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 314
... centre : and con- sequently that the point D is the centre of the circle , and that the three equal lines DA , DB , DC , are radii . THEOREM XLIII . If two circles placed one within another , touch , the centres of the circle and the ...
... centre : and con- sequently that the point D is the centre of the circle , and that the three equal lines DA , DB , DC , are radii . THEOREM XLIII . If two circles placed one within another , touch , the centres of the circle and the ...
Page 315
... centre . LET AB , CD , be any two chords at equal distances from the centre G : then will these two chords AB , CD , be equal to each other . Draw the two radii GA , GC , and the two perpendiculars GE , GF , which are the equal ...
... centre . LET AB , CD , be any two chords at equal distances from the centre G : then will these two chords AB , CD , be equal to each other . Draw the two radii GA , GC , and the two perpendiculars GE , GF , which are the equal ...
Page 316
... centre of the circle . THEOREM XLVIII . The angle formed by a tangent and chord is measured by half the arc of that chord . LET AB be a tangent to a circle , and CD a chord drawn from the point of contact C ; then is the angle BCD ...
... centre of the circle . THEOREM XLVIII . The angle formed by a tangent and chord is measured by half the arc of that chord . LET AB be a tangent to a circle , and CD a chord drawn from the point of contact C ; then is the angle BCD ...
Page 317
... centre of a circle is double the angle at the circumference , when both stand on the same arc . LET C be an angle at the centre C , and D an angle at the circumference , both standing on the same arc or same chord AB : then will the ...
... centre of a circle is double the angle at the circumference , when both stand on the same arc . LET C be an angle at the centre C , and D an angle at the circumference , both standing on the same arc or same chord AB : then will the ...
Page 320
... centre H draw the 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 ...
... centre H draw the 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 ...
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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