DIAGONAL. 
thus: _fuppofe = Aa a -angled parallelogram A BCD 
o. D is the greater diagonal, and A C 
rectangle o by and by the ma lib. n. in the 
triangle DAC, ce fais a the fide AC is equal to the 
fum of the fquares of AD, and CD, abating double the 
reCtangle of the fame, “ al . Confe- 
quently, the former excefs precifely compenfating this defect, 
ft Pita als is equal to 
,£.D. 
‘to the acute ne; or, which amounts to the ree tang, 
if the two contiguous fides of the parallelogram be extended 
dire€tly, end to end, in a right line, the great diagonal be- 
conies the fum of the two fides, and the lefler one, nothing. 
pelled at the fame time by two forces, w 
the fame ratio to each other as the contiguous fides have, 
force corre{ponding thereto. eg 
of the propofition ; for the ratio of two forces, and the angle 
would defcribe in a certain time MPOSITION of 
Motion, and Dyna a lemy, o 
that the reGangle of the two diagonals of any quadrila- 
teral infcribed in a circle, is equal to fum of the two 
‘reCtangles contained under sie onesate fides: for the de- 
smonftration of this property, fee Circe 5 art. 15. 
All the fides of a reCtilinear aa as AB, BC, CD, 
DE, EA (fg. 
And, a 
and ae diagonal BD found. 
nographies, or plans, are beft taken, by having 
all ne fides and diagonals, the ufe of this problem, in plani- 
metry, is of fome importance ; efpecially to fuch as are 
willing to have their work. accurate, though at the expence 
»of calculation. 
is ir tlolved 
Draconat Motion. Application of two, and three forces, 
in different planes, to produce every diverfity of re@ilinear 
and curvilmear motion by the agency of machinery, 
In mo machires commonly ufed, the motions are either 
rotatory or reciprocating, Even the latter motion is feldom 
ufed, unlefs where the defired effect cannot be produced 
by the rotatory movement. fitting machines to fuper- 
fede, or diminifh the necefity of human labour, mechanics 
have, as mnch as poflible, ttudied to reduce the re cipro- 
cating to the rotatory motion, wherever it appeared pradti- 
cable. The cylindrical cards of an engine for carding ool 
or cotton, the barrel organ, and many other machines,, are 
oe proofs of this; and the reafon of this prefer. 
ence is very obvious to every perfon at all converfant with 
the theory, or practice of mechanics, recipro« 
cating motion, the dire€tion ts fo frequently reverfed, that 
the inertia, or vis inertiz, as it is commonly called, fant al- 
ways produce a very confiderable effe@& upon the momentum 
cf the machine, and tend very much to impede its motion 
and diminifh its power. Perhaps, after all thei ee at eas 
for which mankind are indebted to Mr. Watt, in the con- 
firuétion of fteam-engines, this is ftill ae principal defidera- 
tum, in that moft ufeful and valuable machine. rotatory 
motions, on the contrary, the movement being panei 
round a centre, the inertia, fo far from impeding, tends al- 
tions are abfolutely neceffary, fe rotatory motion is he 
rally combined with them, and fly or balance-whezls added 
to countera& the inequalities of power, and velocity pro- 
duced by the a while the dire€tion of the motion is 
changed. But the rotatory movement is too limited in its 
operation to pradi ce the infinite combination of motions of 
which machinery is fufceptible, and the reciprocating mo- 
tions Saguieel at hie are moft frequently confined to‘one 
eh e adaptation of machinery for the diminu- 
tion or fuperfeffion of labour, thofe machines are firft con- 
ructed, where the mechanical sha may be applied in 
great force. ence, in infant ftates, cranes, water-mills, 
and fuch engines are fooner fought co than cloc tches, 
, wate 
and other mechanical — more particularly fuited 
toa refined ftate of foc 
The motions nich ae y be given to any piece of ma- 
nfinite, and Jne lines of direGion in whicn 
may be changed 
The following 
rks, which are the refults of a very long train of prac- 
tical, and ultimately fuccefsful experiments, may be of fome 
ufe in dire€ting the attention of mechanics to the conftruc- 
tion of a {pecies of machinery, psec not generally known, 
ufed in Britain; and only applied by thofe foreigners 
ake have ra€tifed it to pao: of mere fpeculative and 
i aaa curiofity. The purpofe for which the expe- 
riments were made, was to enable one perfon to work any 
given number of needles, for making flowers and other orna- 
ments upon cloths, of various kinds, by the procefs called 
tambouring. It is, however, equally fuitable to any other 
art or manufacture where diverfified motion is required. 
The theorem upon which the principle is founded, is thus 
expreffed in the rft and 2d corollaries to the 5th law of 
motion, as given in Mr. Motte’s oma of the Princi- 
ia of fir Ifaac Newton. ‘ Corollary if. A body, 
