Elements of Geometry and Trigonometry |
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Page 36
... ratio which M has to N , let P have to Q ' , a number greater or less than Q , the same ratio that M has to N ; that is , let M : N :: P : Q ' ; then Mx N = Px Q ' ( Prop . I. ) : hence , Q ' = Mx N P ; but Q = MxN P ; conse- quently Q ...
... ratio which M has to N , let P have to Q ' , a number greater or less than Q , the same ratio that M has to N ; that is , let M : N :: P : Q ' ; then Mx N = Px Q ' ( Prop . I. ) : hence , Q ' = Mx N P ; but Q = MxN P ; conse- quently Q ...
Page 38
... ratio as the quantities themselves . Let M and N be any two quantities , and m any integral number ; then will m . M : m . N :: M : N . For m . MxN = m . Nx M , since the quantities in each member are the same ; therefore , the ...
... ratio as the quantities themselves . Let M and N be any two quantities , and m any integral number ; then will m . M : m . N :: M : N . For m . MxN = m . Nx M , since the quantities in each member are the same ; therefore , the ...
Page 39
... ratio as the antecedents , the resulting quantities and the ante- cedents will be proportional . Let For , since And since Therefore , or , hence MN : P : Q , and let also M : Pm n , then will MP : N ± m : Q ± n . MNP : Q , MxQ = NxP ...
... ratio as the antecedents , the resulting quantities and the ante- cedents will be proportional . Let For , since And since Therefore , or , hence MN : P : Q , and let also M : Pm n , then will MP : N ± m : Q ± n . MNP : Q , MxQ = NxP ...
Page 52
... ratio of the angles ACB , DCE , can be expressed in whole numbers , the arcs AB , DE , will be to each other as the angles ACB , DCE . Scholium . Conversely , if the arcs , AB , DE , are to each other as two whole numbers , the angles ...
... ratio of the angles ACB , DCE , can be expressed in whole numbers , the arcs AB , DE , will be to each other as the angles ACB , DCE . Scholium . Conversely , if the arcs , AB , DE , are to each other as two whole numbers , the angles ...
Page 53
... ratio , the other will be augmented or diminished in the same ratio , we are authorized to establish the one of those magnitudes as the measure of the other ; and we shall henceforth assume the arc AB as the mea- sure of the angle ACB ...
... ratio , the other will be augmented or diminished in the same ratio , we are authorized to establish the one of those magnitudes as the measure of the other ; and we shall henceforth assume the arc AB as the mea- sure of the angle ACB ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone convex surface Cosine Cotang cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides oblique lines opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar sine solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex