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 TrigonometryW.E. Dean, 1839 - 318 σελίδες |
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Σελίδα 66
... radius of a circle is the straight line drawn from the centre to the circumference . I. A straight line is said to touch a circle , when it meets the circle , and being produced does not cut it . II . Circles are said to touch one ...
... radius of a circle is the straight line drawn from the centre to the circumference . I. A straight line is said to touch a circle , when it meets the circle , and being produced does not cut it . II . Circles are said to touch one ...
Σελίδα 102
... radius of the given circle , so that the rectangle contain- " ed by the whole and one of the parts may be equal to the square " of the other ( 11.2 . ) . Apply in the circle , on each side of a given " point , a line equal to the ...
... radius of the given circle , so that the rectangle contain- " ed by the whole and one of the parts may be equal to the square " of the other ( 11.2 . ) . Apply in the circle , on each side of a given " point , a line equal to the ...
Σελίδα 106
... radius of the circle . And if through the points A , B , C , D , E , F , there be drawn straight lines touching the circle , an equilateral and equiangular hexagon shall be described about it , which may be demonstrated from what has ...
... radius of the circle . And if through the points A , B , C , D , E , F , there be drawn straight lines touching the circle , an equilateral and equiangular hexagon shall be described about it , which may be demonstrated from what has ...
Σελίδα 158
... radius AC , the greater of the two sides , describe the circle CFG : produce AB to meet the circumfer- ence in E and F , and CB to meet it in G. Then because AF = AC , BF = AB + AC , the sum of the sides ; and since AE = AC , BE = AC ...
... radius AC , the greater of the two sides , describe the circle CFG : produce AB to meet the circumfer- ence in E and F , and CB to meet it in G. Then because AF = AC , BF = AB + AC , the sum of the sides ; and since AE = AC , BE = AC ...
Σελίδα 165
... radius of the circle ; therefore also , because magnitudes have the same ratio with their equimultiples ( 15.5 . ) , the perimeter of the inscribed polygon is to the perimeter of the circumscribed , as the perpendicular from the centre ...
... radius of the circle ; therefore also , because magnitudes have the same ratio with their equimultiples ( 15.5 . ) , the perimeter of the inscribed polygon is to the perimeter of the circumscribed , as the perpendicular from the centre ...
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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 definition 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 opposite angle parallel parallelogram parallelopipeds perpendicular polygon prism produced proportional 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 parallelopipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore