To Draw From Or To The Circumference Of A Circle Lines Tending Towards The Centre, When The Centre Is Inaccessible

Divide the whole or any given portion of the circumference into the desired number of equal parts; then, with any radius less than the distance of two divisions, describe arcs cutting each other, as Al Bl, C2, D2, etc.; draw the lines C1, B2, D3, etc., which lead to the centre as required.

To Draw The End Lines

As AR, FR, from C describe the arc R, and with the radius CI, from A or F as centres, cut the former arcs at R, or R, and the lines AR, FR, will tend to the centre as required

To Describe An Arc, Or Segment Of A Circle Of Large Radii

Of any suitable material, construct a triangle, as ABC; make AB,BC, each equal in length to the chord of the arc DE, and height, twice that of the arc BB. At each end of the chord DE fix a pin, and at B, in the triangle, fix a tracer, (as a pencil,) move the triangle along the pins as guides; and the traces will describe the arc required.

Or otherwise.

Draw the chord ACB; also, draw the line HDI, parallel with the chord, and equal to the height of the segment; bisect the chord in C, and erect the perpendicular CD; join AD, DB; draw AH perpendicular to AD, and BI perpendicular to BD, erect also the perpendiculars An,Bn; divide AB and HI into any number of equal parts; draw the lines 1, 1, 2, 2, 3, 3, etc.; likewise divide the lines A n, B n, each into half the number of equal parts; draw lines to D from each division in the lines An,Bn, and through where they intersect the former lines, describe a curve, which will be the arc or segment required.

To Describe An Elliptic Arch, The Width And Rise Of Span Been Given

Bisect with a line at right angles the chord or span A B; erect the perpendicular A q, and draw the line q D equal and parallel to AC; bisect AC and A q in r and n; make C I equal to CD, and draw the line I r q; draw also the line n s D; bisect s D with a line at right angles, and meeting the line CD in g; draw the line g q, make CP equal to C k, and draw the line g P i; then from g as a centre, with the radius g D, describe the arc sD i; and from k and P as centres, with the radius A k, describe the arcs A s and B i, which completes the arch as required. Or,

Bisect the chord AB, and fix at right angles any straight guide, as b c; prepare, of any suitable material, a rod or staff, equal to half the chord's length, as d ef; from the end of the staff, equal to the height of the arch, fix a pin e, and at the extremity a tracer f; move the staff, keeping its end to the guide and the fixed pin to the chord; and the tracer will describe one-half the arc required.