela : fifteen miles fouth of Brefci,a. 
ISOJL'IC, adj. [from the Greek one, and koj, whole.] 
Entire; confining of one piece. 
ISOM’EfiRIA, f. in algebra, a term of Vieta, denoting 
the freeing an equation from’ fractions; which is done by 
reducing all the fractions to one comfhon denominator, 
and then multiplying each member of the equation by 
that common denominator, that is, reje&ing it out of 
them all. 
ISO'NA, a town of Spain, in Catalonia: twenty-four 
miles north of Balnguer. 
ISONO'MIA,yi [from urof, Gr. equal, and a dif- 
tribution.] An equal diftribution. 
ISOPERIM'ETERS/yi [from nroj, equal, te^i, round 
about, and purgov, a nteafure.] Plain figures which have 
equal primeters. 
ISOPERIMET'RICAL, adj. Having equal circum¬ 
ferences; having an equal perimeter. It is demonftrated 
in geometry, that among ifoperimetrical figures, that is 
always the greatell which contains the molt fides or an¬ 
gles. From whence it follows, that the circle is the moft 
capacious of all figures which have the fame perimeter 
with it. That of two ifoperimetrical triangles, which 
have the fame bafe, and one of them two fides equal, and 
the other unequal, that is the greater whofe fides are 
equal. That of ifoperimetrical figures, whofe fides are 
equal in number, that is the greateft which is equilateral 
and equiangular. And hence arifes the folution of that 
popular problem, To make the hedging or walling which 
will fence in a certain given quantity of land ; alfo to 
fence in any other greater quantity of the fame. For, let 
x be one fide of a redangle that will contain the quan- 
aa 
tity aa of acres; then will — be its other fide, and dou- 
2 clcl 
ble their fum, viz. zx -|——, will be the perimeter of the 
redangle; let alfo 6b be any greater number of acres, in 
the form of a fquare, then is b one fide of it, and 4b its 
perimeter, which muft be equal to that of the redangle; 
'ida 
and hence the equation zx -]- —— = 4 b, or x* + a* = zbx, 
In which quadratic equation the two roots are x = b ± 
l/ b* —- a z , which are the lengths of the two dimenfions 
of the rectangle, viz. whofe area b 5 is in any proportion 
lefs than the fquare a- of the fame perimeter. As, for 
example, if one fide of a fquare be 10, and one fide of a 
redangle be 19, but the other only 1 ; fuch fquare and 
parallelogram will be ifoperimetrical, viz. each perimeter 
40 5 yet the area of the fquare is 100, and of the paralle¬ 
logram only 19. 
Ifoperimetrical lines and figures have greatly engaged 
the attention of mathematicians at all times. The 5th 
book of Pappus’s Colledions is chiefly upon this fubjed; 
where a great variety of curious and important properties 
are demonftrated, both of planes and folids, fome of which 
were then old in his time, and^nany new ones of his own. 
Indeed it feems he has here brought together into this 
book all the properties relating to ifoperimetrical figures 
then known, and their different degrees of capacity. On 
this head, fee alfo Simpfon’s Trads, p.-g8; and the Phil. 
Tranf. vol. xlix. and 1 . 
ISOPHYL'LUM, f. in botany. See Bupleurum. 
ISOPY'RUM,yi [from icoc, Gr. like, and wvgo?, a grain 
of wheat.] In botany, a genus of the clafs polyandria, 
order polygynia, in the natural order of multifiliquse, (ra- 
VOL. XI. No. 766. 
I S O 441 
nunculace.T, Ju]f. ) The generic characters are—Calyx : 
none. Corolla: petals five, ovate, equal, fpreading, deci¬ 
duous ; nedaries five, equal, tubular, very fhort, with a 
three-lobed mouth, the outer lobe larger, the receptacle 
inferted within the petals. Stamina: filaments numerous, 
capillary, fhorter than the corolla; antherae Ample. Pif- 
tillutn : germs very many, ovate; ftyles Ample, the length 
of the germ ; ftigtnas blunt, the length of the,ftameii.s. 
