A treatise on the application of analysis to solid geometry, commenced by D.F. Gregory, concluded by W. WaltonJ. Deighton, 1852 - 310 pages |
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Page 1
... geometrical quan- tities , such as lines , areas , angles , & c . , but also the positions of points . Our habit of denoting arithmetical quantities by a single symbol naturally leads us also to denote the simplest geometrical ...
... geometrical quan- tities , such as lines , areas , angles , & c . , but also the positions of points . Our habit of denoting arithmetical quantities by a single symbol naturally leads us also to denote the simplest geometrical ...
Page 5
... geometrical interpretation of such equations . Let us take a single equation , such as f ( x , y , z ) = 0 : this may be considered as a relation which enables us to deter- mine any one of the variables when the other two are given ...
... geometrical interpretation of such equations . Let us take a single equation , such as f ( x , y , z ) = 0 : this may be considered as a relation which enables us to deter- mine any one of the variables when the other two are given ...
Page 19
... very convenient , especially in geometrical investigations . For if we add and subtract from the preceding expression the three squares a2x2 , b2y2 , c222 , the expression may be transformed into ( a2 + b2 C 2 FUNDAMENTAL THEOREMS . 19.
... very convenient , especially in geometrical investigations . For if we add and subtract from the preceding expression the three squares a2x2 , b2y2 , c222 , the expression may be transformed into ( a2 + b2 C 2 FUNDAMENTAL THEOREMS . 19.
Page 21
... geometrical definitions are so well known , and their chief geometrical properties are so familiar to us , that it seems more natural to translate these into ana- lytical language than to adopt the inverse process . The surfaces of the ...
... geometrical definitions are so well known , and their chief geometrical properties are so familiar to us , that it seems more natural to translate these into ana- lytical language than to adopt the inverse process . The surfaces of the ...
Page 28
... geometrical inclinations , the expression for sine must always be taken as positive . 32. To find the conditions that two straight lines may be parallel or perpendicular to each other . If the two lines be parallel , their direction ...
... geometrical inclinations , the expression for sine must always be taken as positive . 32. To find the conditions that two straight lines may be parallel or perpendicular to each other . If the two lines be parallel , their direction ...
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Common terms and phrases
axis centre chords coefficients condition cone constant coordinate planes cosines cosn cosß cosv cosy curvature curve of contact cylinder determined developable surface dF dF dF dx diametral plane direction-cosines dv du dv dx dy dz dx² eliminating ellipse ellipsoid equa equal expression find the equation formulæ geometrical given line Hence homogeneous function hyperbolic hyperbolic paraboloid hyperboloid infinite number Let the equations line of intersection lines of curvature locus Multiplying normal plane origin osculating circle osculating plane parameters perpendicular plane curve plane of yz planes parallel positive projection Px² quantities Qy² ratios rectangular ruled surfaces Rz² second degree second order sections shew singular points sphere straight line substitute tangent plane three equations values vanish variables x₁ x²² Y₁ y²² zero
Popular passages
Page 16 - To express the area of a triangle in terms of the coordinates of its angular points.
Page 307 - A Treatise on the Application of Analysis to Solid Geometry. Commenced by DF GREGORY, MA, late Fellow and Assistant Tutor of Trinity College, Cambridge ; Concluded by W. WALTON, MA, Trinity College, Cambridge.
Page 10 - It, so that PR is equal to MN. Now the inclination of a straight line to a plane is the angle which the line makes with the intersection of the plane and a plane perpendicular to it passing through the line. Since, then, PM and QN are perpendicular to ABCD, the plane of PQMN is also perpendicular to it, and the inclination of PQ to the plane AB CD is measured by the angle between PQ and MN or the equal angle QPR.
Page 280 - The sum of the squares of the projections of any three conjugate diameters on a fixed line is constant. Instead of projecting the diameters on the line directly, it is better to project the coordinates of the extremities of each diameter, and add them. Now, if X...