Dialling, plain, concave, convex, projective, reflective, refractive. Shewing, how to make all such dials, and to adorn them with all useful furniture relating to the course of the sun; performed arithmetically, geometrically, instrumentally and mechanically: and illustrated with sculptures, engraven in copper, comprised in XIV distinct tractates... / [William Leybourn].

William Leybourn

Date:: 1700

Credit: Dialling, plain, concave, convex, projective, reflective, refractive. Shewing, how to make all such dials, and to adorn them with all useful furniture relating to the course of the sun; performed arithmetically, geometrically, instrumentally and mechanically: and illustrated with sculptures, engraven in copper, comprised in XIV distinct tractates... / [William Leybourn]. Source: Wellcome Collection.

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$Set one foot in B, and with the other foot crofs the former Arch G F D,’ with two fmall Marks or Arches, in the points D and F, and draw the right line D F.—Thirdly., let one foot of the Compares in the. third given point C, (they hill keeping the fame opening) and with the other foot crofs the lirh drawn ArchGF D, in the points E and G, and draw the right line EG, eroding the former right line DF in the pToint O, So fhall O be the Centre of a Circle; in which, if you fet one foot of the Compailes, and open the other to any of the three given points, the Circle fo deferibed fhall pafs diredly-through all the three points A, B, and C, as was required. P Pv O B L. XII. r Tiro Points mthin Circle being given .^how tojindthe Centre of the Arch of a Great Circle, which jhdlpafs through thofegiven Points. Definition.] \ Great Circle upon the Sphere, is fuch a Circle as divideth the Sphere or Globe into Two equal parts; and fo, the Arch of 'a Great Civch, deferibed upon a Plain, is Juch an Axc\ as divu deth the Perifery or Circumference of the Fundamental or Primitive Cir- ^ cle given.^ into Two eq^ual Parts. - Figure Praclice.JY’ ET G B H D be the Fundamental ox Primitive Circle given, XIL J_^ whofe Centre is C; and let the two points within the fame, through which the Arch of a Great Circle is to pafs, be X and Y. Firtf Through one of the given points X, and*Centreof the Circle C, draw a right line X C, extending it infinitely towards F; upon this line from the Centre C, ereftthe Perpendicular C B, and draw the right line B X, cuttingthe Circle in G, through which point G, and the Cen¬ tre, draw the Diameter, or right line G C H. Lafily\ Through the points B and H draw a right line, extending it till it cut the line X F in R, fo have you found a third point, viz. R, through which the Arch of the great Circle to be deferibed mufl: pafs; and now having three points, X, Y and R, you may through them (by the laft Problem) draw the Arch of a Circle, namely the Arch A X Y L R, whofe Centre will be at K, and whofe Arch will divide the Primitive Circle into two equal parts in the ppints A and L: And that it doth fo, is evident, for that the right line drawn from A to L, doth alfo pafs through C the Centre of the Primitive Circle,.' / ASTRO-$

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