Geometry : the elements of Euclid and Legendre simplified and arranged to exclude from geomtrical reasoning the reductio ad absurdum : with the elements of plane and spherical trigonometry, and exercises in elementary geometry and trigonometry / /c By Lawrence S. Benson (1868)
Benson, Lawrence S. (Lawrence Sluter), Legendre, A. M. (Adrien Marie), 1752-1833 · New York : Pub. for the author by Davies & Kent · leaf 85
D B E D B E pendicular to it; join FA and produce it to E; join also CA, BOOK in.] EUCLID AND LFGKNDRE. 81 CB, C being any point in the arc ACB. Then (TIT. 12, cor.)BF is a diameter, and (III. 11, and I. 9) the angles BAF, BAEare riglit angles. Therefore, in the triangles J^AE, FBE, theangle E is… … right angles; wherefore (I. 20, cor. 5) the remaining angleABE is equal to the remaining angle F, which is an angle inthe remote or alternate segment BFA. Again : the two angles ABD, ABE are equal (I. 9) to tworight angles; and because ACBF is a quadrilateral in the circle,the opposite angles C and…
Geometry · Trigonometry
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