Elementary Illustrations of the Differential and Integral Calculus
Index of terms
Every concept, theorem, method and person the concept graph places in a chapter of this book, with the chapters that teach it and the other books on the shelf that teach it too.
Concepts (137)
- abscissa
Taught in: Algebraical Geometry, On the Connexion of the Signs of Algebraical and the Directions of Geometrical Magnitudes, The Drawing of a Tangent to a Curve, Determination of Curvilinear Areas. The Parabola, Concluding Remarks on the Study of the Calculus
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy, First Course in the Theory of Equations, Mathematical Recreations and Essays
- algebraic expression
Taught in: On Functions
Also in: A First Book in Algebra, The First Steps in Algebra
- antiderivative
Taught in: Connexion of the Integral with the Differential Calculus, Nature of Integration, Determination of Curvilinear Areas. The Parabola
- approximation
Taught in: On the Ratio or Proportion of Two Magnitudes, On the Ratio of Magnitudes that Vanish Together, The Notion of Infinitely Small Quantities, Infinite Series, Differential Coefficients, The Same Problem Solved by the Principles of Leibnitz, Simple Harmonic Motion, Accelerated Motion, Limiting Ratios of Magnitudes that Increase Without Limit, Recapitulation of Results Reached in the Theory of Functions, Approximations by the Differential Calculus, Solution of Equations by the Differential Calculus, Calculus of Finite Differences. Successive Differentiation, Inverse Functions, Method of Indivisibles, Concluding Remarks on the Study of the Calculus
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy, Mathematical Recreations and Essays, Plane Geometry, Spherical Trigonometry, for the Use of Colleges and Schools
- arc of a circle
Taught in: On the Ratio of Magnitudes that Vanish Together, On the Ratios of Continuously Increasing or Decreasing Quantities, The Notion of Infinitely Small Quantities, The Same Problem Solved by the Principles of Leibnitz, Simple Harmonic Motion
Also in: An Introduction to Mathematics, Plane Geometry
- arc of a curve
- area
Taught in: Determination of Curvilinear Areas. The Parabola, Concluding Remarks on the Study of the Calculus
Also in: A Course of Pure Mathematics, Calculus Made Easy, Mathematical Recreations and Essays, Plane Geometry, Spherical Trigonometry, for the Use of Colleges and Schools, Vector Analysis and Quaternions
- arithmetical progression
Taught in: The Integral Calculus
Also in: An Introduction to Mathematics, Mathematical Recreations and Essays, The First Steps in Algebra
- arrangement
Taught in: Limiting Ratios of Magnitudes that Increase Without Limit
Also in: A First Book in Algebra, The First Steps in Algebra
- astronomical ephemeris
Taught in: Approximations by the Differential Calculus
- binomial coefficient
Taught in: Calculus of Finite Differences. Successive Differentiation
Also in: A Course of Pure Mathematics
- calculus
Taught in: Differential and Integral Calculus, The Notion of Infinitely Small Quantities, Taylor's Theorem. Derived Functions, The Notation of the Differential Calculus, Limiting Ratios of Magnitudes that Increase Without Limit, The Integral Calculus, Method of Indivisibles, Concluding Remarks on the Study of the Calculus
Also in: An Introduction to Mathematics, Calculus Made Easy, Mathematical Recreations and Essays
- calculus of finite differences
Taught in: Calculus of Finite Differences. Successive Differentiation
- cartesian coordinates
Taught in: Algebraical Geometry, On the Connexion of the Signs of Algebraical and the Directions of Geometrical Magnitudes, A Geometrical Illustration: Limit of the Intersections of Two Coinciding Straight Lines, Determination of Curvilinear Areas. The Parabola
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Treatise on Thermodynamics, Vector Analysis and Quaternions
- chord
Taught in: On the Ratio of Magnitudes that Vanish Together, On the Ratios of Continuously Increasing or Decreasing Quantities, The Notion of Infinitely Small Quantities, The Drawing of a Tangent to a Curve
Also in: A Course of Pure Mathematics, Plane Geometry, Spherical Trigonometry, for the Use of Colleges and Schools
- circle
Taught in: On the Ratio of Magnitudes that Vanish Together, The Notion of Infinitely Small Quantities, On the Connexion of the Signs of Algebraical and the Directions of Geometrical Magnitudes, Simple Harmonic Motion, Nature of Integration
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, First Course in the Theory of Equations, Mathematical Recreations and Essays, Plane Geometry, Solid Geometry with Problems and Applications, Spherical Trigonometry, for the Use of Colleges and Schools
- coefficient
Taught in: Taylor's Theorem. Derived Functions, Accelerated Motion, Recapitulation of Results Reached in the Theory of Functions, Determination of Curvilinear Areas. The Parabola
