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 297
... angle A to the angle D , and the angle B to the angle E. THEOREM II . When two triangles have two angles and the included side in the one , equal to two angles and the included side in the other , the triangles are identical , or have ...
... angle A to the angle D , and the angle B to the angle E. THEOREM II . When two triangles have two angles and the included side in the one , equal to two angles and the included side in the other , the triangles are identical , or have ...
Page 298
... angles . But the two angles EBC , EBA , are together equal to the angle ABC ( ax . 8 ) . Consequently the two angles ABC , ABD , are also equal to two right angles . Cor . 1. Hence also , conversely , if the two angles ABC , ABD , on ...
... angles . But the two angles EBC , EBA , are together equal to the angle ABC ( ax . 8 ) . Consequently the two angles ABC , ABD , are also equal to two right angles . Cor . 1. Hence also , conversely , if the two angles ABC , ABD , on ...
Page 299
... angle C = the corresponding angle EBF . But the angle CBD is greater than the angle EBF ; consequently , the said outward angle CBD is also greater than the angle C. In like manner , if CB be produced to G , and AB be bisected , it may ...
... angle C = the corresponding angle EBF . But the angle CBD is greater than the angle EBF ; consequently , the said outward angle CBD is also greater than the angle C. In like manner , if CB be produced to G , and AB be bisected , it may ...
Page 300
... 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 than the angle B , opposite the less ...
... 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 than the angle B , opposite the less ...
Page 301
... angle CBD is less than the angle ABD , and conse- quently also less than the equal angle D. And since the greater side of any triangle is opposite to the greater angle ( th . 9 ) , the side CD ( of the triangle BCD ) is less than the ...
... angle CBD is less than the angle ABD , and conse- quently also less than the equal angle D. And since the greater side of any triangle is opposite to the greater angle ( th . 9 ) , the side CD ( of the triangle BCD ) is less than the ...
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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