The Elements of EuclidJohnson and Warner, 1811 - 518 páginas |
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Página 482
... 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 ...
Página 483
... 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 BQ ; and , by conversion , DA to MO as AB to MB . Hence the corol . lary is manifest ; therefore , 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 BQ ; and , by conversion , DA to MO as AB to MB . Hence the corol . lary is manifest ; therefore , if the radius be supposed to be divided into ...
Página 484
... radius , the sides become the sines of the angles opposite to them ; and if either side be made radius , the remaining 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 opposite to them ; and if either side be made radius , the remaining side is the tangent of the angle opposite to it , and the hypothenuse the secant of the same angle . Let ABC be a ...
Página 485
... 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 tan- be gent of the excess of this angle above half ...
... 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 tan- be gent of the excess of this angle above half ...
Página 486
... radius is to the tan- gent of GBD , which is the excess of the angle ABD above ABF half a right angle , But because EB is parallel to GD , BG is to GF as ED is to DF , that is , since ED is the sum of the sides BA , AC and FD their ...
... radius is to the tan- gent of GBD , which is the excess of the angle ABD above ABF half a right angle , But because EB is parallel to GD , BG is to GF as ED is to DF , that is , since ED is the sum of the sides BA , AC and FD their ...
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Términos y frases comunes
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid 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 pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore