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 375
... describe arcs meeting in F. Join FC ; it is the perpendicular required . For , conceive DF , EF , joined : then the equality of the sides of the triangles DCF , ECF , give the angles at C equal ( th . 8 ) , and hence CF perpendicular to ...
... describe arcs meeting in F. Join FC ; it is the perpendicular required . For , conceive DF , EF , joined : then the equality of the sides of the triangles DCF , ECF , give the angles at C equal ( th . 8 ) , and hence CF perpendicular to ...
Page 376
... describe a circle cutting BC in two points D and E ; and from D and E with any equal radii describe circles intersecting at F. Then FA being joined , cutting BC in G , will be the perpendicular required . For conceiving the lines DA ...
... describe a circle cutting BC in two points D and E ; and from D and E with any equal radii describe circles intersecting at F. Then FA being joined , cutting BC in G , will be the perpendicular required . For conceiving the lines DA ...
Page 377
... describe circles intersecting in C and D. Join CD : then it will bisect AB in E. For it may be shown , as before , that CE bisects the vertical angle CB of the isosceles triangle , and hence also it bisects the base ( th . 3. Cor . 1 ) ...
... describe circles intersecting in C and D. Join CD : then it will bisect AB in E. For it may be shown , as before , that CE bisects the vertical angle CB of the isosceles triangle , and hence also it bisects the base ( th . 3. Cor . 1 ) ...
Page 380
... describe any parallelo- gram ABCD , and draw the diagonals AC , BD , intersecting in E ; draw EF parallel to AD , meeting AB in F , and join DF , meeting AC in G ; draw GH parallel to AD , meeting AB in H , and join DH meeting AC in K ...
... describe any parallelo- gram ABCD , and draw the diagonals AC , BD , intersecting in E ; draw EF parallel to AD , meeting AB in F , and join DF , meeting AC in G ; draw GH parallel to AD , meeting AB in H , and join DH meeting AC in K ...
Page 381
... describe arcs intersecting in E and F , and let O be the intersection of EF , AC . Make BP = BO , and from O and P as centres , with radii equal to AO describe arcs intersecting in D. Then DB will be the mean propor- tional between AB ...
... describe arcs intersecting in E and F , and let O be the intersection of EF , AC . Make BP = BO , and from O and P as centres , with radii equal to AO describe arcs intersecting in D. Then DB will be the mean propor- tional between AB ...
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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