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 304
... drawn from a given point to an in- definite line : and , of any other lines drawn from the same point , those that are nearest the perpendicular are less than those more remote . IF AB , AC , AD , .... be lines drawn from the given ...
... drawn from a given point to an in- definite line : and , of any other lines drawn from the same point , those that are nearest the perpendicular are less than those more remote . IF AB , AC , AD , .... be lines drawn from the given ...
Page 305
... drawn . Then , the triangles , ABD , CBD , being mutually equilateral ( hyp . ) , they are also mutually equiangular ... draw the diagonal BD . Then , because AB and DC are parallel , ( hyp . ) VOL . I. X the angle ABD is equal to the ...
... drawn . Then , the triangles , ABD , CBD , being mutually equilateral ( hyp . ) , they are also mutually equiangular ... draw the diagonal BD . Then , because AB and DC are parallel , ( hyp . ) VOL . I. X the angle ABD is equal to the ...
Page 309
... draw KI , making BI the square of the other line BC . G E D H Now , it is obvious , that the square AD is less than the two squares AF , BI , by the two rectangles EF , DI : but GF is equal to the one line AC , and GE or FH is equal to ...
... draw KI , making BI the square of the other line BC . G E D H Now , it is obvious , that the square AD is less than the two squares AF , BI , by the two rectangles EF , DI : but GF is equal to the one line AC , and GE or FH is equal to ...
Page 312
... drawn from the vertex to the middle of the base , together with double the square of the half base , is equal to the sum of the squares of the other two sides . LET ABC be a triangle , and CD the line drawn from the vertex to the middle ...
... drawn from the vertex to the middle of the base , together with double the square of the half base , is equal to the sum of the squares of the other two sides . LET ABC be a triangle , and CD the line drawn from the vertex to the middle ...
Page 313
... drawn from the point D to the circumference , be equal to each other , the point D will be the centre . Draw the chords AB , BC , which let be bisected in the points E , F , and join DE , DF . B E F Then , the two triangles , DAE , DBE ...
... drawn from the point D to the circumference , be equal to each other , the point D will be the centre . Draw the chords AB , BC , which let be bisected in the points E , F , and join DE , DF . B E F Then , the two triangles , DAE , DBE ...
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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