Pericarpium: capfules Afeveral, Emulate, recurved, one- 
celled. Seeds : very many. Allied very nearly to Helle- 
borus, but extremely different in habit. I. thalidroides 
has two or three germs only.— EJfcntial Character. Calyx 
none; petals five; nedary trifid, tubular; capfule re¬ 
curved, many-feeded. 
Species. 1. Ifopyrum fumarioides, or fumitory-leaved 
ifopyrum : fiipules awl-fhaped ; petals acute. This is an 
annual plant, feldom more than three or four inches high. 
The leaves, which are fhaped like thofe of fumitory, are 
fmall, and of a grey colour. The ftalk is naked to the 
top, where there is a circle of leaves juft under the flowers. 
The flowers are fmall, of an herbaceous colour on the out- 
fide, but yellow' within. Capfules ten to fifteen, legumi- 
nofe, compreffed a little, fetaceous-beaked, curved a little 
inwards, veined, pale, thin, opening inwards. Seeds fixed 
in a double row to the edge of the opening future, fmall, 
ovate-globular, covered with little raifed dots, blackifh, 
marked on one fide with a linear liilum or fear. Native 
of Siberia, whence the feeds w'ere fent to the imperial gar¬ 
den at Peterfburgh ; and Dr. Ammann fent a part of the 
feeds to Mr, Miller, who cultivated them at Chelfea in 
1759. It flowers at the beginning of April, and the feeds 
ripen in May. 
2. Ifopyrum thalidroides, or meadow-rue-leaved ifopy¬ 
rum : ftipules ovate ; petals obtufe. All parts of this 
plant are fmootb, except the lower part of the Item and 
radical leaf, which is a little villofe. Root perennial, 
creeping horizontally. Root-leaf one, feldom two, ten¬ 
der, fhorter than the Item, on a long upright petiole, twice 
trifid ; leaflets blunt, widening towards the end, two-lobed 
or three-lobed, netted-veined, afli-coloured, refembling 
the leaves of Thaliftrum minus, or bulbous fumitory. 
Stem commonly Angle, from fix inches to near a foot irt 
height, fimple or very feldom branched, naked below, but 
having a leaf or two towards the top, like the root-leaf, 
only lefs compound; the item terminates in a few fpreading 
flender peduncles, each bearing one fmall flower; the pe¬ 
tals of which are at firft white, but turn red or purple, 
the natural number is five, but there are fometimes fix. 
Native of the fputh of Europe. Mr. Miller had it from 
the neighbourhood of Verona, and cultivated it in 1759. 
It flowers at the end of March, and the feeds ripen in 
May. 
3. Ifopyrum aquilegioides, or columbine-leaved ifopy¬ 
rum : ftipules obfolete. This has leaves like the fecond, 
but a little larger and of a greener colour. The Italks 
rife about fix inches high, fupporting two or three fmall 
white flowers, fhaped like thole of the preceding. It 
flowers in April, And the feeds ripen in June. Accord¬ 
ing to Cafpar Bauhin, and Haller, and Krocker from him, 
it differs from the preceding in having a very fmall root; 
the ftem a long fpan in height, flender, having two or 
three, fhort, entire, ftipular leaves on it, the reft like thofe 
of Thaliclrum minus, only frhaller; and a Angle blue 
flower, five times lefs than that of the preceding. Native 
of the mountains of Swifferland, Moravia, Trent, and the 
Apennines, in meadow’s, flowering in the fpring. It is 
the fame with Aquilegia vifeofa of Linnaeus. See AQVI- 
legia, Helleborus, and Thalictrum. 
Propagation and Culture. Thefe plants delight in afhady 
fituation. All that is required is to fow the feeds in a 
fhady border foon after they ripe, or permit them to fcat- 
ter; and, when they come up, keep them clean from weeds. 
ISO'RA,/. in botany. See Helicteres. 
ISORD'SKICK, or Krot'za, a town of Servia: four- 
5 U teerj 
