Arc

“ Imperceptible in themselves, the heights become perceptible by their shadows. A road illuminated by a distant arc light gives us a startling instance of this; the smooth surface taking on from its shadows the look of a ploughed field. ”

“ The Secant of an arc is a line drawn from the center of the circle to the extremity of the tangent.
8. The Cosecant of an arc is the secant of the complement.
9. The Versed Sine of an arc is the distance from the extremity of the arc to the foot of the sine.
For the sake of brevity, these technical terms are contracted thus: for sine A B, we write sin. A B; for cosine A B, we write cos. A B; for tangent A B, we write tan. A B, etc.
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101]
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Fig. 137.
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Drawing Materials and Instruments.
Drawing tools or instruments are contrived solely for mechanical drawing ”

“ It is only a few seconds of arc per century, one second of arc being less than the 300,000th part of a right-angle, but that she should be apparently slowing down was a disquieting puzzle. The solution of the mystery lies in the fact that the Earth herself is the laggard, turning less and less quickly on her own axis. ”

“ Ark, s. arc, referring to the arc of the horizon extending from sunrise to sunset, B 2 (see note) ; daily course of the sun, E 1795; arc, the apparent angular distance passed over by the sun in a day and a night, A. ii. 7. 7; Arch (the same) , A. ii. 9. 2; Arches, pl. arcs, A. ii. 7. 9.
Arm, s. arm, A 111, 158; Arm in arm, T. ii. 823, 1116, 1725; Armes, pl. arms (an oath) , D 833; arms, 3. 953; T. iii. ”

“ Set off the arc I H, equal to D E and draw F H. The angle F is equal to A as required.
Fig. 111.
Ex. 8.—To bisect an angle, Fig. 111. Let A C B be the angle; on the center C cut the sides at A B. On A and B as centers describe arcs cutting at D dividing the angle into two equal parts.
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Fig. 112.
Ex. 9.—To find the center of a circle or of an arc of a circle. Fig. 112. Draw the chord A B, bisect it by the perpendicular C D, bounded both ways by the circle; and bisect C D for the center G.
Fig. ”

“ But Nature had an admirable way of taking down these rock giants hanging between the heavens and the earth. Arch after arch was at length made in wondrous grandeur from that rugged and distorted atmospheric land; and if ever man's eye rested upon the sublime, in an act of God's creative power, it was when He arcuated the heavens with such a line of stupendous mountains! ”

“ Then, of such equal parts as the whole circumference ABCDEF contains fifteen, the arc ABC, which is the third part of the whole, contains five, and the arc AB, which is tht; fifth part of the whole, contains three; therefore their difference, the arc BC, contains two of the same parts. ”

“ When the foundations of the earth were laid, the Great Architect "measured the waters in the hollow of his hand, and meted out the heavens with a span, and comprehended the dust of the earth in a measure, "and weighed the mountains in scales, and the hills in a balance;" ”

“ One is the visible direction or curve of the arch, which may generally be considered as the under edge of its voussoirs, and which has often no more to do with the real stability of the arch, than a man’s apparent conduct has with his heart. ”

“ An arch formed by the intersection of two short sprouting lines could suggest only a feeble power of growth; but the lines of the tall mediæval arch seem to express a crescent force immensely surpassing that of nature. ”

“ I never met but with two men in my life who knew enough of perspective to draw a Gothic arch in a retiring plane, so that its lateral dimensions and curvatures might be calculated to scale from the drawing. ”

“ We have only further and thirdly to remark with reference to such embellishments that in addition to pointed arches, piers, and circles, the forms once more call to mind those of the real organic world. ”

“ If an arch is 12,000 miles in length, all that we here ask is, whether the materials which compose the arch are sufficiently elastic to allow themselves to be so far stretched that the crown may be raised 200 feet. ”

“ Those archæologists who have racked their brains to find it have vainly added together the measurements of naves and clerestories; they have not yet succeeded in formulating the idea they expected to see emerge from the sums total. ”

“ Straight lines showing the direction of the needle are drawn from those degrees which are marked on the meridian of the earth or a terrella to their proper arcs and the corresponding points on those arcs. ”

“ IT seems rather hard lines that, even if the archæologist goes personally into the field, and gathers with his own hands specimens of stone implements, he is not quite free from the possibility of being imposed upon. ”

“ When one comes to examine the texts, whether written on paper or papyrus, burnt in brick, or cut on stone, which archæologists have obtained from all these sources, we at once realise that man's earliest observations of the heavenly bodies in all the regions we have named may very fairly be divided into three perfectly distinct stages. ”

“ There are, I well know, advocates for the round arch, whose theory appears to be that we ought to go back for some ages, to throw ourselves as it were into the position of men who knew only the round arch, and from this to attempt to develope in some new direction: this is Mr. ”

“ As ’tis in an Arch, where each single stone, which if sever’d from the rest would be perhaps defenceless, is sufficiently secur’d by the solidity and entireness of the whole Fabrick of which it is a part. ”

“ Fond archer, Hope! who tak'st thy aim so far,
That still or short, or wide thine arrows are! ”

“ There are three departments of architecture: the art of building, the making of timepieces, and the construction of machinery. ”

“ The design of a temple depends on symmetry, the principles of which must be most carefully observed by the architect. ”

“ History fades into fable; fact becomes clouded with doubt and controversy; the inscription moulders from the tablet; the statue falls from the pedestal. Columns, arches, pyramids, what are they but heaps of sand, and their epitaphs but characters written in the dust? ”

“ If by the soul you mean the Form or Essence of the living animal, by the circle, the Form of the circle, by the right angle, the Form or Essence thereof, — then this Form is posterior in regard to the notional parts of which it is constituted, but prior in regard to the particular circle or right angle. ”

“ All ornamental work resolves itself into movements of three kinds—angular, circular and straight. From the combination of these with each other, the times where they merge and emerge, where a movement of one kind changes into any other, where an ellipse becomes part of a circle, where circles are generated across the circumferences of other circles, where these patterns are drawn over and upon each other without destroying the character of either—we say, by such movements, and many others which it would be confusing to follow, the most beautiful forms are made. ”

“ Ex. 3.—To draw a perpendicular to a straight line, from a given point in that line, Fig. 100. With any radius from any given point A in the line B C, cut the line at B and C. Next, with a longer radius, describe arcs from B and C, cutting each other at D, and draw the perpendicular D A.
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Second Method, Fig. 101. From any center F above B C, describe a circle passing through the given point A, and cutting the given line at D; draw D F, and produce it to cut the circle at E; and draw the perpendicular A E.
Fig. ”

“ This chain reaches from Eternity to Eternity, ever in triangles—is not my symbol a triangle?—ever in circles—is not the symbol of the Beloved a circle? Therein is all progress base illusion, for every circle is alike and every triangle alike! ”

“ The sod scarce heaved; and that tall flower that wets—
Like a child, half in tenderness and mirth—
Its mother's face with heaven-collected tears
When the low wind, its playmate's voice, it hears.
And in the warm hedge grew lush eglantine,
Green cowbind and the moonlight-colour'd May,
And cherry-blossoms, and white cups whose wine
Was the bright dew yet drain'd not by the day;
And wild roses, and ivy serpentine,
With its dark buds and leaves wandering astray;
And flowers, azure, black, and streak'd with gold,
Fairer than any waken'd eyes behold. ”

“ Indeed, it thus became the second principle, as a circle which, by developing, becomes a figure and a a surface, whose circumference, centre, and rays are distinct, occupying different points. The origin of things is better than their goal. ”

“ You seem to mark out for yourself a certain sphere, and if you go beyond it, you think you do yourself an injury. Thus, while you have an apparent movement, you are only describing a circle, whose centre and circumference is self. ”

“ I can within myself correct the external appearances and impressions of objects, and advance, upon the reports and hints received by my senses, to form ideas of things that are not extant in matter. By seeing a material circle I may learn to form the idea of a circle, or figure generated by the revolution of a ray about its centre ”

