Solid Geometry with Problems and Applications

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 (142)

altitude of a cylinder
Taught in: Prisms and Cylinders
altitude of a prism
Taught in: Prisms and Cylinders
altitude of a pyramid
Taught in: Pyramids and Cones
angle between line and plane
Taught in: Properties of the Plane, PROJECTION OF LINE-SEGMENTS
approximating sequence of polygons
Taught in: VARIABLES. LIMITS
axis of a circle on a sphere
Taught in: The Sphere
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
axis of a cylinder
Taught in: Prisms and Cylinders
base of a cylinder
Taught in: Prisms and Cylinders
base of a prism
Taught in: Prisms and Cylinders
base of a pyramid
Taught in: Pyramids and Cones
birectangular spherical triangle
Taught in: The Sphere
bisector of a dihedral angle
Taught in: Properties of the Plane
center of similitude
Taught in: SIMILAR SOLIDS
circle
Taught in: The Sphere
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Elementary Illustrations of the Differential and Integral Calculus, First Course in the Theory of Equations, Mathematical Recreations and Essays, Plane Geometry, Spherical Trigonometry, for the Use of Colleges and Schools
circular cylinder
Taught in: Prisms and Cylinders
Also in: An Introduction to Mathematics
circumscribed polyhedron
Taught in: The Sphere
circumscribed prism
Taught in: Prisms and Cylinders, Pyramids and Cones, VARIABLES. LIMITS
circumscribed pyramid
Taught in: Pyramids and Cones
closed plane curve
Taught in: Prisms and Cylinders
collinear points
Taught in: Properties of the Plane
Also in: A Course of Pure Mathematics
cone
Taught in: Pyramids and Cones
Also in: A Course of Pure Mathematics, An Introduction to Mathematics
conical surface
Taught in: Pyramids and Cones
constant
Taught in: VARIABLES. LIMITS
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy, Elementary Illustrations of the Differential and Integral Calculus, Elements of Plane Trigonometry, Plane Geometry
convex plane curve
Taught in: Prisms and Cylinders, VARIABLES. LIMITS
convex polyhedron
Taught in: Regular Polyhedrons
corresponding linear dimensions
Taught in: SIMILAR SOLIDS
Also in: Mathematical Recreations and Essays
corresponding parts
Taught in: SIMILAR SOLIDS
cosine
Taught in: PROJECTION OF LINE-SEGMENTS
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy, Elementary Illustrations of the Differential and Integral Calculus, Elements of Plane Trigonometry, Spherical Trigonometry, for the Use of Colleges and Schools, Vector Analysis and Quaternions
cross-section
Taught in: Prisms and Cylinders
Also in: Mathematical Recreations and Essays
cube
Taught in: Prisms and Cylinders
Also in: A First Book in Algebra, Mathematical Recreations and Essays, The First Steps in Algebra
curved surface
Taught in: Prisms and Cylinders
Also in: Plane Geometry
cylinder
Taught in: Prisms and Cylinders
Also in: A Course of Pure Mathematics
cylindrical surface
Taught in: Prisms and Cylinders
Also in: A Course of Pure Mathematics
determination of a plane
Taught in: Properties of the Plane
diameter
Taught in: The Sphere
Also in: Plane Geometry, Spherical Trigonometry, for the Use of Colleges and Schools
dihedral angle
Taught in: Properties of the Plane
distance from a point to a plane
Taught in: Properties of the Plane
dodecahedron
Taught in: Regular Polyhedrons
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
edge
Taught in: Regular Polyhedrons
Also in: Mathematical Recreations and Essays, Spherical Trigonometry, for the Use of Colleges and Schools
element of a cylinder
Taught in: Prisms and Cylinders, VARIABLES. LIMITS
element of a surface
Taught in: Pyramids and Cones
ellipse
Taught in: PROJECTION OF LINE-SEGMENTS
Also in: A Course of Pure Mathematics, An Introduction to Mathematics
equivalent solids
Taught in: Prisms and Cylinders
Also in: Plane Geometry
face
Taught in: Regular Polyhedrons
Also in: Mathematical Recreations and Essays, Spherical Trigonometry, for the Use of Colleges and Schools
face angle
Taught in: Properties of the Plane
foot of a line
Taught in: Properties of the Plane
Also in: Plane Geometry
frustum of a cone
Taught in: Pyramids and Cones
frustum of a pyramid
Taught in: Pyramids and Cones
Also in: Calculus Made Easy
