Treatise on Trigonometry ...Macmillen & Company, 1889 - 504 sider |
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Side 20
... increases the other increases . Then , if the ratio of any two commensurable values of the one is equal to the ratio of the two corresponding values of the other , the same will hold for all pairs of values whether commensurable or ...
... increases the other increases . Then , if the ratio of any two commensurable values of the one is equal to the ratio of the two corresponding values of the other , the same will hold for all pairs of values whether commensurable or ...
Side 24
... increase the number of divisions of the arcs AZ , az , the rectilinear boundaries evidently approximate more and more closely to the arcs . Hence ultimately we may assume that and AB + BC + CD + ab + be + cd + = arc AZ ; ...... = arc az ...
... increase the number of divisions of the arcs AZ , az , the rectilinear boundaries evidently approximate more and more closely to the arcs . Hence ultimately we may assume that and AB + BC + CD + ab + be + cd + = arc AZ ; ...... = arc az ...
Side 47
... increase as we descend . : - 85. The relations of Art . 79 , are summed up thus : - The product of any set of ratios arranged symmetrically about the centre is equal to unity . 86. The relations of Art . 80 , are summed up thus : - The ...
... increase as we descend . : - 85. The relations of Art . 79 , are summed up thus : - The product of any set of ratios arranged symmetrically about the centre is equal to unity . 86. The relations of Art . 80 , are summed up thus : - The ...
Side 51
... increases , it is clear that each of the lines MB , AT , OT , AM , BT increases . Hence the primary ratios sine , tangent , secant , versed sine , sub- tense increase as the angle increases . The functions , having the prefix co- , are ...
... increases , it is clear that each of the lines MB , AT , OT , AM , BT increases . Hence the primary ratios sine , tangent , secant , versed sine , sub- tense increase as the angle increases . The functions , having the prefix co- , are ...
Side 68
... increases to 90 ° , MP becomes equal to OP , and OM vanishes . M Now the ratio of two finite equal lengths is unity : The ratio of zero to any finite length is zero : 0 The ratio of any finite length to zero is infinity : = f f 0 . f ...
... increases to 90 ° , MP becomes equal to OP , and OM vanishes . M Now the ratio of two finite equal lengths is unity : The ratio of zero to any finite length is zero : 0 The ratio of any finite length to zero is infinity : = f f 0 . f ...
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acute angle algebraically antiparallels b₁ base bisector bisects Brocard Circle Brocard Points centre circular measure circumcentre circumcircle circumradius convergent cos² cos³ cosec cosh cosine cot² cotangent decimal difference directed length distance equal equation escribed circles Example expressed factors final line finite formulæ fraction Given log Hence hypothenuse inscribed integral last article Lemoine Circle limit logarithms magnitude middle point multiple nine-points nine-points circle obtuse opposite orthocentre perp perpendicular positive or negative PROP prove quadrant quantity radius ratios respectively right-angle root S₁ S₂ sec² secant sides sin² sin³ sine sinh subtend subtraction tan-¹ tan² tangent theorem triangle trigonometrical unity values zero
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