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 σελίδες |
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Σελίδα 176
... radius contains 1000. The circumference , therefore , has to the diameter a less ratio ( 8. 5. ) than 6285.461 has to 2000 , or than 3142.7305 has to 1000 but the ratio of 22 to 7 is greater than the ratio of 3142.7305 to 1000 ...
... radius contains 1000. The circumference , therefore , has to the diameter a less ratio ( 8. 5. ) than 6285.461 has to 2000 , or than 3142.7305 has to 1000 but the ratio of 22 to 7 is greater than the ratio of 3142.7305 to 1000 ...
Σελίδα 177
... radius contains 1000 ; or than 3141.009 of the parts of which the radius contains 500 , or the diameter contains 1000. Now , 3141.009 has to 1000 a greater ratio than 3- + ; 10 71 to 1 ; therefore the circumference of the circle has a ...
... radius contains 1000 ; or than 3141.009 of the parts of which the radius contains 500 , or the diameter contains 1000. Now , 3141.009 has to 1000 a greater ratio than 3- + ; 10 71 to 1 ; therefore the circumference of the circle has a ...
Σελίδα 178
... radius to the area of the circle nearly . For it has been shewn , that ( 1. Cor . 5. 1. Sup . ) the diameter of ą circle is to its circumference as the square of the radius to the area of the circle ; but the diameter is to the ...
... radius to the area of the circle nearly . For it has been shewn , that ( 1. Cor . 5. 1. Sup . ) the diameter of ą circle is to its circumference as the square of the radius to the area of the circle ; but the diameter is to the ...
Σελίδα 179
... radius . Also , as the num- bers in the second column , are less than the perimeters of the in- scribed polygons , they are each of them less than the circumference , of the circle ; and for the same reason , each of those in the third ...
... radius . Also , as the num- bers in the second column , are less than the perimeters of the in- scribed polygons , they are each of them less than the circumference , of the circle ; and for the same reason , each of those in the third ...
Σελίδα 223
... radius . VII . The straight line BE , between the centre and the extremity of the tangent AE is called the Secant of the arch AC , or of the angle ABC . COR . to Def . 4 , 6 , 7 , the sine , tangent and secant of any angle ABC , are ...
... radius . VII . The straight line BE , between the centre and the extremity of the tangent AE is called the Secant of the arch AC , or of the angle ABC . COR . to Def . 4 , 6 , 7 , the sine , tangent and secant of any angle ABC , are ...
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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 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