function
Taught in: VARIABLES. LIMITS
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy, Elementary Illustrations of the Differential and Integral Calculus, Elements of Plane Trigonometry
generator
Taught in: Prisms and Cylinders, Pyramids and Cones
great circle
Taught in: The Sphere
Also in: Mathematical Recreations and Essays, Spherical Trigonometry, for the Use of Colleges and Schools
half-plane
Taught in: Properties of the Plane
hemisphere
Taught in: VARIABLES. LIMITS
hexahedron
Taught in: Regular Polyhedrons
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
icosahedron
Taught in: Regular Polyhedrons
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
incommensurable magnitudes
Taught in: VARIABLES. LIMITS
Also in: An Introduction to Mathematics, Elementary Illustrations of the Differential and Integral Calculus, Mathematical Recreations and Essays, Plane Geometry
infinite sequence
Taught in: VARIABLES. LIMITS
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Elementary Illustrations of the Differential and Integral Calculus
inscribed prism
Taught in: Prisms and Cylinders, Pyramids and Cones, VARIABLES. LIMITS
inscribed pyramid
Taught in: Pyramids and Cones
irrational number
Taught in: VARIABLES. LIMITS
Also in: A Course of Pure Mathematics
isosceles spherical triangle
Taught in: The Sphere
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
lateral surface
Taught in: Prisms and Cylinders, Pyramids and Cones
least upper bound
Taught in: VARIABLES. LIMITS
Also in: A Course of Pure Mathematics
limit
Taught in: VARIABLES. LIMITS
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy, Elementary Illustrations of the Differential and Integral Calculus, Elements of Plane Trigonometry, Plane Geometry
line
Taught in: Properties of the Plane
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy, Elementary Illustrations of the Differential and Integral Calculus, Plane Geometry
line parallel to a plane
Taught in: Properties of the Plane
locus
Taught in: INTRODUCTION, Properties of the Plane
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Plane Geometry, Spherical Trigonometry, for the Use of Colleges and Schools
lune
Taught in: The Sphere
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
mutually perpendicular planes
Taught in: Properties of the Plane
nappe
Taught in: Pyramids and Cones
oblique cylinder
Taught in: Prisms and Cylinders
oblique line
Taught in: Properties of the Plane
oblique prism
Taught in: PROJECTION OF LINE-SEGMENTS
octahedron
Taught in: Regular Polyhedrons
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
one-dimensional figure
Taught in: INTRODUCTION
order of parts
Taught in: Properties of the Plane
parallel lines
Taught in: INTRODUCTION, Properties of the Plane
Also in: An Introduction to Mathematics, Plane Geometry
parallel planes
Taught in: Properties of the Plane
parallelepiped
Taught in: Prisms and Cylinders
Also in: Spherical Trigonometry, for the Use of Colleges and Schools, Vector Analysis and Quaternions
perimeter
Taught in: VARIABLES. LIMITS
Also in: A Course of Pure Mathematics, Elementary Illustrations of the Differential and Integral Calculus, Plane Geometry
perpendicular
Taught in: INTRODUCTION, Properties of the Plane, The Sphere
Also in: Elementary Illustrations of the Differential and Integral Calculus, Plane Geometry, Spherical Trigonometry, for the Use of Colleges and Schools
plane
Taught in: INTRODUCTION, Properties of the Plane
Also in: A Course of Pure Mathematics, Plane Geometry, Vector Analysis and Quaternions
plane angle
Taught in: Properties of the Plane
Also in: Plane Geometry, Spherical Trigonometry, for the Use of Colleges and Schools
point
Taught in: INTRODUCTION, Properties of the Plane
Also in: A Course of Pure Mathematics, Elementary Illustrations of the Differential and Integral Calculus, Plane Geometry
polar distance of a circle
Taught in: The Sphere
polar triangle
Taught in: The Sphere
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
pole of a circle
Taught in: The Sphere
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
polyhedral angle
Taught in: Properties of the Plane, The Sphere
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
polyhedron
Taught in: Regular Polyhedrons
