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the Sum of the Squares of 3 and 6, viz. 45, divided by o, the Sum of the Roots, gives 5.
Proportion is alio ufed for the Relation between un- equal Things of the fame kind, whereby their feveral Parts correfpond to each other with an equal Augmentation, or Diminution.
Thus, in reducing a Figure into little, or in inlargmg it, Care is taken to obferve an equal Diminution, or Enlarge- ment, thro' all iis parts 5 fo that if one Line, e.gr. be contrafled by one third of its Length; all the reft fliall be contracted in the fame Proportion.
The making of Reductions of this kind, is the great ule of the proportional Compaffes. See Compasses. See alfo Reduction, and Draught.
Proportion, in Law. See Deonerando/™ ratapor-
tionis. , . _ ' . , - ,
Proportion, in Architeflure, the juft Magnitude of the Members of each part of a Building, and the Relation ot the feveral Parts to the Whole; e.gr. of the Dimensions of a Column, (£c. with regard to the Ordonnance of the Buil- ding. See Symmetry. See alfo Building.
One of the grcatefl Differences among Architefls, M. Terraidt obferves, is in the Proportions of the Heights of Entablatures with refpea to theThicknefs of the Columns, to which they are always to be accommodated. See En- tablature. , t 1* L «
In effca, there is fcarce any Work, either ot the An- tients cr Moderns, wherein this Proportion is not different; fome Entablatures are even near twice as high as others — let 'tis certain, this Proportion ought of all others to be mod regulated; none being of greater Importance, as there is none wherein a Defect is fooner fpied, nor any wherein it is more ihocking. See Column.
Proportion is likewife understood of the Magnitudes of the Members of Architeflure, Statues, or the like, with regard to the Ditknce whence they are to be view'd.
The molt celebrated Architefts are much divided in their Opinions on this Subjea : Some will have it, that the parts ought to be enlarg'd in proportion to their Eleva- tion; and others, that they ought to temain in their natu- ral Dimenfions. See Statue.
Proportion, in Painting, is the juft Magnitude of the feveral Members of a Figure, a Group, iSc. with regard to one another, to the Figure, the Group, and the whole Piece. SeePAiNTiNG. _ • , ■
Proportion makes one of the moft important Articles in the Art of Painting, the principal Subjea it is employ'd in, being the human Body; for which reafon, the Curious in that Art will thank us for the following Scheme of the Rules and Laws thereof.
By the way, let it be obferv'd, 1°. That to meafure and fet off Proportions, we either divide the Module into twelve Parts, and fubdivide each of thofe into four; or divide the Face into three Lengths of the Nofe; fubdividing each Length into twelve : " Or lallly, divide the whole Face into three, and fubdivide each of thofe into four : which lad Method is what we fhall here follow.
a . That the Multiplicity of little Meafures are to be iludioully avoided, becaufe they confound; and becaufe they require great Skill in Ofteology, to hit juftly.
3 . That in Meafuring, there be a regard had to the Relievo, or Juttings out of Figures.
The Rides of Proportion in Painting.
In the Proportions of a human Figure, regard is had to the Ago, Sex, and Quality.
As 10 Age; we confider three Stages thereof; Infancy, Youth and'Manhood. For the firft; at three Yearsof Age, we count five Lengths of the Face, from Top to Toe; viz. from the Tip of the Head to the Bottom of the Belly, three; thence to the Foot, two; Breadth about the Shoul- ders, one Face, one eighth : and in the place of the Hips, one Face.
At lour Years, the Height is fix Faces }. viz. from the Top of the Head to the Bottom of the Belly, three Faces {, thence to the Sole of the Foot, three Faces. The Breadth about the Shoulders one Face f. about the Haun- ches, one Face \.
At five Tears, the Height is fix Faces i. -» abated, the lower being Shorter.
In Youth at twelve Years, we have two Proportions; the one from Nature, which gives nine Faces for the Height; the Breadth about the Shoulders, two Faces; about the Haunches, I Face f. The other from the antique Statues, as that of Laocoon, t£c. which give the Height, ten Faces ~. the Breadth from one Shoulder to another, one Face f. at* the Haunches, 1 \. at the place of the Mufcle, call'd FaP.us Extermts, 2. The Thigh 1, the Knee f and I a Subdivision, and at the Ankles 1.
In the State of Manhood, when the Meafures are arriv'd at perfeflion; we reckon the Height ten Faces : the iff, from
the Top of the Head to fhcNoftril; the =d, to the Hole in the Neck between the Clavicles; the 3d, to the Pit „f the Stomach, cM'd Cartilage Enfifortnis; the 4th, to the Navel; the 5th, to the pyramidal Mufcles; thence to the Knee i;, and as much to the Sole of the Foot -The Ex- tent of the Arms is the fame with the Height; viz. from the Tip of the long Finger to the Joints of the Wrifls, one Face; thence to the Elbow 1 f; thence to the Juncture of the Shoulders, 1 j; thence to the Hole in the Neck 1 -J-; in all five Hea^s, which with the five of the other Arm gives ten : The Thicknefs of the Arms to be adjusted by the Quality or Charaaer.
