From these authors we shall here collect such extracts as relate to mechanical principles, or to geometrical construc tion, in the order of the above list.
Moxon treats the subject merely as a manual art. The following is extracted from lIalfpenny's Art of Sound Build ing: he seems to have been the first writer who considered joinery in a geometrical point of view ; his knowledge, how ever, is entirely confined to hand-railing.
" To find the raking arch, or mold!, for the hand-rail to a circular pair of stairs, in such a manner that it shall stand perpendicularly over its haw, or arch of the well-hole.
Figure 95.—" First describe a circle equal to the breadth of the. Nr el 1-h ol e, whose diameter is u w; as also another from the same centre, whose diameter is A Or, to represent the plan of the rail ; and divide the circumference of the greater circle into the same munber of equal parts as you would have steps once round the circle.
"This being done, take the back, or rake, of the bracket, equal to c in your compasses, and setting one foot in A, with the other strike the arch h: also take the height of one step, as A c, Figure 96, and setting one foot in n, with the other strike the arch i; and when this is done, take the distance from A to h in your eonipasses, and setting one foot in h, with the other strike the arch k, and take the height of two steps, and with one foot in c, draw the arch 1, to intersect the arch k, and so on.
"The intersecting points of the arehes h i, and k 1, and n o, and r s, and t n, are all at the same distance front one another, and the lines B h, c E 2), F r, and a t, being the risings or heights of the steps, in Figure 90, B It being the height of one step, c k of D n of three, E p of four, F r of five, and G t of six. Now, if these lines are raised up perpendicular on the circle a D 0, it is evident that the point of intersection of the arches h and i, will stand perpendicularly over the point B; of the arches k, 1, over c of the arches n and o, over D ; of the arches p, g, over E ; of the arches r and s, over F ; and of the arches t and a, over G. Now, if nails be struck into the intersecting points of the said arches, and a thin rule be bent round them, you may describe the arch, A h k n p r t, by the edge thereof, being the mould to strike the arch of the rail with.
" The arch or mould of the rail being found, as above, how to prepare the stuff of which the roil is to be made, and work the twist thereof without setting it up in its due position." Figure 97. "First strike two circles, whose diameters are equal to u w and A G, in Figure 95, and next consider into how many pieces you glue the rail, which in the semicircle let be six, as in the example.
"Now divide the semicircle into six equal parts, as E F,