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" Find an expression for the area of a triangle in terms of the coordinates of its angular points. "
The Principles of Analytical Geometry: Designed for the Use of Students - Strona 72
autor: Henry Parr Hamilton - 1826 - Liczba stron: 326
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A Treatise on the Application of Analysis to Solid Geometry

Duncan Farquharson Gregory, William Walton - 1845 - Liczba stron: 276
...planes, and then to take the sum of these projections projected on the second plane. (20) To cxpress the area of a triangle in terms of the coordinates of its angular points. This may be most conveniently done by first finding the projection of the area of a triangle, one of...
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A treatise on the application of analysis to solid geometry, commenced by D ...

Duncan Farquharson Gregory - 1845
...planes, and then to take the sum of these projections projected on the second plane. (20) To express the area of a triangle in terms of the coordinates of its angular points. This may be most conveniently done by first finding the projection of the area of a triangle, one of...
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The Mathematician, Tom 1

1845
...quadrilateral, PB the positive axis of x, and the points A, B, C, D, respectively, Now the expression for the area of a triangle in terms of the co-ordinates of its three angular points (#1^1, x^y- a .r 3 ^ 3 ) in reference to rectangular axes is ( Young's Analytical...
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A collection of examples in pure and mixed mathematics, with hints and ...

Alfred Wrigley - 1852
...36. Find the area included between the lines, x—y = o, x + y = o, x—y = a, x + y=b. 3?. Express the area of a triangle in terms of the coordinates of its angular points a, b ; a', b' ; a", 6". II. CIRCLE. 38. Find the equation to a circle referred to oblique axes. 39....
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Arithmetic, algebra, differential and integral calculus, by W. Rutherford ...

Royal Military Academy, Woolwich - 1853
...then will these lines meet in the same point on В К produced. Prove this by coordinates. 5. Express the area of a triangle in terms of the coordinates of its three angles. 6. Three lines AB, AC, AD, which emanate from the same point A, are given in position....
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A treatise on plane co-ordinate geometry

Isaac Todhunter - 1855 - Liczba stron: 299
...require the co-ordinates of a point midway between two given points ; then nl = w2 and 11. To express the area of a triangle in terms of the coordinates of its angular points. Let ABC be a triangle ; let ^ yv be the co-ordinates of x those of B ; x3, y3, those of C. Draw the...
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A History of the Progress of Calculus of Variations During the Nineteenth ...

Isaac Todhunter - 1861 - Liczba stron: 532
...rfy/r [74. There are two methods of arriving at this result ; we may take the ordinary expression for the area of a triangle in terms of the co-ordinates of its angular points, and substitute the values of the co-ordinates just given. Or we may proceed thus — find the area...
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A Treatise on Plane Co-ordinate Geometry as Applied to the Straight Line and ...

Isaac Todhunter - 1862 - Liczba stron: 326
...require the co-ordinates of the point midway between two given points ; then nt = nt and 11. To express the area of a triangle in terms of the coordinates of its angular points. Let ABC be a triangle; let a^, y. be the co-ordinates of A ; a;,, yt those of B; xt, yt those of 0....
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Collection of Examples and Problems in Pure and Mixed Mathematics: With ...

Alfred Wrigley - 1862 - Liczba stron: 294
...b". 38. Find the area included between the lines, x—y=O, x + y = 0, x—y = a, x + y=b. 39. Express the area of a triangle in terms of the coordinates of its angular points a, b ; a', V ; a", b", 40. Show that the lines, of which the equations are, all pass through one point....
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The Quarterly Journal of Pure and Applied Mathematics, Tom 5

1862
...then 2 A = It , dbc 1=(2A? ft flS* therefore 2A' and «' = - 2 /37 |« - 22 which are expressions for the area of a triangle in terms of the coordinates of its angular poiuts ; and for the length of a line in terms of the coordinates of its extremities. II.— The Plane....
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