Also in: A First Book in Algebra, First Course in the Theory of Equations, The First Steps in Algebra
- commensurable magnitudes
Taught in: On the Ratio or Proportion of Two Magnitudes
Also in: Plane Geometry
- common logarithm
Taught in: The Drawing of a Tangent to a Curve, Illustration of the Rules for Differentiation, The Differential Coefficient Considered with Respect to its Magnitude
Also in: A Course of Pure Mathematics, Calculus Made Easy, Elements of Plane Trigonometry
- composition of functions
Taught in: Inverse Functions
- constant
Taught in: On Functions, Inverse Functions, Nature of Integration, Determination of Curvilinear Areas. The Parabola
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy, Elements of Plane Trigonometry, Plane Geometry, Solid Geometry with Problems and Applications
- contiguous values
Taught in: The Differential Coefficient Considered with Respect to its Magnitude
- continuous quantity
Taught in: On the Ratios of Continuously Increasing or Decreasing Quantities
Also in: An Introduction to Mathematics
- convergent series
Taught in: Convergent and Divergent Series, Taylor's Theorem. Derived Functions, Differential Coefficients
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy
- cosine
Taught in: Taylor's Theorem. Derived Functions, Simple Harmonic Motion, Rules for Differentiation, Illustration of the Rules for Differentiation, The Integral Calculus
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy, Elements of Plane Trigonometry, Solid Geometry with Problems and Applications, Spherical Trigonometry, for the Use of Colleges and Schools, Vector Analysis and Quaternions
- curve
Taught in: The Drawing of a Tangent to a Curve, Determination of Curvilinear Areas. The Parabola
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, First Course in the Theory of Equations
- curvilinear figure
Taught in: Determination of Curvilinear Areas. The Parabola, Concluding Remarks on the Study of the Calculus
Also in: Plane Geometry
- decreasing without limit
Taught in: On the Ratios of Continuously Increasing or Decreasing Quantities
- decrement
Taught in: The Notation of the Differential Calculus, Calculus of Finite Differences. Successive Differentiation
- degree
Taught in: Solution of Equations by the Differential Calculus
Also in: A First Book in Algebra, First Course in the Theory of Equations, The First Steps in Algebra
- dependent
Taught in: On Functions
Also in: A Course of Pure Mathematics
- derivative
Taught in: Taylor's Theorem. Derived Functions, Differential Coefficients, The Notation of the Differential Calculus, The Drawing of a Tangent to a Curve, An Illustration from Dynamics: Velocity, Acceleration, etc, Accelerated Motion, Recapitulation of Results Reached in the Theory of Functions, Approximations by the Differential Calculus, Solution of Equations by the Differential Calculus, Differential Coefficients of Differential Coefficients, Calculus of Finite Differences. Successive Differentiation, Total and Partial Differential Coefficients. Implicit Differentiation, Inverse Functions, Implicit Functions, Fluxions, and the Idea of Time, The Differential Coefficient Considered with Respect to its Magnitude, Connexion of the Integral with the Differential Calculus, Determination of Curvilinear Areas. The Parabola
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy, First Course in the Theory of Equations
- diagonal
Taught in: On the Ratio or Proportion of Two Magnitudes
Also in: Mathematical Recreations and Essays, Plane Geometry, Spherical Trigonometry, for the Use of Colleges and Schools
- difference
Taught in: On the Ratio or Proportion of Two Magnitudes, The Notation of the Differential Calculus, Calculus of Finite Differences. Successive Differentiation
Also in: A First Book in Algebra
- differential
Taught in: The Notation of the Differential Calculus, The Drawing of a Tangent to a Curve, Simple Harmonic Motion, The Method of Fluxions, Accelerated Motion, Recapitulation of Results Reached in the Theory of Functions, Approximations by the Differential Calculus, Rules for Differentiation, Calculus of Finite Differences. Successive Differentiation, Total and Partial Differential Coefficients. Implicit Differentiation, Inverse Functions, Implicit Functions, Connexion of the Integral with the Differential Calculus, Nature of Integration, Determination of Curvilinear Areas. The Parabola
Also in: A Course of Pure Mathematics, Calculus Made Easy, Treatise on Thermodynamics
- divergent series
Taught in: Convergent and Divergent Series
Also in: A Course of Pure Mathematics, An Introduction to Mathematics
- dominant term
Taught in: Limiting Ratios of Magnitudes that Increase Without Limit
- dynamics
Taught in: An Illustration from Dynamics: Velocity, Acceleration, etc
Also in: An Introduction to Mathematics
- equality
Taught in: On the Ratio or Proportion of Two Magnitudes
Also in: A First Book in Algebra, An Introduction to Mathematics, Plane Geometry, The First Steps in Algebra
