A Course of Mathematics: In Two Volumes. Composed for the Use of the Royal Military Academy, Volume 1Longman, Orme & Company, 1841 - Mathematics |
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Page 292
... diameter . The half circumference is sometimes called the Semicircle . 22. A sector is any part of a circle which is bounded by an arc , and two radii drawn to its extremities . 23. A quadrant , or quarter of a circle , is a sector ...
... diameter . The half circumference is sometimes called the Semicircle . 22. A sector is any part of a circle which is bounded by an arc , and two radii drawn to its extremities . 23. A quadrant , or quarter of a circle , is a sector ...
Page 314
... diameter AFC . Then , if the centre of the other circle can be out of this line AC , let it be supposed in some other point as G ; through which draw the line FG , cutting the two circles in B and D. F E B D Now , in the triangle AFG ...
... diameter AFC . Then , if the centre of the other circle can be out of this line AC , let it be supposed in some other point as G ; through which draw the line FG , cutting the two circles in B and D. F E B D Now , in the triangle AFG ...
Page 316
... diameter . Cor . 2. Hence also one right angle must have for its measure a quarter of the circumference , or 90 degrees . THEOREM XLIX . An angle at the circumference of a circle is measured by half the arc that subtends it . LET BAC be ...
... diameter . Cor . 2. Hence also one right angle must have for its measure a quarter of the circumference , or 90 degrees . THEOREM XLIX . An angle at the circumference of a circle is measured by half the arc that subtends it . LET BAC be ...
Page 320
... diameter FG ; also , from the 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 ...
... diameter FG ; also , from the 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 ...
Page 321
... diameter of the circumscribing circle . A D B LET CD be the perpendicular , and CE the diameter of the circle about the triangle ABC ; then CA . CB = CD . CE . For , join BE : then in the two triangles ACD , ECB , the angles A and E are ...
... diameter of the circumscribing circle . A D B LET CD be the perpendicular , and CE the diameter of the circle about the triangle ABC ; then CA . CB = CD . CE . For , join BE : then in the two triangles ACD , ECB , the angles A and E are ...
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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