To the extent possible under law, the Text Creation Partnership has waived all copyright and related or neighboring rights to this keyboarded and encoded edition of the work described above, according to the terms of the CC0 1.0 Public Domain Dedication (http://creativecommons.org/publicdomain/zero/1.0/). This waiver does not extend to any page images or other supplementary files associated with this work, which may be protected by copyright or other license restrictions. Please go to http://www.textcreationpartnership.org/ for more information.
Three points in the circumference of a circle being given, to find a dia∣meter▪ upon which there being perpendiculars let fall from the points given; the segments of the diameter intercepted by these perpendiculars shall be proportional to another proportion given.
In the circle B C D whose center is A, let the points given be B, C, D, and let it be required to find the diameter of that circle upon which per∣pendiculars
being let fall fall from the points B, C, D, the segments of the Diameter shall be proportional to another proportion given: let the pro∣portion of the segments intercepted by the perpendiculars let fall from B and C be required to be as S to R.
Let the line C B be cut in E, so as C B may be to E B, as S to R, and let D E, cut the Diameter F G at right angles in H. Then is F G the Diameter sought, upon which seeing the lines B I, C K, D H doe fall perpendicularly, K I shall be to H I as S to R.
For the right lines C B are parallel, or not parallel, if they be parallel, C B shall be equal to K I, and E B to H I, and then by construction K I shall be H I, that is C B to E B, in the given proportion as S to R. But if they can meet, let the point of their meeting be at L. Then it shall be as L C to L K, so L E to L H, and so is L B to L I. And then dividing and changing the termes, it shall be as K I to H I, so is C B to E B, or so is S to R as was required.
And thus likewise K H and H I, with the arches B C, C D, and B D, being given, we may find the arch B G, and the Diameter F G in the same parts with K H and H I, for the arches C D and D B being given, the subtenses of those arches and angles opposite to them in the triangle B C D shall be given also in the parts of the Diameter F G, and there∣fore the sides E B and D B with the angle E B D being given, the angle E D B or D B M shall be given also, which being deducted from the arch B M D shall leave B M or the double of B G.