## 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

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Page 288

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**tangents**of 68 ° 54 ' , 68 ° 55 ' , 68 ° 56 ' , 68 ° 57 ' , to find that of 68 ° 56'20 " . Ex . 5. Given the natural**tangents**of the same arcs , to find the natural**tangent**of 68 ° 56′20 ′′ : and compare its logarithm with the answer to ... Page 294

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**tangent**to a circle , or other curve , when it touches it , without cutting , although both are produced . 56. The height or altitude of a figure is a perpendicular let fall from an angle , or its vertex , to the opposite side , called ... Page 315

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**tangent**to a circle , a radius drawn to the point of contact is perpendicular to the**tangent**. LET the line AB touch the circumference of a circle at the point D ; then will the radius CD be perpendicular to the**tangent**AB . See the ... Page 316

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**tangent**, at the point of contact , passes through the 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 ... Page 317

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**tangent**to a circle , and a chord drawn from the point of contact , is equal to the angle in the alternate segment . IF AB be a**tangent**, and AC a chord , and D any angle in the alternate segment ADC ; then will the angle D be equal ...### 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