A treatise on the application of analysis to solid geometry, commenced by D.F. Gregory, concluded by W. Walton |
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Page 5
... results of the applications of Analysis to Geometry are expressed in equations involving the co - ordinates which have been denoted by x , y , z ; we must therefore , before proceeding further , consider what is the geometrical ...
... results of the applications of Analysis to Geometry are expressed in equations involving the co - ordinates which have been denoted by x , y , z ; we must therefore , before proceeding further , consider what is the geometrical ...
Page 6
... results . If the equation cannot be satisfied by combinations of possible values of the variables , its interpretation does not come within the scope of our present purpose . Should however it be pos- sible to satisfy the equation by ...
... results . If the equation cannot be satisfied by combinations of possible values of the variables , its interpretation does not come within the scope of our present purpose . Should however it be pos- sible to satisfy the equation by ...
Page 7
... result of any such combination is the equation to some surface which passes through the intersection of the two given surfaces . Any such result may be used instead of one of the given equations , if such a change conduce to simplicity ...
... result of any such combination is the equation to some surface which passes through the intersection of the two given surfaces . Any such result may be used instead of one of the given equations , if such a change conduce to simplicity ...
Page 19
... result of any process that a function of x is equal to a function of y in which y is involved in a man- ner similar to that in which x is involved in the other , then , as there is nothing to distinguish one co - ordinate from another ...
... result of any process that a function of x is equal to a function of y in which y is involved in a man- ner similar to that in which x is involved in the other , then , as there is nothing to distinguish one co - ordinate from another ...
Page 29
... result being independent of r , r ' ( the only quantities which particularize the position ) must be true for all positions . The elimination is readily effected by cross - multiplication , which gives us - - - ( m'n – mn ' ) ( x − a ) ...
... result being independent of r , r ' ( the only quantities which particularize the position ) must be true for all positions . The elimination is readily effected by cross - multiplication , which gives us - - - ( m'n – mn ' ) ( x − a ) ...
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Common terms and phrases
Ax² axis centre chords co-ordinate axes co-ordinate planes coefficients condition cone considered constant cos² cosines curve of contact cylinder d²x d²z d³x d³y d³z determined developable surface dF dx diameters diametral plane differential equation direction-cosines ds² dx² dy² eliminating ellipse ellipsoid equal expression find the equation formula given Hence homogeneous function hyperbolic hyperboloid Let the equations line of intersection lines of curvature locus Multiplying normal plane normal sections origin osculating circle osculating plane P'y² P'z² P₁ parameters perpendicular plane curve plane of xy Points of Inflected positive projections Px² quantities r₁ radii radius of curvature satisfied second degree second order sin² sphere straight line substitute suppose tangent plane torsion values vanish variables x₁ x² y² y₁ y²² zero
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