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 297
... triangles ABC , DEF , have the angle A equal to the angle D , the angle B equal to the angle E , and the side AB equal to the side DE ; then these two triangles will be identical . A A For , conceive the triangle ABC to be placed on the ...
... triangles ABC , DEF , have the angle A equal to the angle D , the angle B equal to the angle E , and the side AB equal to the side DE ; then these two triangles will be identical . A A For , conceive the triangle ABC to be placed on the ...
Page 298
... triangle , having the side AB produced to D ; then will the outward angle CBD be greater than either of the inward ... triangles AEC , BEF , 298 GEOMETRY .
... triangle , having the side AB produced to D ; then will the outward angle CBD be greater than either of the inward ... triangles AEC , BEF , 298 GEOMETRY .
Page 299
... triangle BCD to revolve about CD till the plane of it coin- cides with that of CDA . Then since CDA and CDB are ... triangle is also equilateral . THEOREM VIII . When two triangles have all the three sides in the one , equal to all the ...
... triangle BCD to revolve about CD till the plane of it coin- cides with that of CDA . Then since CDA and CDB are ... triangle is also equilateral . THEOREM VIII . When two triangles have all the three sides in the one , equal to all the ...
Page 300
... triangle is opposite to the greater angle ; and the greater angle opposite to the greater side . LET ABC be a triangle , having the side AB greater than the side AC ; then will the angle ACB , opposite the greater side AB , be greater ...
... triangle is opposite to the greater angle ; and the greater angle opposite to the greater side . LET ABC be a triangle , having the side AB greater than the side AC ; then will the angle ACB , opposite the greater side AB , be greater ...
Page 301
... triangle is opposite to the greater angle ( th . 9 ) , the side CD ( of the triangle BCD ) is less than the side BC . Otherwise . Set off upon AB , a distance AI , equal to AC . Then ( th . 20 ) ACCB is greater than AB , that is ...
... triangle is opposite to the greater angle ( th . 9 ) , the side CD ( of the triangle BCD ) is less than the side BC . Otherwise . Set off upon AB , a distance AI , equal to AC . Then ( th . 20 ) ACCB is greater than AB , that is ...
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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