“ A circle has proverbially neither beginning nor end. In what order then are we to consider these signs? In the heavens they form a never-ending circle. Where is the beginning and where is the end of this circle through which the sun is constantly moving? ”

“ When a circle is made, and from its centre a number of lines are drawn to the circumference, all these lines, though ever so distant in the circumference, meet together in the point, which is in the middle. ”

“ For the first, indeed, and most proximate circle is that which every one describes about his own mind as a centre, in which circle the body, and whatever is assumed for the sake of the body, are comprehended. ”

“ Convito di Dante, Opere, t. i. p. 48, ed. Ven. 1793. “Upon the back of this circle, in the heaven of Venus, whereof we are now treating, is a little sphere, which has in that heaven a revolution of its own: whose circle the astronomers term epicycle.” ”

“ The outer circle, coat, or contour, of which you have heard others besides myself speak, is the surface crust of our globe, the great sphere of land and water on which man is at present an inhabitant. ”

“ This also holds for higher moments, provided that the edges of the elementary strips or prisms are parallel to the line or plane with regard to which the moments are taken.
33. Solids and Surfaces of Revolution.—The solid or surface generated by the revolution of a plane closed figure or a plane continuous line about a straight line in its plane, not intersecting it, is a solid of revolution or surface of revolution, the straight line being its axis. The revolution need not be complete, but may be through any angle. ”

“ The circle represents the Infinite, without beginning or end; the straight line represents the finite, which has both beginning and end. The sphere represents self-existent and eternal individuality and Mind; the straight line, a belief in a self-existent and temporary material existence. ”

“ And so, through a brilliant circle of equally holy acts, the beauty of which we have only briefly hinted at, the cradle and the grave, however far asunder they may chance to be, are bound in one continuous circle. ”

“ Then a body that is by nature heavy will hang in the air. Al. "Why not ? as steel does, being borne up by the loadstone. What wonder is it that one stone hang in the very middle of the air, when the whole earth laden with so many rocks hangs after the same manner ?
Cu. But where is the centre of the earth? AL Where is the centre of a circle ? Cu. That is a point that is indivisible ; if the centre of the earth be so small, whosoever bores through the centre takes it away, and then heavy bodies have nowhere to tend to. ”

“ A body of men walking in a circle remain together as a body within the circumference of the circle as it moves with the earth; change their paths to a cycloid directed to a distant point, and the body of men will move away in that direction; change their paths to parallel right lines, and as a body they may soon be a mile away and still in a circle. ”

“ The long lines define the measure and rhythm of the work. Lines are the vibrations of the soul; lines are reflections of the will, the rigidity of that which endures. Like currents of forces they flow against each other and unite into one. ”

“ Let A be the centre of a plane surface, and B the point to which the shadow of the gnomon reaches in the morning. Taking A as the centre, open the compasses to the point B, which marks the shadow, and describe a circle. ”

“ Nevertheless, movement in a circle is the most “natural” movement; and the long arm of the lever, moving, as it does, in the larger circle, has the greater amount of this natural motion, and consequently requires the lesser force. ”

“ Another important line is AB, the Base or Ground line, as it is on this that we measure the width of any object to be represented, such as ef, the base of the square efgh, on which the cube C is raised. E is the position of the eye of the spectator, being drawn in perspective, and is called the Station-point. ”

“ The outer surface of a pencil line represents the surface of the earth; the inner surface of the line represents the depth of man's explorations; the highest mountain would be represented by a comma resting on the line. ”

“ The lilacs and laburnums, lit with the glory-fires of autumn, hung burning and flashing in the upper air, a fairy bridge provided by kind nature for the wingless wild things that have their home in the tree-tops and would visit together; the larch and the pomegranate flung their purple and yellow flames in brilliant broad splashes along the slanting sweep of woodland, the sensuous fragrance of innumerable deciduous flowers rose upon the swooning atmosphere, far in the empty sky a solitary oesophagus slept upon motionless wing; everywhere brooded stillness, serenity, and the peace of God. ”