\y],: l® 1 *' line only touches the circle in a mathematical point,H a ° . ^as no parts nor dimensions, and lias consequently no8 tud e . but a t i ia t j las ne ither magnitude nor
a thing
bears no proportion to another that has, anddi v -T l therefore measure it. Hence we see the reason of the$ ee A ° n of circles into 360 parts or arcs, called degrees.
, , of circles into 360 parts orilFo 3 ’ Circle , and Mensuration.of p r C1IANICS (from the Greek grjygivi), art ) that branchpo\p c l* ca l mathematics which treats of motion and movingp 'f. their nature, laws, effects, &c. This term, in a1%; ar sense > > s applied equally to the doctrine of the equi-8 c j eri 111 °f powers, more properly called statics, and to thatttiQti Ce w hich treats of the generation and communication ofc a n , n > which constitutes dynamics, or mechanics strictly so“See Force, Motion, Power, and Statics.
13 science is divided by Newton into practical andn^ch . mechanics, the former of which relates to the- ' nif,nl powers, viz., the lever, balance, wheel and axis,
Pull
fati Q -f’Wedge, screw, and inclined plane ; and the latter, ortlia p Q 1 Mechanics, to the theory of motion ; showing, whenthat, r< i? s or powers are given, how to determine the motionCua, ‘h result from them ; and, conversely, when the cir-or j, nces of the motion are given, how to trace the forcesfyte ) 6rS / rom which they arise.
Coiigiq lan ' ca > according to the ancient sense of the word,aiith or 18 ° n ^ t ^ le ener gy °f organs, or machines. TheCal]„> 8 v '' ao have treated the subject of mechanics systemati-
■> have ,.i-- .. . i. , • , • •" m
l *ottigive
ave observed, that all machines derive their efficacyt s * na Pi e forms and dispositions, which may bean Ce t 0 °, or S ans interposed between the agent and the resist-friVf ;ri ,“ e overcome; and to those simple forms they havene name of mechanical powers, simple powers , or
f'h m<lc ^ nes '
^^oubt^T 01 * 0 ^ US6S ^ ie severa f mechanical powers wereHoU v known to the ancients, but they were almost8c '®nce ^«, ae< l ua i n f e< i with the theoretical principles of this. nl a vwt info . an( j ^ j s therefore not a little
HioU , book, enumerates several ingenious machines,then been in use from time immemorial. Weraising or transporting heavy bodies, they■ for tv* 108 ^ °f fhe means which are at present commonlyill.
- lutn ' they seem to have been unacquainted till the
8 Ui'p r jV ui a very late period ; . __ .
Petits a p *kat the construction of machines, or the instru-•^tstr ^chanics, should have been pursued with suchlr| hi s carried by them to such perfection. Vitruvius ,
fi ' icl1
U^'oyed for
n 6(1 Cth
l ‘e p u jj nat purpose, such as the crane, the inclined plane,^iliV,^- 6 ^’ ^" c -! but with the theory or true principles of
NofA m > th ey S . . .
of p c n . me d e s. This celebrated mathematician, in hisf Cr Utn Jl 'l Ul P on d e rants, considers a balance supported on a8 ^ aa w^ havi, ?g a weight in each scale ; and taking as aJ 6 e< Jual v. f rinc ^d e , that when the two arms of the balance; s ° of ’ tae .two weights supposed to be in equilibrio are( p Cr eas e( ] ec , eas ’ t y equal, he shows, that if one of the arms bej l,r| ini s j 1( \ t le weight applied to it must be proportionallyi 0 Wei„i ‘ Hence he deduces the general conclusion, thatp §th, ar | , s sus pended to the arms of a balance of unequalK°Porti 0n , rer uaining in equilibrio, must be reciprocallyt; ace ativ, ^ to arms of the balance ;
and this is the first
, - meet • .. °f an y theoretical investiga-
of 8 , die t ft , o ani -l 8c >ence. Archimedes also further observed,af( le b;\] an Weiglits exert the same pressure on the fulcrum^Wards pw as ,^' the y were directly applied to it; and he
Q^ftomoth •-»-
gep 8 ° on • ( P°mts of the balance, then to two others,
extended the same idea to two other weights sus-
OQl , ’ ^
i(3 e * a hence, step by step, advanced towards theSioag ^ 0 the centre of gravity, a point which he proved
gravity, a point ■
every assemblage of small bodies,
provedand conse-
quently to every large body, which might be considered asformed of such an assemblage. This theory he applied toparticular cases, and determined the situation of the centreof gravity in the parallelogram, triangle, trapezium, parabola,parabolic trapezium, &c. &c. To him we are also indebtedfor the theory of the inclined plane, the pulley, and the screw,besides the invention of a multitude of compound machines ;of these, however, he has left us no description, and thereforelittle more than their names remain.
We may judge of the very imperfect state in which thetheory of mechanics was at that time, by the astonishmentexpressed by king Hiero, when Archimedes exclaimed, “ Giveme a place to stand on, and I will move the earth!’’ a pro-position which could have excited no surprise in any personpossessing a knowledge of the simple property of the lever.Of the theory of motion, however, it does not appear thateven Archimedes possessed any adequate idea ; the proper-ties of uniform motion seem only to have engaged theattention of the ancients, and with those of accelerated andvariable motion they were totally unacquainted : these weresubjects to which their geometry could not be applied, themodern analysis being necessary to bring this branch of thescience to perfection.
From the time of Archimedes till the commencement ofthe sixteenth century, the theory of mechanics appears tohave remained in the same state in which it was left by thisprince of Grecian science, little or no additions having beenmade to it during so many ages; but about this time,Stevinus, a Flemish mathematician, made known directly,without the introduction of the lever, the laws of equilibriumof a body placed on an inclined plane : he also investigated,with the same success, many other questions on statics, anddetermined the conditions of equilibrium between severalforces concurring in a common point, which comes, in fact,to the celebrated proposition relating to the parallelogram offorces ; but it does not appear that he was at all aware of itsconsequences and application. In 1592, Galileo composed atreatise on statics, which he reduced to this single principle,viz:—It requires an equal power to raise two different bodiesto heights having the inverse ratio of their weights : that is,whatever power will raise a body of two pounds to the heightof one foot, will raise a body of one pound to the height oftwo feet. On this simple principle he investigated the theoryof the inclined plane, the screw, and all the mechanicalpowers ; and Descartes afterwards employed it in consideringthe statical equilibriums of machines in general, but withoutquoting Galileo , to whom he had been indebted for the firstidea. After Stevinus and Galileo, Torricelli, Descartes ,Huygens, Wallis, Wren, Newton, Leibnitz , Dechales,Oughtred, Keil, Delahire, Lagrange, Atwood, Prony, Emer-son, Watt, Gregory, Young, &c., have, in succession, sincethe period to which we have alluded, explained and appliedthe principles of this civilizing science in a wonderfulmanner.
MECHANICAL CARPENTRY, that part of the art ofconstruction in timber which treats of the proper dispositionof framing, so as to enable it to resist its own weight, orany additional load or pressure that may be casually laidupon it.
Mechanical Carpentry is so called from the principlesof mechanics being employed in the construction of truss-framing, or other parts of the art ; while ConstructiveCarpentry shows the rules for cutting and framing thetimbers according to the proposed design. See that article.
The mechanical principles of a piece of carpentry aretherefore first to be considered ; because they must, in somemeasure, regulate the disposition and size of the timbers in