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
polyhedron inscribed in a sphere
Taught in: The Sphere
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
prism
Taught in: Prisms and Cylinders
prismatic surface
Taught in: Prisms and Cylinders
projection
Taught in: Properties of the Plane
Also in: Elements of Plane Trigonometry, Treatise on Thermodynamics, Vector Analysis and Quaternions
projection of a line
Taught in: Properties of the Plane, PROJECTION OF LINE-SEGMENTS
Also in: Elements of Plane Trigonometry
pyramid
Taught in: Pyramids and Cones
pyramidal surface
Taught in: Pyramids and Cones
quadrant
Taught in: The Sphere
Also in: An Introduction to Mathematics, Plane Geometry, Spherical Trigonometry, for the Use of Colleges and Schools, Vector Analysis and Quaternions
ratio of similitude
Taught in: SIMILAR SOLIDS
rational number
Taught in: VARIABLES. LIMITS
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Mathematical Recreations and Essays
rectangular parallelepiped
Taught in: Prisms and Cylinders, VARIABLES. LIMITS
regular polyhedron
Taught in: Regular Polyhedrons
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
regular prism
Taught in: Prisms and Cylinders
regular pyramid
Taught in: Pyramids and Cones
right circular cone
Taught in: Pyramids and Cones
Also in: A Course of Pure Mathematics
right circular cylinder
Taught in: Prisms and Cylinders
Also in: First Course in the Theory of Equations
right cylinder
Taught in: Prisms and Cylinders
right dihedral angle
Taught in: Properties of the Plane
right prism
Taught in: Prisms and Cylinders
right section
Taught in: Prisms and Cylinders, PROJECTION OF LINE-SEGMENTS, VARIABLES. LIMITS
right spherical triangle
Taught in: The Sphere
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
right triangle
Taught in: PROJECTION OF LINE-SEGMENTS
Also in: A Course of Pure Mathematics, Elementary Illustrations of the Differential and Integral Calculus, Plane Geometry
similar cones
Taught in: SIMILAR SOLIDS
similar cylinders
Taught in: SIMILAR SOLIDS
similar polyhedron
Taught in: SIMILAR SOLIDS
similar solids
Taught in: SIMILAR SOLIDS
Also in: Plane Geometry
sine
Taught in: PROJECTION OF LINE-SEGMENTS
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy, Elementary Illustrations of the Differential and Integral Calculus, Elements of Plane Trigonometry, Mathematical Recreations and Essays, Spherical Trigonometry, for the Use of Colleges and Schools, Vector Analysis and Quaternions
skew lines
Taught in: INTRODUCTION, Properties of the Plane
slant height
Taught in: Pyramids and Cones
small circle
Taught in: The Sphere
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
solid geometry
Taught in: INTRODUCTION
Also in: An Introduction to Mathematics, Plane Geometry
sphere
Taught in: INTRODUCTION, The Sphere
Also in: A Course of Pure Mathematics, An Elementary Treatise on Electricity, Mathematical Recreations and Essays, Spherical Trigonometry, for the Use of Colleges and Schools
sphere inscribed in a polyhedron
Taught in: The Sphere
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
spherical angle
Taught in: The Sphere
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
spherical cone
Taught in: The Sphere
spherical distance
Taught in: The Sphere
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
spherical polygon
Taught in: The Sphere
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
spherical sector
Taught in: The Sphere
spherical segment
Taught in: The Sphere
spherical triangle
Taught in: The Sphere
Also in: Spherical Trigonometry, for the Use of Colleges and Schools, Vector Analysis and Quaternions
spherical zone
Taught in: The Sphere
surface of a polyhedron
Taught in: Regular Polyhedrons
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
tangent function
Taught in: PROJECTION OF LINE-SEGMENTS
Also in: A Course of Pure Mathematics, Calculus Made Easy, Elementary Illustrations of the Differential and Integral Calculus, Elements of Plane Trigonometry, Mathematical Recreations and Essays, Spherical Trigonometry, for the Use of Colleges and Schools
tangent plane to a cylinder
Taught in: Prisms and Cylinders
tangent plane to a sphere
Taught in: The Sphere
tetrahedron
Taught in: Regular Polyhedrons, Pyramids and Cones, The Sphere
Also in: Spherical Trigonometry, for the Use of Colleges and Schools, Vector Analysis and Quaternions
three-dimensional figure
Taught in: INTRODUCTION
Also in: Elementary Illustrations of the Differential and Integral Calculus, Plane Geometry
trihedral angle
Taught in: Properties of the Plane
truncated prism
Taught in: Prisms and Cylinders
truncated pyramid
Taught in: Pyramids and Cones
two-dimensional figure
Taught in: INTRODUCTION
Also in: Plane Geometry
variable
Taught in: VARIABLES. LIMITS
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy, Elementary Illustrations of the Differential and Integral Calculus, Elements of Plane Trigonometry, Plane Geometry, The First Steps in Algebra
vertex
Taught in: Regular Polyhedrons, Pyramids and Cones
Also in: Spherical Trigonometry, for the Use of Colleges and Schools

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Theorems (107)

acute angle with projection is the least angle with lines in the plane
Taught in: Properties of the Plane
altitude of an oblique prism or cylinder
Taught in: PROJECTION OF LINE-SEGMENTS
angle and corresponding arc of polar triangle sum to 180 degrees
Taught in: The Sphere
angles opposite equal sides of a spherical triangle are equal
Taught in: The Sphere
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
angles whose sides are parallel are equal
Taught in: Properties of the Plane
area and volume ratios of similar solids
Taught in: SIMILAR SOLIDS
area of a circle
Taught in: INTRODUCTION
Also in: Calculus Made Easy, Plane Geometry
area of a rectangle
Taught in: VARIABLES. LIMITS
Also in: Plane Geometry
area of a sphere
Taught in: The Sphere, VARIABLES. LIMITS
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
area of a spherical polygon
Taught in: The Sphere
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
area of a spherical triangle
Taught in: The Sphere
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
area of a spherical zone
Taught in: The Sphere
area of an ellipse
Taught in: PROJECTION OF LINE-SEGMENTS
Also in: A Course of Pure Mathematics
area of the projection of a plane-segment
Taught in: PROJECTION OF LINE-SEGMENTS
areas of parallel cross-sections of a cone are proportional to the squares of their distances from the vertex
Taught in: Pyramids and Cones
assumption on the area of a sphere
Taught in: The Sphere
bases of a cylinder are equal
Taught in: Prisms and Cylinders
bounded monotone sequence has a limit
Taught in: VARIABLES. LIMITS
circumferences and areas of circles vary as radii and squares of radii
Taught in: VARIABLES. LIMITS
construction postulates
Taught in: Properties of the Plane
cross-sections of a prism made by parallel planes are equal
Taught in: Prisms and Cylinders
determination of a plane by a line and point, two intersecting lines, or two parallel lines
Taught in: Properties of the Plane
dihedral angle of an oblique prism
Taught in: PROJECTION OF LINE-SEGMENTS
dihedral angles equal when plane angles are equal
Taught in: Properties of the Plane
equal circles on a sphere have equidistant planes
Taught in: The Sphere
equal cross-sections imply equal volumes
Taught in: VARIABLES. LIMITS
equal face angles give equal opposite dihedral angles
Taught in: Properties of the Plane
figures with a center of similitude are similar
Taught in: SIMILAR SOLIDS
intersecting planes meet in a straight line
Taught in: Properties of the Plane
intersection of two spherical surfaces is a circle
Taught in: The Sphere
lateral area formula for a cylinder
Taught in: Prisms and Cylinders, VARIABLES. LIMITS
lateral area formula for a prism
Taught in: Prisms and Cylinders
lateral area of a frustum of a cone
Taught in: Pyramids and Cones
lateral area of a regular pyramid
Taught in: Pyramids and Cones
lateral area of a right circular cone
Taught in: Pyramids and Cones
limits of equal variables are equal
Taught in: VARIABLES. LIMITS
Also in: Elements of Plane Trigonometry
line perpendicular to two intersecting lines is perpendicular to their plane
Taught in: Properties of the Plane
line through two points of a plane lies in the plane
Taught in: Properties of the Plane
lines perpendicular to the same plane are parallel
