 | Charles Davies - 1836 - 370 pàgines
...diagonal. Scholium 4. This last result offers an easy method of determining a relation that exists between the cosines of the angles which a straight line makes with the co-ordinate axes. Let us designate the length of the line passing through the origin of co-ordinates by r, and the angles... | |
 | Charles Davies - 1838 - 366 pàgines
...diagonal. Scholium 4. This last result offers an easy method of determining a relation that exists between the cosines of the angles which a straight line makes with the co-ordinate axes. Let us designate the length 'of the line passing through the origin of co-ordinates by r, and the angles... | |
 | Duncan Farquharson Gregory - 1852 - 352 pàgines
...substituting for these quantities, we have r2 = r" (cos2 a + COS*/9 + COS2 7), or cos2 a + cos2 ft + cos2 7 = 1, a very important relation, to which we shall frequently...the direction of the line, we shall call them the direction_cosines of the line ; and when we wish to speak of a straight line with reference to its... | |
 | Gerardus Beekman Docharty - 1865 - 328 pàgines
...squares of the three edges. (128.) From this we may easily determine a relation which exists between the cosines of the angles which a straight line makes with the co-ordinate axes. Thus, let r=the line passing through the origin ; X, Y, Z the angles which this line makes with the... | |
 | James Booth - 1873 - 426 pàgines
...tangential equation determines the point, three are necessary to fix the tangential plane. 62.] To express the cosines of the angles which a straight line makes with the axes of coordinates in terms of the constants fa, v, a, /3 of t/te tangential equations of the given... | |
 | Charles Smith - 1884 - 256 pàgines
...PQcosy=PN. Square and add, then PQ? {cos2a + cos2/3 + cos27} = P Hence cos2a + cos2/3 +«os2y = 1. The cosines of the angles which a straight line makes with the positive directions of the co-ordinate axes are called its direction-cosines, and we shall in future... | |
 | Charles Smith - 1886 - 268 pàgines
...and add, then PQ* {cos2a + cos"/3 + cos"?} = PL2 + PM* + PN* = PQ2. Hence cos2a + cos2/3 + cos2y = 1. The cosines of the angles which a straight line makes with the positive directions of the co-ordinate axes are called its direction-cosines, and we shall in future... | |
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This last result offers an easy method of determining a relation that exists between the cosines of the angles which a straight line makes with the co-ordinate axes. 