## A Course of Mathematics: In Two Volumes. Composed for the Use of the Royal Military Academy, Volume 1Longman, Orme & Company, 1841 - Mathematics |

### From inside the book

Results 1-5 of 53

Page 298

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**intersect**each other , the opposite angles are equal . LET the two lines AB , CD ,**intersect**in the point E ; then will the angle AEC be equal to the angle BED , and the angle AED equal to the angle CEB . For , since the line CE meets ... Page 313

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**intersect**at right angles . THEOREM XLI . If a line , drawn through or from the centre of a circle , bisect a chord , it will be perpendicular to it ; or , if it be perpendicular to the chord , it will bisect both the chord and the arc ... Page 319

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**intersection**of two chords , is measured by half the sum of the two intercepted arcs . LET the two chords AB , CD ,**intersect**at the point E : then the angle AEC , or DEB , is measured by half the sum of the two arcs AC , DB . A C KE ... Page 320

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**intersections**with the circumference . LET the two lines AB , CD , meet each other in E ; then the rectangle of AE , EB , will be equal to the rectangle of CE , ED . Or , AE . EB = CE . ED . For , through the point E draw the diameter ... Page 339

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**intersections**made in the sides produced and unpro- duced . In the latter theorem , there are always two or none ...**intersect**in P , and draw BP to meet AC in E ' . Then ( th . 96 ) AE ' E'C :: AF . BD : FB . DC . Whence AE ' : E ...### Other editions - View all

### 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