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 132
... describe the manner in which the coefficients of the several powers of x in the product are formed of the quantities a , b , c , d , ... - · ( bc ) 2 7. Prove that a2 = ( a b + c ) ( a + = ( a + b + c ) ( —a + b + c ) ; and hence that ...
... describe the manner in which the coefficients of the several powers of x in the product are formed of the quantities a , b , c , d , ... - · ( bc ) 2 7. Prove that a2 = ( a b + c ) ( a + = ( a + b + c ) ( —a + b + c ) ; and hence that ...
Page 310
... describe the square AE , and on AC , CB , the squares AG , BH ; then draw CK parallel to AD or BE ; and join AI , BF , CD , CE . F D C KE H Now , because the line AC meets the two CG , CB , so as to make two right angles , these two ...
... describe the square AE , and on AC , CB , the squares AG , BH ; then draw CK parallel to AD or BE ; and join AI , BF , CD , CE . F D C KE H Now , because the line AC meets the two CG , CB , so as to make two right angles , these two ...
Page 372
... describe arcs from the centres A and D ; the first BC meeting AB , AC , in B and C , and the second EH meeting DE in E. With centre E , and radius equal to BC , describe an arc to meet HE in F. The line DF being drawn , will make the ...
... describe arcs from the centres A and D ; the first BC meeting AB , AC , in B and C , and the second EH meeting DE in E. With centre E , and radius equal to BC , describe an arc to meet HE in F. The line DF being drawn , will make the ...
Page 373
... describe arcs DB , CH , the former meeting AB in B. Then with centre C and radius BD describe an arc to meet CH at E. The line CE being drawn will be parallel to AB . E B For by the construction of the second problem , the alternate ...
... describe arcs DB , CH , the former meeting AB in B. Then with centre C and radius BD describe an arc to meet CH at E. The line CE being drawn will be parallel to AB . E B For by the construction of the second problem , the alternate ...
Page 374
... describe circles cutting in D. Then BD being drawn will bisect the angle ABC . For if AD , CD be drawn , the three sides of the triangle ABC are equal each to each to those of the triangle CBD . Hence , Geom . th . 8 , the angles ABD ...
... describe circles cutting in D. Then BD being drawn will bisect the angle ABC . For if AD , CD be drawn , the three sides of the triangle ABC are equal each to each to those of the triangle CBD . Hence , Geom . th . 8 , the angles ABD ...
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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