Proceedings of the Edinburgh Mathematical Society, Volume 12Scottish Academic Press, 1894 - Electronic journals |
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Page 31
... expression as x2 - 7x - 120 the difficulty for beginners lies in finding the pair of factors of 120 which satisfy the middle term : in this case so that their difference is 7. They may write down the pairs in order ( 1 x 120 ; 2 x 60 ...
... expression as x2 - 7x - 120 the difficulty for beginners lies in finding the pair of factors of 120 which satisfy the middle term : in this case so that their difference is 7. They may write down the pairs in order ( 1 x 120 ; 2 x 60 ...
Page 32
Edinburgh Mathematical Society. q we know that an expression of the form x2 + px + q may be resolved into factors ... expressions ( abx + an ) and ( abx + bm ) , viz . , ( bx + n ) { ax + m ) . $ 5 . One or two numerical examples will ...
Edinburgh Mathematical Society. q we know that an expression of the form x2 + px + q may be resolved into factors ... expressions ( abx + an ) and ( abx + bm ) , viz . , ( bx + n ) { ax + m ) . $ 5 . One or two numerical examples will ...
Page 35
... expression a ' , where α is a complex number . We first observe that -1 ( a1 ) 2 = a2 = a ̄1 ; so that the effect of the operation ( ) 2 , if performed twice upon a , is to give us the reciprocal of a ; or the operation is one which ...
... expression a ' , where α is a complex number . We first observe that -1 ( a1 ) 2 = a2 = a ̄1 ; so that the effect of the operation ( ) 2 , if performed twice upon a , is to give us the reciprocal of a ; or the operation is one which ...
Page 90
... expressions may be obtained . specimen : Ir r2 gr22 + rrirs r2 rrori ( 8 ) + N r3 r rr1 = 8283 881 = r2r3 rr2 = 8381 rr3 = 8182 ( 9 ) 882 = r3r1 SS3 = rir2 rr1 + r2r3 = bc rr2 + r3r1 = ca rr3 + r1r2 = ab ( 10 ) See VIII . 2 ( r2r3 + ...
... expressions may be obtained . specimen : Ir r2 gr22 + rrirs r2 rrori ( 8 ) + N r3 r rr1 = 8283 881 = r2r3 rr2 = 8381 rr3 = 8182 ( 9 ) 882 = r3r1 SS3 = rir2 rr1 + r2r3 = bc rr2 + r3r1 = ca rr3 + r1r2 = ab ( 10 ) See VIII . 2 ( r2r3 + ...
Page 91
... expressions may be obtained for r1 , 72 , 73 and for 81 , 82 , 83 . r2r3 + r3r1 + r1r2 = s2 2 r3r2 - r2r - r r3 = s12 r1r3r3r -r r1 = 822 rrrrrr2 = 832 ( 15 ) See VII . − r2r3 + r3r1 + r12r2 = 8 ( 2α − s ) - r2r3 + r2r + rr3 = 81 ( 2a ...
... expressions may be obtained for r1 , 72 , 73 and for 81 , 82 , 83 . r2r3 + r3r1 + r1r2 = s2 2 r3r2 - r2r - r r3 = s12 r1r3r3r -r r1 = 822 rrrrrr2 = 832 ( 15 ) See VII . − r2r3 + r3r1 + r12r2 = 8 ( 2α − s ) - r2r3 + r2r + rr3 = 81 ( 2a ...
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Acos Asin Au² B.Sc B₁ bisects C₁ centre circle cutting circonscrit circumcircle coefficients College compasses conique construction convergence coordonnées cube D.Sc d'une denote describe a circle deux Diary for 1843 differentiating Edinburgh Edinburgh Mathematical Society effected by 2R₁ Émile Lemoine equation Euclid's excircles finite number Fourier series function Gentleman's Diary geometrical Geometrography George Watson's College Gergonne point given circle given point given rectilineal figure given straight line Glasgow h₁ h₂ Hence hyperbola integral intersect JOHN ALISON l'équation Lady's and Gentleman's moduli nine-point circle operation which consists orthocentre pedal triangle perpendicular place the edge plan tangent point de contact polar Professor quadrique r₁ r₂ racine radius describe révolution rr₁ ruler in coincidence sides sinma solution sommet tangentielle tetrahedra theorem trois vanishes with h Weddle λ²
Popular passages
Page 1 - To draw a straight line perpendicular to a given straight line from a given point without it . 26 4.
Page 3 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Page 10 - ABC be the given rectilineal figure, to which the figure to be described is required to be similar, and D that to which it must be equal. It is required to describe a rectilineal figure similar to ABC, and equal to D. Upon the straight line BC describe (cor.
Page 5 - SEGMEBTT of a circle being given to describe the circle of which it is the segment.* Let ABC be the given segment of a circle ; it is required to describe the circle of which it is the segment.
Page 70 - ... the sum of the squares on half the line and on the line between the points of section*.
Page 6 - In a given circle to inscribe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle ; it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF.
Page 6 - UPON a given straight line to describe a segment of a circle containing an angle equal to a given rectilineal angle.
Page 2 - At a point in a given straight line to make an angle equal to a given angle.
Page 69 - If a straight line be divided into any two, parts, the square on the whole line is equal to the sum of the rectangles contained by the whole and each of the parts*.