x 
DEM 
eae wage born at Vitri,. in beak in hg year 1667. 
rev i 
His ve 
fons to private pupils, and alfo to read public leGures on 
the branches of f{cience in which he was moft converfant. 
Sir Ifaac Newton’s “ Principia” falling in his way, led him 
to pay particular attention to geometrical invelligations, and 
he fhortly after became a firft rate mathematician. 
foon affociated with the principal philofophers of his own 
times, and was eleled member of the Royal Society of 
London, and alfo of the academies Berlin and Paris. 
By the former he was fixed on as a fit perfon to decide the 
famous conteft between Newton and Leibnitz concerning 
the invention of fluxions. ‘Towards che clofe of his life he 
was confulted on all queftions relating to chances, gaming, 
and annuities, and by his anfwers he ‘chiefly fubfitted. He 
died at London November 154s at the great age of 87 
vears. Bef es many impa nt and interefting naners in 
ten or twelve volumes of ie Philofophical Tranfaétions of 
London, he publifhed, 1. “ Mifcelianea Analytica de Serie- 
“et 
oy 
n 
as firft ae in the year 1724. A fe 
mas Simpfon publifhed a work 
e hand{ome com- 
Mr. Sin 
the philofophers of that day as having acted in an uncandid 
and ungracious manner eee a young man of high merit 
and extraordinary talen 
S) rer in Natural Hiflory, a name given to 
a ftone famous among the writers of the middle ages for a 
number of imaginary virtues, fuch as rendering people vic 
torious over their enemies, and the like. All the deferip- 
tion they have left us of it is, ee it was variegated with 
two colours laid in lines fo as to reprefent a rainbow. It 
was probably an agat 
DEMONSTRABLE, a term ufed in the fchools, to 
fignify fomewhat that may be clearly and evidently proved : 
thus, it is de noaivabie: that the fide of a f{quare is incom- 
menfurable with the diagonal. 
DEMONSTRATION, in Logic, a fyllogifm in form, 
containing a clear and irrefragable proof of the truth of a : 
propofition. 
A demonftration is a convincing argument, the two frft 
vident; whence 
tion, aie alia on, and conclufi 
explication ig the fying down of the things fuppofed 
w the demonftration is to 
es cules to eal natu m 
nelufion ropofition that con the 
thing ] oe semunknied, * fully perfuading, and cou cneine 
the m 
method of demonftrating things in mathematics is 
the fame with pe of drawing conclutions from princip ales 
n lo I seen of mathematicians 
er a feri es: every thing is con- 
cluded by force of ‘login, ily omitting the premifes, 
- by means of quotations. To hav 
w tics, through want of obferving the fyllogiftic form. 
DEM 
which either occur of their own —o or are recollected 
the demonftration per- 
fect, the premifes of the Grllogitins fhould be proved by 
new fyllogifms, till at length you arrive at a fyllogifm, 
Paci the premifes are either definitions, or identic propo- 
Iti 
Indeed it might be demonftrated, Al ays cannot be a 
genuine demonftration, i. e. fuch a s fhall give full 
conviction, untlefs the thoughts be diretted therein accord- 
into fyllogifm: Herlinus, and Dafipoc 
the whole fix firft books of Euclid, and Heatchue all arith 
metic, in the fyllogift:c form 
Yet people, and even mathematicians, ufually i pe et 
that mathematical demonftrations are condu€ted in 
ner far remote from the laws of fyllogifm 3 fo far-are oe 
from allowing that thofe derive 7 their force and conviction 
from thefe. But we have men of the firft rank on our fide 
the states M. Leibnitz, be inftance, declares that ate 
moan vn fr atio 2 fo. rm an ee 
QO be rm ang ae valli 
WF ich te in tr ers 
edi in mat cr, is de 
or ifms at H 
ee ce oe Taaiee ee uentl 
Syiiocism. 
Problems confiit of three parts: a propofition, refolution, 
and demonftration. 
In the propofition is indicated the thing to be don 
In the refolution, the feveral fteps are orderly rehearfed, 
whereby the thing propofed is performed. 
Lattly, in the demonttration it is thewn, that the things 
enjoined by the refolution being done, that which was re- 
s often, therefore, 
folution las perfo : 
The fchoolmen cae wo kinds of demonftration; the 
one te bens or propter quod ; wherein an cffc&t is prove ed by 
the next ca when it is proved, that the moon is 
a Beenie the earth is then between the fun and 
fecond re 6s, or guia; wherein the caufe is 
prod from aremote effe& : as when it is proved, that fire 
is hot, becaufe it burns ; or that plants do not breathe, be- 
caufe they are not animals; or that there isa God, from 
works of creation. e former is called ene 
a priori, and the latter Senos on a potterio 
DEMONSTRATION, rmative, is that whic hb, proceed- 
ing by affirmative and evident ig pa dependent on 
each odice ends in the thing to be ea 
ONSTRATION, Apagog PAGO 
ONSTRATION, Geometrical is tha framed of > een 
ings pet from the elem ometry. 
EMONSTRATION, Mechanicay is that the reafonings 
aad are drawn from the rules of mech 
penal te ha is that ar era an effet is 
pro a caufe, either a next, or remote one; or a con- 
Hanon proved pel fomething previous, whether it be a caufe, 
r only an antecede nt. 
Dz erp a se i ahaha is that whereby either a 
caufe is proved from an effe&t, or a conclufion is proved by 
i pofterior ; hee it be an effet, or only a con- 
SS SEMONSTRATIVE, in Rhetoric, one of the genera, 
: or 
g 
3 
