Weekly problem papers, with notes. [With] Solutions1885 |
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Page 10
... common factor a , and let the arithmetic logarithm of X be α . ..x . e2n = √1 = = 2 log x = a + 2ñπ √— I. Thus we see that a quantity has an infinite number of logs , one being real and the rest imaginary , and the latter are found by ...
... common factor a , and let the arithmetic logarithm of X be α . ..x . e2n = √1 = = 2 log x = a + 2ñπ √— I. Thus we see that a quantity has an infinite number of logs , one being real and the rest imaginary , and the latter are found by ...
Page 11
... common chord cut AB in D , E , F respectively , so that A and D are on the same side of the common chord CFG . - Then a DCE = DCG + ECG = CBA + CAB = π ACB ..CF = BC sin CAB CF = AB sin ACB ab sin a = 1 = CA sin a ab sin a AB √a2 + b2 ...
... common chord cut AB in D , E , F respectively , so that A and D are on the same side of the common chord CFG . - Then a DCE = DCG + ECG = CBA + CAB = π ACB ..CF = BC sin CAB CF = AB sin ACB ab sin a = 1 = CA sin a ab sin a AB √a2 + b2 ...
Page 49
... Then MN = AN ; NG = AS . , SM = .. QM2 = † PN2 = AS . AN = AS . SM . ..the locus of Q is a parabola , vertex S , and latus rectum that of the original parabola . E PAPER XXV . 1. Let x a be the common WEEKLY PROBLEM PAPERS . 49.
... Then MN = AN ; NG = AS . , SM = .. QM2 = † PN2 = AS . AN = AS . SM . ..the locus of Q is a parabola , vertex S , and latus rectum that of the original parabola . E PAPER XXV . 1. Let x a be the common WEEKLY PROBLEM PAPERS . 49.
Page 50
... common difference being 1 = x , and y2 xy + y2 = X y + 1 ; C + A cos B + cos C + cos C + cos 4 + cos 4 + cos B } tan 0 ; 4 . 2 cot 20 = .. - Then if we write a for a in .. a2 + aa +6 a2 + a'a + b ' a2 = at ' a'b b - = α - 0 , 0 ; b ...
... common difference being 1 = x , and y2 xy + y2 = X y + 1 ; C + A cos B + cos C + cos C + cos 4 + cos 4 + cos B } tan 0 ; 4 . 2 cot 20 = .. - Then if we write a for a in .. a2 + aa +6 a2 + a'a + b ' a2 = at ' a'b b - = α - 0 , 0 ; b ...
Page 60
... common ratio of the G.P. we get an + 1 ... if the theorem is true for n terms , it is also true for n + 1. Now we know that it is true when n = 3 , and when n = 4. .. it is true universally . 3. cos 4+ cos B + cos C = 1+ 4 sin A B C sin ...
... common ratio of the G.P. we get an + 1 ... if the theorem is true for n terms , it is also true for n + 1. Now we know that it is true when n = 3 , and when n = 4. .. it is true universally . 3. cos 4+ cos B + cos C = 1+ 4 sin A B C sin ...
Common terms and phrases
a+b+c ABCD axis bisects the angle Cambridge centre chord circle round circle will go circum-circle Clifton College coef College conic const coordinates cos² cosec Crown 8vo denote diameter directrix draw Edition ellipse envelope equal equation Fcap fixed point geometrical given expression hyperbola inscribed circle intersect Join Let ABC Let the tangent locus Mathematics meet middle point Monday afternoon morning nine-point circle nth term orthocentre PAPER parabola parallel perpendicular plane Professor quadrilateral radical axis radius right angles shew shewn sides Similarly sin² sin³ straight line tan² tangent Todh triangle Trinity College Tripos velocity vertex vertical
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