Proceedings of the Edinburgh Mathematical Society, Volume 12Scottish Academic Press, 1894 - Electronic journals |
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Page 19
... then and P is l : m : n = cos A : cosB : cosC , asin2A = ẞsin2B = ysin2C . 15. If l : m : n = s - as - b : s - c , then P is the Gergonne point , and ( iii . ) is the In - circle . 16. If P is the Symmedian - point , then 20.
... then and P is l : m : n = cos A : cosB : cosC , asin2A = ẞsin2B = ysin2C . 15. If l : m : n = s - as - b : s - c , then P is the Gergonne point , and ( iii . ) is the In - circle . 16. If P is the Symmedian - point , then 20.
Page 30
... cosC and ( s -- a ) a2a2 + ( s − b ) b2ß2 + ( s − c ) c2y2 respectively the minimum values . - - In the first example given we have a function of the second degree of aa , bẞ , cy as a critical value at the centroid . This point would ...
... cosC and ( s -- a ) a2a2 + ( s − b ) b2ß2 + ( s − c ) c2y2 respectively the minimum values . - - In the first example given we have a function of the second degree of aa , bẞ , cy as a critical value at the centroid . This point would ...
Page 70
... cosC ) - bcosBẞ ( 1 - cos A ) + ccosCy ( 1 - cosA ) = 0 , and Ap , Bq2 , Cr2 meet in acos Aa = bcos BB = ccosCy . 2 The polar of the circumcentre is A B - C aacos- sin 2 2 bẞsin ( C - 4 ) sin + cysin ( B - 4 ) sin4 = 0 , 6 / 6sin ( C ...
... cosC ) - bcosBẞ ( 1 - cos A ) + ccosCy ( 1 - cosA ) = 0 , and Ap , Bq2 , Cr2 meet in acos Aa = bcos BB = ccosCy . 2 The polar of the circumcentre is A B - C aacos- sin 2 2 bẞsin ( C - 4 ) sin + cysin ( B - 4 ) sin4 = 0 , 6 / 6sin ( C ...
Page 84
... B ( 1 + cos A ) + ycos A cosC = 0 ; hence they intersect on AD ; in fact , in the point where AD cuts EF . The polar of His - a ( 1 + cos2A ) + ( B + y ) cosA = 0 . The Pedal Triangle . By Professor J. E. A. STEGGALL 84.
... B ( 1 + cos A ) + ycos A cosC = 0 ; hence they intersect on AD ; in fact , in the point where AD cuts EF . The polar of His - a ( 1 + cos2A ) + ( B + y ) cosA = 0 . The Pedal Triangle . By Professor J. E. A. STEGGALL 84.
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Common terms and phrases
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*.