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
... perpendicular to it . Cor . 2. Hence too it appears , that every equilateral triangle , is also equi- angular , or has all its angles equal . THEOREM IV . When one line meets another , the angles which it makes on the same side of the ...
... perpendicular to it . Cor . 2. Hence too it appears , that every equilateral triangle , is also equi- angular , or has all its angles equal . THEOREM IV . When one line meets another , the angles which it makes on the same side of the ...
Page 298
... perpendicular to CD . Then , since the two angles EBC , EBD , are right angles ( def . 25 ) , and the angle EBD is equal to the two angles EBA , ABD , together ( ax . 8 ) , the three angles , EBC , EBA , and ABD , are equal to two right ...
... perpendicular to CD . Then , since the two angles EBC , EBD , are right angles ( def . 25 ) , and the angle EBD is equal to the two angles EBA , ABD , together ( ax . 8 ) , the three angles , EBC , EBA , and ABD , are equal to two right ...
Page 299
... perpendicular to the base ; and conceive the triangle BCD to revolve about CD till the plane of it coin- cides with that of CDA . Then since CDA and CDB are right angles ( def . 25 ) , the line BD will coincide with DA . Now if B ...
... perpendicular to the base ; and conceive the triangle BCD to revolve about CD till the plane of it coin- cides with that of CDA . Then since CDA and CDB are right angles ( def . 25 ) , the line BD will coincide with DA . Now if B ...
Page 301
... perpendicular to one of two parallel lines , are also perpendicular to the other . THEOREM XIII . When a line , cutting two other lines , makes the alternate angles equal to each other , those two lines are parallel . LET the line EF ...
... perpendicular to one of two parallel lines , are also perpendicular to the other . THEOREM XIII . When a line , cutting two other lines , makes the alternate angles equal to each other , those two lines are parallel . LET the line EF ...
Page 302
... perpendicular to EF . Then will this line be also perpendicular to both the lines AB , CD ( cor . th . 12 ) , and consequently the two lines AB , CD , are parallels ( cor . th . 13 ) . G A B C H E L THEOREM XVI . When one side of a ...
... perpendicular to EF . Then will this line be also perpendicular to both the lines AB , CD ( cor . th . 12 ) , and consequently the two lines AB , CD , are parallels ( cor . th . 13 ) . G A B C H E L THEOREM XVI . When one side of a ...
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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