Davies, Charles, 1798-1876 · New York and Chicago, A. S. Barnes and company · leaf 52
THEOREM XVIII. An angle formed by two tangents is measured by half thedifference of the intercepted arcs. Let CD and DA be two tangents tothe circle at the points C and A : thenwill the angle CD A be measured by halfthe difference of the intercepted arcs CEAand CFA. For, draw the chord AF parallel… … 52 G E O ;f E T R V Of the Circle half the aic AF, that is, by half thedifference of CFA and CF. But since the tangent DC and thechord A F are parallel, the arc CF isequal to the arc CA : hence the angleBAF, or its equal BDC, which is meas-/ured by half the difference of CFA andCF, is also measured…
Geometry · Plane trigonometry
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![An illustration from Nicolai Copernici Torinensis De reuolutionibus orbium coelestium, libri VI : Habes in hoc opere iam recens nato, & aedito, studiose lector, motus stellarum, tam fixarum, quàm erraticarum, cum ex ueteribus, tum etiam ex recentibus obseruationibus restitutos: & nouis insuper ac admirabilibus hypothesibus ornatos. Habes etiam tabulas expeditissimas, ex quibus eosdem ad quoduis tempus quàm facillime caculare poteris. Igitur eme, lege, fruere. [Line in Greek] (1543)](https://img.insideoutlibrary.com/img/200/ia-nicolaicopernici00cope-329-220.webp)