A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
From inside the book
Page xxiii
... POLAR COORDINATES . SECTION 1. - Extension of the modes of interpretation , and on the equations to some polar curves . 251. Interpretation of r and when affected with negative signs 411 262-265 . Equations to the Spiral of Archimedes ...
... POLAR COORDINATES . SECTION 1. - Extension of the modes of interpretation , and on the equations to some polar curves . 251. Interpretation of r and when affected with negative signs 411 262-265 . Equations to the Spiral of Archimedes ...
Page xxiv
... polar curves . 298-300 . Length of radius of curvature 456 301. On the chord of curvature , its definition and value 458 302. Examples in illustration 458 SECTION 4. - Evolutes of polar curves . 303. Method of finding the equation to ...
... polar curves . 298-300 . Length of radius of curvature 456 301. On the chord of curvature , its definition and value 458 302. Examples in illustration 458 SECTION 4. - Evolutes of polar curves . 303. Method of finding the equation to ...
Page xxv
... polar envelope 480 319. The degree of the first polar envelope 481 320. Reciprocal curves 483 321. Properties of reciprocal polars 484 SECTION 4. - On caustics . 322. On the formation of caustics .... 486 323 , 324. Caustic by reflexion ...
... polar envelope 480 319. The degree of the first polar envelope 481 320. Reciprocal curves 483 321. Properties of reciprocal polars 484 SECTION 4. - On caustics . 322. On the formation of caustics .... 486 323 , 324. Caustic by reflexion ...
Page xxvii
... polar surface 556 386 , 387. The polar line and locus of polar lines 557 388. The osculating sphere 557 389. Evolutes of non - plane curves 559 390 , 391. Geometrical illustrations 561 392. Complex flexure and its measure 564 393. The ...
... polar surface 556 386 , 387. The polar line and locus of polar lines 557 388. The osculating sphere 557 389. Evolutes of non - plane curves 559 390 , 391. Geometrical illustrations 561 392. Complex flexure and its measure 564 393. The ...
Page 312
... polar coordinates , the equa- tion is r = 2a sin 0 tan 0 . 195. ] The Witch of Agnesi . Fig . 35 . ( 13 ) DEF . In the ordinate MQ of a circle a point P is taken , so that MP : MQ OA : OM ; the locus of the point p is the Witch of ...
... polar coordinates , the equa- tion is r = 2a sin 0 tan 0 . 195. ] The Witch of Agnesi . Fig . 35 . ( 13 ) DEF . In the ordinate MQ of a circle a point P is taken , so that MP : MQ OA : OM ; the locus of the point p is the Witch of ...
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Common terms and phrases
according algebraical angles applicable assume axis becomes Calculus called changes sign Chapter circle coefficients consider constant continuous corresponding curve derived derived-functions determine differential dimensions direction divided drawn dx dy dy dx elimination equal equation examples expression factors finite function geometrical given gives greater Hence homogeneous function increases independent infinite infinitesimal infinity involved less limit maxima maximum means method minima minimum value negative observed origin partial particular pass plane positive powers preceding properties quantity relation replaced represent respectively result roots sides similar Similarly singular value straight line substituted successive suppose symbols tangent Theorem tion true values vanish variables variation vary whence zero