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'DUPLICATE, adj. Duplicate ratio is the proportion 
•»f fquares. Thus, in a rank of geometrical proportions, 
the firft term to the third is faid to be in a duplicate ratio 
of the firft to the fecond, or as its fquare is to the fquare 
of the fecond : fo in 2, 4, S, 16, the ratio of 2 to 8 is a 
duplicate of that of 2 to 4, or as the fquare of 2 to the 
fquare of 4. Phillips. Harris.- —It has been found, that the 
attraction is aimed reciprocally in a duplicate proportion 
of the didance of the middle of the drop front the con- 
courfe of the glajfes, viz. reciprocally in a fimple pro¬ 
portion, by realon of the fpreading of the drop, and its 
touching each glafs in a larger furface ; and again reci¬ 
procally in a fimple proportion, by reafon of the attrac¬ 
tions growing Stronger within the fame quantity of attract¬ 
ing furface. Newton. 
DU'PLICATE,y; Another correfpondent to the fird; 
a fecond thing of the fame kind.—Nothing is more need¬ 
ful for perfecting the natural hidory of bodies, than the 
fubjeCting them to the fire; to which end I have re- 
ferved duplicates of the mod confiderable. Woodward. 
•DU'PLICATE, f. in law, is ufed for the fecond let- 
ters-patent, granted by the lord chancellor, in a cafe 
wherein he had before done the fame ; which were there¬ 
fore thought void. But it is more commonly a copy or 
tranfcript of any deed or writing, account, &c. or a fe¬ 
cond letter, written and fent to the fame party and pur- 
pofe as a former, or a copy'of difpatches for fear of a 
mifearriage of the fird, or for other reafon's. 4 Car. II. 
c. 10. It is alfo the name of the difeharge, given by the 
quarter fedions, &c. to an infolvent debtor, who takes the 
benefit of an act, for relief of infolvent debtors, with r.e- 
fpeCt to th.e imprifonment of their perfons. 
DUPLICA'TION, f. The a< 5 t of doubling.—What 
■ great pains hath been taken concerning the quadrature of 
a circle, and the duplication of a cube, and fome other ma¬ 
thematical problems! Hale. —The aft of folding together. 
A fold ; a doubling.—The peritonaeum is a (trong mem¬ 
brane, every where double ; in the duplications of which 
ail the vifeera of the abdomen are hid. Wijeman. 
The duplication of a cube, is finding out the fide of a 
cube that fhall be double in folidity to a given cube: 
which is a celebrated problem, cultivated by the ancient 
geometricians upwards of 2000 years ago. It was firft 
propofed by the oracle of Apollo at Delphos; which, 
being confulted about the manner of ftopping a plague 
then raging at Athens, returned for anfwer, that the 
plague fliould ceafe when Apollo’s altar, which was cu¬ 
bical, (hould be doubled. Upon this they applied them- 
felves in good earned to feek the duplicature ot the cube, 
which from thence was c. lled the Delian problem. This 
problem cannot be effefted geometrically, as it requires 
the folution of a cubic equation, or requires the finding 
of two mean proportionals, viz. between the fide of the 
given cube and the double of the fame, the firft ot which 
two mean proportionals is the fide ot the double cube, 
as was firft obferved by Hippocrates of Chios. For, let 
a be the fide of the given cube, and z the fide of the 
double cube fought; then it is z 3 = 2a 3 , or a 2 : z 3 :: z : 
2a ; fo that, if a and z be the firft and fecond terms-of a 
fetof continued proportionals, then a 2 : z 2 is the ratio of 
the fquare of tire firft to the fquare of the fecond, which, 
it is known, is the fame &s the ratio of the firft term to 
the third, or of the fecond to the fourth, that is, of z to 
2a; therefore z being the fecond term, za will be the 
fourth. So that z, the fide of the cube fought, is the 
fecond of four terms in continued proportion, the firft and 
fourth being a and 2 a, that is, the fide of tire double cube 
is the firft of two mean proportionals between a and 2 a. 
Eutocius, in his Commentaries on Archimedes, gives fe- 
vefal ways of performing this by the mefolabe. In Pap¬ 
pus, too, are found three different ways ; the firft accord¬ 
ing to Archimedes, the fecond according to Hero, and the 
third by an inftruntent invented by Pappus, which gives 
all the proportions required. The lieur de Comiers has 
Jikewifc publiftted a demonftration of the fame problem, 
Vop. VI. No. 336. 