- equation
Taught in: On the Connexion of the Signs of Algebraical and the Directions of Geometrical Magnitudes, Solution of Equations by the Differential Calculus, Implicit Functions
Also in: A Course of Pure Mathematics, A First Book in Algebra, An Introduction to Mathematics, Mathematical Recreations and Essays, The First Steps in Algebra
- error of measurement
Taught in: On the Ratio or Proportion of Two Magnitudes, Approximations by the Differential Calculus, Application of the Theorem for Total Differentials to the Determination of Total Resultant Errors, Concluding Remarks on the Study of the Calculus
- Euler's number
Taught in: Rules for Differentiation
- explicit function
Taught in: Implicit Functions
- exponent
Taught in: Rules for Differentiation, Determination of Curvilinear Areas. The Parabola
Also in: A First Book in Algebra, Calculus Made Easy, The First Steps in Algebra, Vector Analysis and Quaternions
- exponential function
Taught in: Taylor's Theorem. Derived Functions, Rules for Differentiation
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy
- falling bodies
Taught in: An Illustration from Dynamics: Velocity, Acceleration, etc
- fluxional notation
Taught in: Differential and Integral Calculus, The Method of Fluxions, Fluxions, and the Idea of Time
Also in: An Introduction to Mathematics, Calculus Made Easy, Mathematical Recreations and Essays
- focus
Taught in: Determination of Curvilinear Areas. The Parabola
Also in: A Course of Pure Mathematics, An Introduction to Mathematics
- function
Taught in: On Functions, Infinite Series, On the Connexion of the Signs of Algebraical and the Directions of Geometrical Magnitudes, Recapitulation of Results Reached in the Theory of Functions, Approximations by the Differential Calculus, Solution of Equations by the Differential Calculus, Rules for Differentiation, Calculus of Finite Differences. Successive Differentiation, Total and Partial Differential Coefficients. Implicit Differentiation, Inverse Functions, Fluxions, and the Idea of Time, The Differential Coefficient Considered with Respect to its Magnitude, The Integral Calculus, Connexion of the Integral with the Differential Calculus, Determination of Curvilinear Areas. The Parabola, Concluding Remarks on the Study of the Calculus
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy, Elements of Plane Trigonometry, Solid Geometry with Problems and Applications
- function notation
Taught in: On Functions, Taylor's Theorem. Derived Functions, Solution of Equations by the Differential Calculus
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy
- function of several variables
Taught in: On Functions
- general power
Taught in: Taylor's Theorem. Derived Functions
Also in: A Course of Pure Mathematics
- geometric series
Taught in: Infinite Series, Convergent and Divergent Series
Also in: Calculus Made Easy
- geometrical progression
Taught in: Infinite Series
Also in: A Course of Pure Mathematics, An Elementary Treatise on Electricity, An Introduction to Mathematics, Mathematical Recreations and Essays, The First Steps in Algebra
- graph of a function
Taught in: On the Connexion of the Signs of Algebraical and the Directions of Geometrical Magnitudes
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, First Course in the Theory of Equations
- higher-order derivative
Taught in: Taylor's Theorem. Derived Functions, Differential Coefficients, Recapitulation of Results Reached in the Theory of Functions, Differential Coefficients of Differential Coefficients, Calculus of Finite Differences. Successive Differentiation, Inverse Functions
Also in: A Course of Pure Mathematics, Calculus Made Easy, First Course in the Theory of Equations
- higher-order difference
Taught in: Calculus of Finite Differences. Successive Differentiation, Inverse Functions
- hypotenuse
Taught in: Approximations by the Differential Calculus
Also in: A Course of Pure Mathematics, Plane Geometry, Spherical Trigonometry, for the Use of Colleges and Schools
- implicit function
Taught in: Implicit Functions
- impulse
Taught in: Accelerated Motion
Also in: Mathematical Recreations and Essays
- incommensurable magnitudes
Taught in: On the Ratio or Proportion of Two Magnitudes
Also in: An Introduction to Mathematics, Mathematical Recreations and Essays, Plane Geometry, Solid Geometry with Problems and Applications
- increment
Taught in: The Notion of Infinitely Small Quantities, Infinite Series, Differential Coefficients, The Notation of the Differential Calculus, The Drawing of a Tangent to a Curve, The Method of Fluxions, Recapitulation of Results Reached in the Theory of Functions, Approximations by the Differential Calculus, Rules for Differentiation, Illustration of the Rules for Differentiation, Applications of the Theorem for Implicit Differentiation, Fluxions, and the Idea of Time, The Differential Coefficient Considered with Respect to its Magnitude, The Integral Calculus, Nature of Integration
