An elementary treatise on coordinate geometry of three dimensions . = a& sin a. sin 7 (1) 3,. Pig. 67. Fig. 6S. This equation represents a cylinder which intersects the cone in thegeodesic. If the arcs , DoDs. ... are each equal to the circumference ofthe circle in the plane ADC. the positions of OB, when in addition tothe curved sector OAB of the surface of the cone, one, two, ... com-plete sheets are successively developed into a plane, are 01B2, OjBg ....If Ax and are joined and the plane sector A^Bj is wrappedagain on the cone, AjB2 becomes a second geodesic passing throughA and B
An elementary treatise on coordinate geometry of three dimensions . = a& sin a. sin 7 (1) 3,. Pig. 67. Fig. 6S. This equation represents a cylinder which intersects the cone in thegeodesic. If the arcs , DoDs. ... are each equal to the circumference ofthe circle in the plane ADC. the positions of OB, when in addition tothe curved sector OAB of the surface of the cone, one, two, ... com-plete sheets are successively developed into a plane, are 01B2, OjBg ....If Ax and are joined and the plane sector A^Bj is wrappedagain on the cone, AjB2 becomes a second geodesic passing throughA and B and completely surrounding the cone. Similarly AjB3 be-comes a third geodesic. A-^, however, does not lie on the sheetsthat have been unrolled from the cone, and hence the only geodesies,(in our figure), through A and B are those which develop into Aj^Bj,AjB,,, AXB3. It is clear from the figure, that if (ft + 1) geodesies pass through twopoints A and B, and the angle between the planes through the axisof the cone and A and B is (3, sinoL((3 + 2)nr)<-. The equations to surfaces through
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