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by means of a compafs with three legs. But all thefe 
methods are only mechanical. See Valerius Maximus, lib. 
viii. alfo Eutocius's Com. on lib. ii. Archimedes de Sphnra, 
& Cylindro-, and Pappus, lib. iii. prop. 5. and lib. iv. 
prop. 22. 
DU'PLICATURE,yi A fold ; any thing doubled'.— 
The lymphedufts, either dilacerated or obftrufted, exo¬ 
nerate themfelves into the foldings, or’between the duplL 
catures of the membranes. Ray. 
DUPLPCITY, f. iduplicis, Lat.] Doublenefs; the 
number of two.—Do not ailed! duplicities nor triplicities., 
nor any certain number of parts, in your divifion of things. 
Watts. —Deceit ; doublenefs of heart or of tongue. 
DU'PLIN, a county of the American States, in Wil¬ 
mington diftrift, North Carolina, bounded eaft by- On¬ 
flow, and fouth-weft by Sampfon. The number of in¬ 
habitants 5662. The chief town is S are ftp', on the north- 
eaft branch of Cape Fear. 
DUPON'DIUS,/! in antiquity, a weight of two pounds, 
or a money of the value of two affes. See As, vol. ii. 
p. 249. 
DUP'PA (Brian), a refpeftable Englilh prelate, born 
at Lewilham in Kent, in 1588-9. He was educated at 
Weftminfter fchool ; whence he fvas elefted ftudent of 
Chriftchurch college, Oxford, in 1605. He took his 
degree of bachelor of arts in 1609; and in 1612 vvqs 
chofen a fellow of All-Souls college. In 1619, he was 
chofen one of the proctors to the univerlity of Oxford, 
which office lie palled through with reputation and ge¬ 
neral refpett. He was made chaplain to the earl of Dor- 
let, by whole intereft with the king he was appointed 
to the deanery of Chriftchurch, Oxford, in 1629. To,this 
church and college he was, during his relidence in it, 
and at his death, a liberal benefadtor. In 1634, he was 
conftituted chancellor of the church of Sarum, and loon 
afterwards made chaplain to Charles I. who, in 163S, ap¬ 
pointed him tutor to Charles prince of Wales, and after¬ 
wards to his brother the duke of York. In 1638, Dr. 
Duppa was prefented to the reftory of Petworth in 
Suffex, and in the fame year nominated to the bifhopric 
of Chichefter. In 1640, he was tranflated to the fee of 
Salt (bury ; but was .prevented from deriving any benefit, 
from it by the civil war of Charles I. Bifhop Duppa 
joined the king at Oxford, and frequently attended him 
during his imprifonment in the Ifle of Wight. Accord¬ 
ing to fome writers lie was not only privy to the compo- 
lition of the Eikon Bafilikc, but alfo contributed his aid 
towards it. It is certain that great confidence was placed 
in him by the king, who entrufted him with the delicate 
bulinefs of fupplying the vacant bifhoprics ; which office 
he retained under Charles II. After the reftoration, his 
fteady loyalty was rewarded by a tranftation to the rich 
bilhopric of Winclfofter, in 1660. He was alfo made lord 
almoner, and appointed one of the vifitors of the univer- 
fity of Oxford. About the year 1661, he began to ereft 
an hofpital for th.e maintenance of poor people at Rich¬ 
mond ; and projected other works of piety and charity, 
which he was prevented from completing by his death, 
which took place in 1662, in the feventy-fourth year of 
his age. He was the author only of a few fermons and 
devotional pieces ; and of a collection of veries in praife 
of BenJonfon and hisAvorks. 
DUPRATC See Prat. 
DUPRE' de St. MAUR (Nicolas Francis), born at 
Paris about the clofe of the feventeenth century, brought 
up for the long robe, and obtained a place of matter of 
accompts. He was greatly relpefted, as well for his of¬ 
ficial conduft, as for his literary talents and focial quali¬ 
ties. He was one of the firft of the French men of let¬ 
ters who acquired a tafte for Englilh literature, and en¬ 
deavoured to promote it among their countrymen. For 
this purpofe he undertook a tranftation of Milton’s P&- 
radife Loft in profe, the fpirit and elegance of which ren- 
dered it popular, though doubtlefs it could convey but 
a very imperfedt idea of the great original. This,work 
K k gained 
