Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical TrigonometryE. Duyckinck, and George Long, 1824 - 333 sider |
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Side 228
... tangent of half their sum , that is , of 45o , is equal to the radius , And the arch BC being the excess of DC above ... tangent of the difference between either of them and 45 ° . PROP . IV . The sum of any two sides of a triangle is to ...
... tangent of half their sum , that is , of 45o , is equal to the radius , And the arch BC being the excess of DC above ... tangent of the difference between either of them and 45 ° . PROP . IV . The sum of any two sides of a triangle is to ...
Side 229
... tangent of the angle EFB , and BG the tangent of the angle BFG to the radius FB ; and BE is therefore to BG as the tangent of half the sum of the angles ACB , ABC to the tangent of half their difference . Also CE is the sum of the sides ...
... tangent of the angle EFB , and BG the tangent of the angle BFG to the radius FB ; and BE is therefore to BG as the tangent of half the sum of the angles ACB , ABC to the tangent of half their difference . Also CE is the sum of the sides ...
Side 232
... ) : ( BC + ( AB -AC ) ) ( BC- ( AB - AC ) ) :: ( cos . BAC ) : ( sin . 1 BAC ) . But the cosine of any arch is to the sine , as the radius to the tangent of the same arch ; therefore , ( AB + AC 232 PLANE TRIGONOMETRY : N ...
... ) : ( BC + ( AB -AC ) ) ( BC- ( AB - AC ) ) :: ( cos . BAC ) : ( sin . 1 BAC ) . But the cosine of any arch is to the sine , as the radius to the tangent of the same arch ; therefore , ( AB + AC 232 PLANE TRIGONOMETRY : N ...
Side 235
... tangent of C , by the analogy in the Table , AC : AB :: R : tan . C ; but if C it- self is not required , it is sufficient , having found tan . C by this pre- portion , to take from the Trigonometric Tables the cosine that cor- responds ...
... tangent of C , by the analogy in the Table , AC : AB :: R : tan . C ; but if C it- self is not required , it is sufficient , having found tan . C by this pre- portion , to take from the Trigonometric Tables the cosine that cor- responds ...
Side 239
... tangent , is not liable to this objection ; nevertheless , when an arch approaches very near to 90 , the variations of the tangents become excessive , and are too irregular to allow the proportional parts to be found with exact- ness ...
... tangent , is not liable to this objection ; nevertheless , when an arch approaches very near to 90 , the variations of the tangents become excessive , and are too irregular to allow the proportional parts to be found with exact- ness ...
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Vanlige uttrykk og setninger
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore