The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner CorrectedT. Desilver and R. Desilver, 1825 - 516 sider |
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Side 480
... radius of the circle of which the measure of a given angle is an arch , that arch will contain the same number of degrees , minutes , seconds , & c . as is manifest from Lemma 2 . III . Let AB be produced till it meet the circle again ...
... radius of the circle of which the measure of a given angle is an arch , that arch will contain the same number of degrees , minutes , seconds , & c . as is manifest from Lemma 2 . III . Let AB be produced till it meet the circle again ...
Side 481
... radius . CB to the radius NB , and AE to MP as AB to BM , and BC or BA to BD as BN or BM to BO ; and , by conversion , DA to MO as AB to MB . Hence the corollary is manifest ; there- fore , if the radius be supposed to be divided into ...
... radius . CB to the radius NB , and AE to MP as AB to BM , and BC or BA to BD as BN or BM to BO ; and , by conversion , DA to MO as AB to MB . Hence the corollary is manifest ; there- fore , if the radius be supposed to be divided into ...
Side 482
... radius , the sides become the sines of the angles op- posite to them and if either side be made radius , the re- maining side is the tangent of the angle opposite to it , and the hypothenuse the secant of the same angle . Let ABC be a ...
... radius , the sides become the sines of the angles op- posite to them and if either side be made radius , the re- maining side is the tangent of the angle opposite to it , and the hypothenuse the secant of the same angle . Let ABC be a ...
Side 483
... radius , BE , BG , are the tangents of the angles EFB , BFG ; but it is manifest that EC is the sum of the sides BA ... radius is to the tangent of an angle ; and the radius is to the tangent of the excess of this angle above half a ...
... radius , BE , BG , are the tangents of the angles EFB , BFG ; but it is manifest that EC is the sum of the sides BA ... radius is to the tangent of an angle ; and the radius is to the tangent of the excess of this angle above half a ...
Side 484
... radius is to the tangent of the angle ABD ; and because BGD is a right angle , BG is to GD or GF as the radius is to the tangent of GBD , which is the excess of the angle ABD above ABF half a right angle . But because EB is parallel to ...
... radius is to the tangent of the angle ABD ; and because BGD is a right angle , BG is to GD or GF as the radius is to the tangent of GBD , which is the excess of the angle ABD above ABF half a right angle . But because EB is parallel to ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
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altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore