The action and reaction between adjacent voussoirs occur along the lines of the forces R, therefore the polygon composed of these forces is appropriately named the Line of Resistance. It may be obtained as the funicular polygon of the forces P with the end-reactions K as the terminal sides.
Why do you speak to me of the stones? It is only the arch that matters to me." Polo answers: "Without stones there is no arch.
Wherefore a monk's whole attention should thus be fixed on one point, and the rise and circle of all his thoughts be vigorously restricted to it; viz., to the recollection of God, as when a man, who is anxious to raise on high a vault of a round arch, must constantly draw a line round from its exact centre, and in accordance with the sure standard it gives discover by the laws of building all the evenness and roundness required....
Centres, or centre-pieces of wood, are put by builders under an arch of stone while it is in the process of construction till the key-stone is put in. Just such is the use Satan makes of pleasures to construct evil habits upon; the pleasure lasts till the habit is fully formed; but that done, the habit may stand eternal. The pleasures are sent for firewood, and the hell begins in this life.
The exact shape of funicular (sometimes called linear or theoretical) arch[es] that carry all applied loads by axial compression only, may be developed by the same methods as used for finding the shape of cables. ...If the actual shape of the arch is different from funicular shape, the bending moment at any section of an arch is proportional to the ordinate or intercept between the given arch and funicular arch... This principle is called Eddy's Theorem.
From all ages architects have made use of arches in public buildings, as well for strength as beauty. Yet what was the true geometrical figure of an arch was not known before my demonstrations came out.
The true Mathematical and Mechanical Form of all manner of es for building with the true butment necessary to each of them, a Problem which no Architectonick Writer hath ever yet attempted, much less perform'd. ...Ut pendet continaum flexile, sic stabit contiguum rigidum, which is the Linea Catenaria.
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?
So counsel'd he, and both together wentHigh overarch'd, and echoing walks between.
The Romans were the first builders in Europe, perhaps the first in the world, fully to appreciate the advantages of the arch, the vault and the dome.