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 TrigonometryCollins & Hannay, 1860 - 333 σελίδες |
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Σελίδα 225
... radius is a mean proportional between the tangent and the cotangent of any angle ABC ; that is , tan . ABCXcot . ABC = R2 . - For , since HK , BA are parallel , the angles HKB , ABC are equal , and KHB , BAE are right angles ; therefore ...
... radius is a mean proportional between the tangent and the cotangent of any angle ABC ; that is , tan . ABCXcot . ABC = R2 . - For , since HK , BA are parallel , the angles HKB , ABC are equal , and KHB , BAE are right angles ; therefore ...
Σελίδα 230
... radius to the cosine of B. Wherefore , & c . Q. E. D. COR . If the radius = 1 , BD - BA Xcos . B , ( E ) , and 2BC.BA × cos . B = 2BC.BD , and therefore when B is acute , 2BC . BAXcos . BBC2 + BA2 - AC2 , and adding AC2 to B both ; AC2 ...
... radius to the cosine of B. Wherefore , & c . Q. E. D. COR . If the radius = 1 , BD - BA Xcos . B , ( E ) , and 2BC.BA × cos . B = 2BC.BD , and therefore when B is acute , 2BC . BAXcos . BBC2 + BA2 - AC2 , and adding AC2 to B both ; AC2 ...
Σελίδα 331
... radius passing through the other ; but in strictness the sine is not the perpendicular itself , but the ratio of that perpen- dicular to the radius , for it is this ratio which remains constant , while the angle continues the same ...
... radius passing through the other ; but in strictness the sine is not the perpendicular itself , but the ratio of that perpen- dicular to the radius , for it is this ratio which remains constant , while the angle continues the same ...
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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 and similar 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 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 side BC sine solid angle solid parallelopipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore