 | Isaac Todhunter - 1866 - 386 pàgines
...determine the position of equilibrium. 31. Forces P, Q, R act along the sides BC, CA, AB of a triangle, and their resultant passes through the centres of the inscribed and circumscribed circles ; shew that P : Q : R :: cos B — cos C : cos C — cos A : cos A — cos B. 32. Find the position... | |
 | 1870 - 586 pàgines
...den Winkeln A, B, C der eine stumpf, die beiden anderen sind spitz, und die Grossen cos A cos B cos C cos B cos C' cos C cos A ' cos A cos B sind also offenbar sämmtlich negativ. Wegen der aus dem Obigen bekannten Gleichungen: . tang B tang... | |
 | W. G. Willson - 1874 - 294 pàgines
...rotation in the opposite direction. 6. Forces P, Q, R act along the sides PC, CA, AB of a triangle, and their resultant passes through the centres of the inscribed and circumscribed circles ; shew that P : Q : R : : cosB-coaC : coaC-cosA : coaA-cosB. T. ABCD is a quadrilateral inscribed in... | |
 | George Salmon - 1874 - 339 pàgines
...der drei Seitenhalbierungslinien verbindet. Denn die Coordinaten des Durchschnitts der Höhen sind cos B cos C> cos C cos A> cos A cos B , und die des Durchschnittspunktes der Seitenhalbierungslinien sind sin B sin C, sin C sin A, sin A... | |
 | Dublin city, univ - 1876 - 420 pàgines
...equal to half their ium ; find the angle between them. 9. Forces act along the sides of a triangle, and their resultant passes through the centres of the inscribed and circumscribed circles ; find the ratio of the forces. 10. A body is projected vertically upwards with a velocity which will... | |
 | George Minchin Minchin - 1877 - 470 pàgines
...A/« 4 + 4* + c 1 - «-A- - 0-c- - c'ti* abc where A is the area of the triangle. n. Forces P. Q, £, act along the sides of a triangle, ABC, and their...the inscribed and circumscribed circles : prove that PQ Ji cos B — cos C cos 6'— cos A cos A — cos B CWolstenholme's Book of Mathematical Problems).... | |
 | Joseph Wolstenholme - 1878 - 538 pàgines
...is equivalent to the system OA, OB, 00. [The result is true when 0 is not in the plane ABC.] 2209. Forces P, Q, R act along the sides of a triangle ABC...PQR cos B — cos C cos C — cos A cos A — cos B ' 2210. Four points A, B, C, D lie on a circle and forces act along the chords AB, BC, CD, DA in the... | |
 | George Minchin Minchin - 1880 - 568 pàgines
...resultant of the system of forces in the last example is 4A , 5abc where A is the area of the triangle. 11. Forces P, Q, R act along the sides of a triangle,...the inscribed and circumscribed circles: prove that P Q _ _ R cos B—cos C cos(7—cos/1 cosA—cosB (Wohtenholme's Book of Mathematical Problems). being... | |
 | George Minchin Minchin - 1880 - 536 pàgines
...resultant of the system of forces in the last example is aoc where A is the area of the triangle. 11. Forces P, Q, R act along the sides of a triangle,...resultant passes through the centres of the inscribed ami circumscribed circles : prove that P _ QB cos.6 — cosC' cos(7 — cosA cos A — cosJi ("Wolsteuholme's... | |
 | George Minchin Minchin - 1884 - 372 pàgines
...system of forces in the last example is 4A . 5-5 J-~; jjabc where A is the area of the triangle; 11. Forces P, Q, R, act along the sides of a triangle,...the inscribed and circumscribed circles : prove that P _ Q _ R cos B — cos G cos G — cos A cos A — cos B ("Wolstenholme's Book of Mathematical Problems);... | |
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E, act along the sides of a triangle, ABC, and their resultant passes through the centres of the inscribed and circumscribed circles : prove that P _ Q _ R cos B — cos C ~~ cos C — cos A cos A — cos B ("Wolstenholme's Book of Mathematical Problems). 