- independent variable
Taught in: On Functions
Also in: Calculus Made Easy
- indeterminate form
Taught in: The Notation of the Differential Calculus
Also in: A Course of Pure Mathematics
- indirect function
Taught in: Total and Partial Differential Coefficients. Implicit Differentiation
- infinite sequence
Taught in: Infinite Series, Convergent and Divergent Series, Limiting Ratios of Magnitudes that Increase Without Limit
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Solid Geometry with Problems and Applications
- infinitesimal
Taught in: The Notion of Infinitely Small Quantities, Rational Explanation of the Language of Leibnitz, Orders of Infinity, The Same Problem Solved by the Principles of Leibnitz, Simple Harmonic Motion, The Method of Fluxions, Nature of Integration, Method of Indivisibles
Also in: An Introduction to Mathematics, Calculus Made Easy, Treatise on Thermodynamics, Vector Analysis and Quaternions
- infinity
Taught in: Limiting Ratios of Magnitudes that Increase Without Limit, The Integral Calculus, Method of Indivisibles
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, First Course in the Theory of Equations
- integral
Taught in: Limiting Ratios of Magnitudes that Increase Without Limit, The Integral Calculus, Connexion of the Integral with the Differential Calculus, Nature of Integration, Determination of Curvilinear Areas. The Parabola, Method of Indivisibles, Concluding Remarks on the Study of the Calculus
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy
- intersection of two curves
Taught in: On the Connexion of the Signs of Algebraical and the Directions of Geometrical Magnitudes, A Geometrical Illustration: Limit of the Intersections of Two Coinciding Straight Lines
Also in: Calculus Made Easy
- interval
Taught in: The Differential Coefficient Considered with Respect to its Magnitude, The Integral Calculus
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, First Course in the Theory of Equations
- inverse function
Taught in: Inverse Functions
- limit
Taught in: On the Ratio of Magnitudes that Vanish Together, On the Ratios of Continuously Increasing or Decreasing Quantities, The Notion of Infinitely Small Quantities, Infinite Series, Convergent and Divergent Series, Taylor's Theorem. Derived Functions, Differential Coefficients, The Notation of the Differential Calculus, The Drawing of a Tangent to a Curve, Orders of Infinity, A Geometrical Illustration: Limit of the Intersections of Two Coinciding Straight Lines, The Same Problem Solved by the Principles of Leibnitz, An Illustration from Dynamics: Velocity, Acceleration, etc, Simple Harmonic Motion, The Method of Fluxions, Accelerated Motion, Limiting Ratios of Magnitudes that Increase Without Limit, Recapitulation of Results Reached in the Theory of Functions, Rules for Differentiation, Illustration of the Rules for Differentiation, Calculus of Finite Differences. Successive Differentiation, Total and Partial Differential Coefficients. Implicit Differentiation, Applications of the Theorem for Implicit Differentiation, Implicit Functions, Fluxions, and the Idea of Time, The Differential Coefficient Considered with Respect to its Magnitude, The Integral Calculus, Connexion of the Integral with the Differential Calculus, Nature of Integration, Determination of Curvilinear Areas. The Parabola, Method of Indivisibles, Concluding Remarks on the Study of the Calculus
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy, Elements of Plane Trigonometry, Plane Geometry, Solid Geometry with Problems and Applications
- limit of intersections
Taught in: A Geometrical Illustration: Limit of the Intersections of Two Coinciding Straight Lines
- limits of integration
Taught in: The Integral Calculus, Connexion of the Integral with the Differential Calculus, Nature of Integration
- line
Taught in: On the Connexion of the Signs of Algebraical and the Directions of Geometrical Magnitudes, A Geometrical Illustration: Limit of the Intersections of Two Coinciding Straight Lines, Method of Indivisibles
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy, Plane Geometry, Solid Geometry with Problems and Applications
- logarithm
Taught in: Taylor's Theorem. Derived Functions, Rules for Differentiation, Total and Partial Differential Coefficients. Implicit Differentiation, Applications of the Theorem for Implicit Differentiation, Inverse Functions
Also in: A Course of Pure Mathematics, Calculus Made Easy, Elements of Plane Trigonometry, Mathematical Recreations and Essays, Spherical Trigonometry, for the Use of Colleges and Schools
- magnitudes vanishing together
- mathematical notation
Taught in: Differential Coefficients of Differential Coefficients, Calculus of Finite Differences. Successive Differentiation
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Mathematical Recreations and Essays, Vector Analysis and Quaternions
- mathematics
Taught in: Concluding Remarks on the Study of the Calculus
Also in: An Introduction to Mathematics, Calculus Made Easy, Mathematical Recreations and Essays
- mechanics
Taught in: Method of Indivisibles
Also in: An Introduction to Mathematics, Mathematical Recreations and Essays
- natural logarithm
Taught in: Taylor's Theorem. Derived Functions, The Drawing of a Tangent to a Curve, Rules for Differentiation, Illustration of the Rules for Differentiation
Also in: Calculus Made Easy
- negative direction
Taught in: On the Connexion of the Signs of Algebraical and the Directions of Geometrical Magnitudes
Also in: Elements of Plane Trigonometry
- negative number
Taught in: On the Connexion of the Signs of Algebraical and the Directions of Geometrical Magnitudes
Also in: A First Book in Algebra, An Introduction to Mathematics, Calculus Made Easy, The First Steps in Algebra
- number
Taught in: On the Ratio or Proportion of Two Magnitudes
Also in: An Introduction to Mathematics, The First Steps in Algebra
- operation
Taught in: On Functions, Calculus of Finite Differences. Successive Differentiation
- order of smallness
Taught in: The Notion of Infinitely Small Quantities, Orders of Infinity, The Same Problem Solved by the Principles of Leibnitz
- ordinate
Taught in: Algebraical Geometry, On the Connexion of the Signs of Algebraical and the Directions of Geometrical Magnitudes, The Drawing of a Tangent to a Curve, Determination of Curvilinear Areas. The Parabola, Concluding Remarks on the Study of the Calculus
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy, First Course in the Theory of Equations
- origin
Taught in: On the Connexion of the Signs of Algebraical and the Directions of Geometrical Magnitudes, Determination of Curvilinear Areas. The Parabola
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Elements of Plane Trigonometry, First Course in the Theory of Equations
- parabola
Taught in: Determination of Curvilinear Areas. The Parabola
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Mathematical Recreations and Essays
- parallelogram
Taught in: Determination of Curvilinear Areas. The Parabola
Also in: A Course of Pure Mathematics, Plane Geometry
- partial derivative
Taught in: Partial and Total Differentials, Applications of the Theorem for Implicit Differentiation, Implicit Functions
Also in: A Course of Pure Mathematics, Calculus Made Easy, Treatise on Thermodynamics
- partial differential
Taught in: Total and Partial Differential Coefficients. Implicit Differentiation
Also in: Calculus Made Easy
- perimeter
Taught in: The Notion of Infinitely Small Quantities
Also in: A Course of Pure Mathematics, Plane Geometry, Solid Geometry with Problems and Applications
- perpendicular
Taught in: The Same Problem Solved by the Principles of Leibnitz
Also in: Plane Geometry, Solid Geometry with Problems and Applications, Spherical Trigonometry, for the Use of Colleges and Schools
- point
Taught in: On the Ratio of Magnitudes that Vanish Together, The Differential Coefficient Considered with Respect to its Magnitude, Method of Indivisibles
Also in: A Course of Pure Mathematics, Plane Geometry, Solid Geometry with Problems and Applications
- polygon
Taught in: The Notion of Infinitely Small Quantities
Also in: Plane Geometry, Spherical Trigonometry, for the Use of Colleges and Schools, Vector Analysis and Quaternions
- positive direction
Taught in: On the Connexion of the Signs of Algebraical and the Directions of Geometrical Magnitudes
Also in: A Course of Pure Mathematics, Elements of Plane Trigonometry
- power
Taught in: Infinite Series, Limiting Ratios of Magnitudes that Increase Without Limit
Also in: A Course of Pure Mathematics, A First Book in Algebra, Calculus Made Easy, The First Steps in Algebra
- power series
Taught in: Infinite Series, Taylor's Theorem. Derived Functions, Orders of Infinity
Also in: A Course of Pure Mathematics
- product
Taught in: The Integral Calculus
Also in: A Course of Pure Mathematics, A First Book in Algebra, Calculus Made Easy, The First Steps in Algebra, Vector Analysis and Quaternions
- proportion
Taught in: On the Ratio or Proportion of Two Magnitudes, The Notion of Infinitely Small Quantities, The Same Problem Solved by the Principles of Leibnitz
Also in: Plane Geometry
- rate of change
Taught in: The Differential Coefficient Considered with Respect to its Magnitude
- ratio
Taught in: On the Ratio or Proportion of Two Magnitudes, On the Ratio of Magnitudes that Vanish Together, On the Ratios of Continuously Increasing or Decreasing Quantities, The Notion of Infinitely Small Quantities, Convergent and Divergent Series, Taylor's Theorem. Derived Functions, Limiting Ratios of Magnitudes that Increase Without Limit, Illustration of the Rules for Differentiation, The Differential Coefficient Considered with Respect to its Magnitude, The Integral Calculus, Method of Indivisibles
Also in: An Introduction to Mathematics, Calculus Made Easy, Elements of Plane Trigonometry, Plane Geometry, Treatise on Thermodynamics
- ratio decreasing without limit
- ratio of successive terms
Taught in: Convergent and Divergent Series
- reciprocal
Taught in: On the Ratio of Magnitudes that Vanish Together, Inverse Functions
Also in: A Course of Pure Mathematics, Calculus Made Easy, The First Steps in Algebra, Vector Analysis and Quaternions
- rectangle
Taught in: Determination of Curvilinear Areas. The Parabola
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy, Plane Geometry
- rectilinear figure
Taught in: Concluding Remarks on the Study of the Calculus
Also in: Plane Geometry
- regular polygon
Taught in: Nature of Integration
Also in: Elements of Plane Trigonometry, Mathematical Recreations and Essays, Plane Geometry
- relation between variables
Taught in: Inverse Functions, Implicit Functions
- right angle
Taught in: The Integral Calculus
Also in: A Course of Pure Mathematics, Plane Geometry
- right triangle
Taught in: The Same Problem Solved by the Principles of Leibnitz
Also in: A Course of Pure Mathematics, Plane Geometry, Solid Geometry with Problems and Applications
- root
Taught in: On the Ratio or Proportion of Two Magnitudes
Also in: A Course of Pure Mathematics, A First Book in Algebra, An Introduction to Mathematics, Calculus Made Easy, First Course in the Theory of Equations, The First Steps in Algebra
- root of an equation
Taught in: Solution of Equations by the Differential Calculus
Also in: A Course of Pure Mathematics, First Course in the Theory of Equations
- sign
Taught in: On the Connexion of the Signs of Algebraical and the Directions of Geometrical Magnitudes
Also in: First Course in the Theory of Equations, The First Steps in Algebra
- similar
Taught in: On the Ratios of Continuously Increasing or Decreasing Quantities
- similarity
Taught in: The Same Problem Solved by the Principles of Leibnitz
Also in: An Introduction to Mathematics, Mathematical Recreations and Essays, Plane Geometry
- simple harmonic motion
Taught in: Simple Harmonic Motion
- sine
Taught in: On the Ratios of Continuously Increasing or Decreasing Quantities, Taylor's Theorem. Derived Functions, Simple Harmonic Motion, Rules for Differentiation, Illustration of the Rules for Differentiation, The Integral Calculus
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy, Elements of Plane Trigonometry, Mathematical Recreations and Essays, Solid Geometry with Problems and Applications, Spherical Trigonometry, for the Use of Colleges and Schools, Vector Analysis and Quaternions
- singular value
Taught in: Infinite Series
Also in: Treatise on Thermodynamics
- slope of a curve
Taught in: The Drawing of a Tangent to a Curve
Also in: An Introduction to Mathematics, Calculus Made Easy, First Course in the Theory of Equations
- specific gravity
Taught in: Method of Indivisibles
Also in: An Introduction to Mathematics
- square root of 2
Taught in: On the Ratio or Proportion of Two Magnitudes
Also in: A Course of Pure Mathematics
- standard of approximation
Taught in: The Notion of Infinitely Small Quantities
Also in: An Introduction to Mathematics
- sum
Taught in: The Integral Calculus, Connexion of the Integral with the Differential Calculus, Method of Indivisibles
Also in: A Course of Pure Mathematics, Calculus Made Easy, Mathematical Recreations and Essays, Vector Analysis and Quaternions
- surface
Taught in: Method of Indivisibles
Also in: A Course of Pure Mathematics, Plane Geometry
- tangent
Taught in: On the Connexion of the Signs of Algebraical and the Directions of Geometrical Magnitudes, The Drawing of a Tangent to a Curve
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy, Elements of Plane Trigonometry, First Course in the Theory of Equations, Mathematical Recreations and Essays, Plane Geometry, Treatise on Thermodynamics
- tangent function
Taught in: The Drawing of a Tangent to a Curve, Rules for Differentiation, The Integral Calculus
Also in: A Course of Pure Mathematics, Calculus Made Easy, Elements of Plane Trigonometry, Mathematical Recreations and Essays, Solid Geometry with Problems and Applications, Spherical Trigonometry, for the Use of Colleges and Schools
- tends to infinity
Taught in: On the Ratios of Continuously Increasing or Decreasing Quantities, The Integral Calculus
Also in: A Course of Pure Mathematics
- three-dimensional figure
Taught in: Method of Indivisibles
Also in: Plane Geometry, Solid Geometry with Problems and Applications
- total differential
Taught in: Partial and Total Differentials, Total and Partial Differential Coefficients. Implicit Differentiation
Also in: Calculus Made Easy
- uniform motion
Taught in: An Illustration from Dynamics: Velocity, Acceleration, etc, Simple Harmonic Motion, Accelerated Motion
Also in: Mathematical Recreations and Essays
- uniformly accelerated motion
Taught in: Accelerated Motion
- variable
Taught in: On Functions, Recapitulation of Results Reached in the Theory of Functions, Total and Partial Differential Coefficients. Implicit Differentiation, Implicit Functions, Fluxions, and the Idea of Time, The Differential Coefficient Considered with Respect to its Magnitude, The Integral Calculus, Determination of Curvilinear Areas. The Parabola
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy, Elements of Plane Trigonometry, Plane Geometry, Solid Geometry with Problems and Applications, The First Steps in Algebra
- vertex of a conic section
Taught in: Determination of Curvilinear Areas. The Parabola
Also in: An Introduction to Mathematics
- weight
Taught in: Method of Indivisibles
Also in: Mathematical Recreations and Essays
Theorems (21)
- area of a parabolic segment
- binomial theorem
Taught in: Taylor's Theorem. Derived Functions
Also in: A Course of Pure Mathematics, A First Book in Algebra, Calculus Made Easy, First Course in the Theory of Equations, Vector Analysis and Quaternions
- Chain rule
Taught in: Applications of the Theorem for Implicit Differentiation
Also in: A Course of Pure Mathematics
- cosine addition formula
Taught in: Simple Harmonic Motion
- equal order from a finite limiting ratio
Taught in: Orders of Infinity
- expansion of a function by increments
Taught in: Recapitulation of Results Reached in the Theory of Functions
- fundamental theorem of calculus
Taught in: Connexion of the Integral with the Differential Calculus
Also in: A Course of Pure Mathematics
- infinitesimal arc coincides with its chord
- necessary condition for convergence
Taught in: Convergent and Divergent Series
Also in: A Course of Pure Mathematics
- power rule
Taught in: Rules for Differentiation
- product rule
Taught in: Applications of the Theorem for Implicit Differentiation
- propagation of small errors
Taught in: Approximations by the Differential Calculus
- pythagorean theorem
Taught in: On the Connexion of the Signs of Algebraical and the Directions of Geometrical Magnitudes
Also in: Calculus Made Easy, Plane Geometry
- quotient rule
Taught in: Applications of the Theorem for Implicit Differentiation
- ratio of series of the same order
Taught in: Orders of Infinity
- ratio test
Taught in: Convergent and Divergent Series
- ratio test for convergence
Taught in: Convergent and Divergent Series
- sine addition formula
Taught in: Simple Harmonic Motion
- sum of the first x natural numbers
- Taylor's theorem
Taught in: Infinite Series, Taylor's Theorem. Derived Functions, Calculus of Finite Differences. Successive Differentiation, Connexion of the Integral with the Differential Calculus
Also in: A Course of Pure Mathematics, First Course in the Theory of Equations, Treatise on Thermodynamics
- total differential
Taught in: Application of the Theorem for Total Differentials to the Determination of Total Resultant Errors, Applications of the Theorem for Implicit Differentiation
Also in: A Course of Pure Mathematics
Methods (15)
- comparison of series
Taught in: Convergent and Divergent Series
- composition of proportions
Taught in: The Same Problem Solved by the Principles of Leibnitz
Also in: Plane Geometry
- differentiating from first principles
Taught in: Differential Coefficients, Fluxions, and the Idea of Time
Also in: Calculus Made Easy
- differentiation
Taught in: Rules for Differentiation, Illustration of the Rules for Differentiation, Differential Coefficients of Differential Coefficients, Inverse Functions, The Integral Calculus, Connexion of the Integral with the Differential Calculus, Nature of Integration, Determination of Curvilinear Areas. The Parabola
Also in: A Course of Pure Mathematics, Calculus Made Easy, First Course in the Theory of Equations, Mathematical Recreations and Essays
- dividing numerator and denominator by the highest power
Taught in: Limiting Ratios of Magnitudes that Increase Without Limit
- finding a limit by rejecting negligible terms
Taught in: Limiting Ratios of Magnitudes that Increase Without Limit
- implicit differentiation
Taught in: Total and Partial Differential Coefficients. Implicit Differentiation, Implicit Functions
Also in: A Course of Pure Mathematics
- integration
Taught in: The Integral Calculus, Connexion of the Integral with the Differential Calculus, Nature of Integration, Determination of Curvilinear Areas. The Parabola, Method of Indivisibles, Concluding Remarks on the Study of the Calculus
- linear approximation
Taught in: Approximations by the Differential Calculus
- method of indivisibles
Taught in: Method of Indivisibles
- neglecting higher-order small quantities
Taught in: The Notion of Infinitely Small Quantities, Differential Coefficients
Also in: Calculus Made Easy, Spherical Trigonometry, for the Use of Colleges and Schools
- Newton's method
Taught in: Solution of Equations by the Differential Calculus
Also in: A Course of Pure Mathematics, First Course in the Theory of Equations
- solving an equation
Taught in: Implicit Functions
Also in: A First Book in Algebra, The First Steps in Algebra
- substitution
Taught in: On the Connexion of the Signs of Algebraical and the Directions of Geometrical Magnitudes
Also in: A Course of Pure Mathematics, A First Book in Algebra, Calculus Made Easy, The First Steps in Algebra
- verification
Taught in: Taylor's Theorem. Derived Functions
Also in: Spherical Trigonometry, for the Use of Colleges and Schools, The First Steps in Algebra
Quantities (14)
- acceleration
Taught in: An Illustration from Dynamics: Velocity, Acceleration, etc, Accelerated Motion
- angle
Taught in: Simple Harmonic Motion, Illustration of the Rules for Differentiation
Also in: An Introduction to Mathematics, Calculus Made Easy, Elements of Plane Trigonometry, Mathematical Recreations and Essays, Plane Geometry, Solid Geometry with Problems and Applications, Vector Analysis and Quaternions
- angular velocity
Taught in: Simple Harmonic Motion
- arc of a circle
Taught in: On the Ratios of Continuously Increasing or Decreasing Quantities
Also in: Elements of Plane Trigonometry
- circumference
Taught in: Nature of Integration
Also in: An Introduction to Mathematics, Elements of Plane Trigonometry, Mathematical Recreations and Essays, Plane Geometry, Solid Geometry with Problems and Applications
- density
Taught in: Method of Indivisibles
Also in: Mathematical Recreations and Essays, Treatise on Thermodynamics
- distance
Taught in: Fluxions, and the Idea of Time
Also in: An Introduction to Mathematics, Calculus Made Easy, Elements of Plane Trigonometry, Plane Geometry
- force
Taught in: Accelerated Motion, The Differential Coefficient Considered with Respect to its Magnitude
Also in: An Elementary Treatise on Electricity, An Introduction to Mathematics, Calculus Made Easy, Mathematical Recreations and Essays, Spherical Trigonometry, for the Use of Colleges and Schools, Vector Analysis and Quaternions
- length
Taught in: Accelerated Motion, The Differential Coefficient Considered with Respect to its Magnitude
Also in: An Introduction to Mathematics, Vector Analysis and Quaternions
- magnitude
Taught in: On the Ratio or Proportion of Two Magnitudes, On the Ratio of Magnitudes that Vanish Together
- radius
Taught in: The Same Problem Solved by the Principles of Leibnitz, Simple Harmonic Motion, Illustration of the Rules for Differentiation
Also in: An Introduction to Mathematics, Elements of Plane Trigonometry, Plane Geometry, Solid Geometry with Problems and Applications, Spherical Trigonometry, for the Use of Colleges and Schools
- solar longitude
Taught in: Approximations by the Differential Calculus
- time
Taught in: Accelerated Motion, Fluxions, and the Idea of Time
Also in: An Introduction to Mathematics, Calculus Made Easy, Mathematical Recreations and Essays, The First Steps in Algebra
- velocity
Taught in: An Illustration from Dynamics: Velocity, Acceleration, etc, Simple Harmonic Motion, The Method of Fluxions, Accelerated Motion, Fluxions, and the Idea of Time, The Differential Coefficient Considered with Respect to its Magnitude
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy, Mathematical Recreations and Essays, Vector Analysis and Quaternions
Units (3)
- degree of angle
Taught in: On the Ratios of Continuously Increasing or Decreasing Quantities
Also in: Calculus Made Easy, Elements of Plane Trigonometry, Plane Geometry, Spherical Trigonometry, for the Use of Colleges and Schools
- minute of arc
Taught in: On the Ratios of Continuously Increasing or Decreasing Quantities
Also in: Elements of Plane Trigonometry
- unit
Taught in: On the Ratio or Proportion of Two Magnitudes, Illustration of the Rules for Differentiation
Also in: An Introduction to Mathematics, Plane Geometry, The First Steps in Algebra
Instruments (1)
- transit instrument
Taught in: Application of the Theorem for Total Differentials to the Determination of Total Resultant Errors
Also in: An Introduction to Mathematics
People (4)
- Archimedes
Taught in: Determination of Curvilinear Areas. The Parabola
Also in: Elements of Plane Trigonometry, Mathematical Recreations and Essays
- Gottfried Wilhelm Leibniz
Taught in: The Notion of Infinitely Small Quantities, Orders of Infinity, The Same Problem Solved by the Principles of Leibnitz, Simple Harmonic Motion, The Method of Fluxions, Nature of Integration, Method of Indivisibles
- Isaac Newton
Taught in: The Notion of Infinitely Small Quantities, The Method of Fluxions, Fluxions, and the Idea of Time
Also in: An Introduction to Mathematics, Calculus Made Easy, Elements of Plane Trigonometry, First Course in the Theory of Equations, Mathematical Recreations and Essays
- Leonhard Euler
Taught in: The Notation of the Differential Calculus
Also in: First Course in the Theory of Equations, Mathematical Recreations and Essays, Spherical Trigonometry, for the Use of Colleges and Schools, Treatise on Thermodynamics