As to the Breadth of the Figure feen Front wife; the Width of the Shoulders a-crofs the Seltoides, is » Faces-' - Breadth of the peaoral Mufcle, to the Joncture of the Arm, a. About the Haunches, where the Obliqtli extey. ni are, 1 f> and three Subdivisions. The Thighs, at the biggeit place, I : The Knee }, three Subdivisions g. fj^ Leg at the thickeft, 1 and 1 Subdivifion. The Extr eme f the Ankle, f, 1 Subdivifion i. The Feet, J, and t a Sub- division. Their Length, 1 Face ^, 1 Subdivifion.
Others, meafuring by the Length of the whole Head make only eight Heads, in Height and Breadth; thus! The Head, one; thence to the bottom of the Breads, one; thence to the Navel, one; thence to the Yard, one; thence to the middle of the Thigh, one; thence to the lower parts of the Knee, one; thence to the fmall of the Leg, one; thence to the bottom of the Foot, one.
The Breadth, thus : From the End of the long Finger to the Wrift, one; thence to the Bend of the Arm, one; thence to the bottom of the Shoulder, one; thence over to the other Shoulder, two; thence to the End of the other long Finger, three.
To thefe general (Proportions, may be added others, which ufually obtain; as, rhat the Hand is the Length of the Face; the Thumb the Length of the Nofe; and the great Toe the fame : The two Nipples, and the Hole in the Neck, make a juft equilateral Triangle : The Spice between the Eyes, is the breadth of an Eye : The breadth of the Thigh, at the thickeft, is double that of the thickeft part of the Leg, and treble that of the fmalleft : From the top of the Head to the Nofe, the fame as from the top of the Nofe to the Chin. The distance from rhe Chin to the Throat-pit, is the breadth of the Throat; the distance of the Centre of rhe Eye from the Eye-brow,the fame as the Prominency of the Nostrils; and the Space between them and the upper Lip. The Length of the Fore-Finger, the fame as the Space thence to the Wrift; the Space from the tip of the F'ore- Finger to the Wrift, the Length of the Face.
For the Sex : The ^Proportions of Man and Woman dif- fer in height; in that the Woman has a longer Neck; the parrs at the Breads, and the lower parts of the Belly, big- ger by half a part; which makes the fpace from the Bread to the Navel, lefs by one part; and the Thigh iliorter by * a third part.
As to breadth, a Woman has her Breads and Shoulders narrower, and Haunches larger; and Thighs, at the place of their Articulation, larger; Arms and Legs thicker, Feet {freighter; and becaufe Women are more fat and flefhy, their Mufcles are lefs feen, and therefore the Contours more fmooth and even.
Young Maids have little Heads, long Necks, low or down Shoulders, flender Bodies, Haunches big, Legs and Thighs long, Feet little.
Young Men have the Neck thicker than Women, the Shoulders and Breads larger, the Belly and Haunches nar- , rower, Legs and Thighs ilenderer, and Feet larger.
As to the Quality of Subjeas,we are either to follow Sim- ple Nature, or fine and agreeable Nature, or to chufe Na- ture, or exceed ir. In following fimple Nature, in com- mon and Country Subjeas, Men of dull Wit, and a moid Temperament to be of an heavier and rougher Propor- tion, the Mufcles appearing but little diftingui/h'd; the Head big, Neck fhorr, Shoulders high, Stomach little, Knees and Thighs thick, and Feet large.
In Nature, as fine and agreeable, for ferious Histories, £&• the Figures of the Heroes to be well fliaped, the Haunches high and uptight, the Joints well knit, little and compacf, free from Flefh and Fat,
Military Men, to have the Head little, Neck thick and nervous, Shoulders large and high, Body and Paps elevated, Haunches and Belly little, Thighs mufcly, principal Muf- cles rais'd up and knit together at the Heads; the Legs fmooth, Feet flender, Soles hollow.
Nature is fomerimesto be feleaed, i.e. made up ofpa rts from various good Originals, to form extraordinary and perfea Figures for great and heroic Subjeas, as in Ro&all Hiftories; giving, thus, a Charaaer of Force fufEcient to execute Aftions agreeable to the Defcriptions the Poets, &c. make. t
Ladly, fometimes Nature is to be exceeded, as in Re- prefentations of fabulous Deities, of Heroes and Giants:
In
