A Course of Mathematics: In Two Volumes. For the Use of the Royal Military Academy, Volume 1Gilberte and Rivington, 1841 - Mathematics |
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Page 320
... radius DH , and draw HI per- pendicular to CD . Then , since DEH is a triangle , and the perp . HI bisects the chord CD ( th . 41 ) , the line CE is equal to the difference of the segments DI , EI , the sum of them being DE : and ...
... radius DH , and draw HI per- pendicular to CD . Then , since DEH is a triangle , and the perp . HI bisects the chord CD ( th . 41 ) , the line CE is equal to the difference of the segments DI , EI , the sum of them being DE : and ...
Page 336
... radius CL , and therefore , à fortiori , less than the corresponding arch of circle with radius CA. Also CE is less than CA. Therefore the polygon of which one side is GL , is less than the rectangle whose base is half the circum ...
... radius CL , and therefore , à fortiori , less than the corresponding arch of circle with radius CA. Also CE is less than CA. Therefore the polygon of which one side is GL , is less than the rectangle whose base is half the circum ...
Page 343
... radius of a circle be a mean proportional to two distances from the centre in the same straight line , the lines drawn from their extremities to any point in the circumference will have the same ratio that the distances of these points ...
... radius of a circle be a mean proportional to two distances from the centre in the same straight line , the lines drawn from their extremities to any point in the circumference will have the same ratio that the distances of these points ...
Page 347
... radius of a circle be divided in extreme and mean ratio , the greater segment is the side of the regular decagon inscribed in that circle ; and the sum of the squares of the radius and its greater segment is equal to the square of the ...
... radius of a circle be divided in extreme and mean ratio , the greater segment is the side of the regular decagon inscribed in that circle ; and the sum of the squares of the radius and its greater segment is equal to the square of the ...
Page 356
... radius of the circular base . In like manner it is shown that LH is equal to the radius KB ; and that any other lines , drawn from the point L to the circumference of the section GHI , are all equal to radii of the base ; consequently ...
... radius of the circular base . In like manner it is shown that LH is equal to the radius KB ; and that any other lines , drawn from the point L to the circumference of the section GHI , are all equal to radii of the base ; consequently ...
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Common terms and phrases
ABCD algebraic altitude arithmetical arithmetical progression base bisect breadth centre chord circle circumference coefficients common cone cosec cube root decimal denominator denoted diagonal diameter difference dihedral angle distance divided divisor draw drawn equal equation equiangular EXAMPLES expression figure fraction frustum geometrical given line greater hence inscribed integer intersection join length less lineation logarithms mantissa measure meeting method multiplied parallel parallel ruler parallelogram perpendicular plane polygon prism PROBLEM proportional quantity quotient radii radius ratio rectangle Reduce right angles rule Scholium segment sides sine solid angle solution square root straight line subtraction tangent THEOREM third trapezium triangle ABC u₁ vulgar fraction Whence