Taught in: Properties of the Plane
locus of points equidistant from the faces of a dihedral angle
Taught in: Properties of the Plane
longitudinal section of a cylinder is a parallelogram
Taught in: Prisms and Cylinders
mutually bounded decreasing sequences have the same limit
Taught in: VARIABLES. LIMITS
mutually bounded increasing sequences have the same limit
Taught in: VARIABLES. LIMITS
oblique lines at equal distances from the foot are equal
Taught in: Properties of the Plane
opposite faces of a parallelepiped are equal and parallel
Taught in: Prisms and Cylinders
parallel planes intercept equal segments on every transversal
Taught in: Properties of the Plane
parallel planes intercept proportional segments
Taught in: Properties of the Plane
parallel postulate
Taught in: INTRODUCTION
Also in: Mathematical Recreations and Essays
perpendicular from one of two perpendicular planes to their intersection is perpendicular to the other
Taught in: Properties of the Plane
perpendicular is the shortest distance from a point to a plane
Taught in: Properties of the Plane
plane containing a perpendicular line is perpendicular to the plane
Taught in: Properties of the Plane
plane determined by a line and point, two intersecting lines, or two parallel lines
Taught in: Properties of the Plane
plane parallel to two intersecting lines is parallel to their plane
Taught in: Properties of the Plane
plane perpendicular to two planes is perpendicular to their intersection
Taught in: Properties of the Plane
plane section of a sphere is a circle
Taught in: The Sphere
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
planes perpendicular to the same line are parallel
Taught in: Properties of the Plane
points of a circle on a sphere are equidistant from its pole
Taught in: The Sphere
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
polar triangle relation is symmetric
Taught in: The Sphere
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
polyhedral angle has at least three face angles
Taught in: Regular Polyhedrons
projection of a line is a straight line
Taught in: Properties of the Plane
pyramids with equal altitudes and equal base areas have equal volumes
Taught in: Pyramids and Cones, VARIABLES. LIMITS
ratios of similar cones
Taught in: SIMILAR SOLIDS
ratios of similar cylinders
Taught in: SIMILAR SOLIDS
section of a cone parallel to its base is circular
Taught in: Pyramids and Cones
section of a pyramid parallel to its base
Taught in: Pyramids and Cones
shortest distance on a sphere follows a great circle arc
Taught in: The Sphere
sphere may be circumscribed about a tetrahedron
Taught in: The Sphere
spherical angle measured by arc of great circle
Taught in: The Sphere
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
spherical triangles equal by two angles and included side
Taught in: The Sphere
spherical triangles equal by two sides and included angle
Taught in: The Sphere
sum of angles of a spherical triangle lies between two and six right angles
Taught in: The Sphere
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
sum of face angles of a polyhedral angle is less than 360 degrees
Taught in: Regular Polyhedrons
sum of two sides of a spherical triangle exceeds the third
Taught in: The Sphere
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
symmetrical spherical triangles are equal in area
Taught in: The Sphere
tangent plane perpendicular to radius
Taught in: The Sphere
there are exactly five regular polyhedrons
Taught in: Regular Polyhedrons
three non-collinear points determine a plane
Taught in: Properties of the Plane
through a point not in a plane there is one parallel plane
Taught in: Properties of the Plane
through a point there is one line perpendicular to a plane
Taught in: Properties of the Plane
through a point there is one plane perpendicular to a line
Taught in: Properties of the Plane
through one of two skew lines there is one plane parallel to the other
Taught in: Properties of the Plane
trihedral angles equal by a face angle and two adjacent dihedral angles
Taught in: Properties of the Plane
trihedral angles equal by equal face angles
Taught in: Properties of the Plane
trihedral angles equal by two face angles and included dihedral angle
Taught in: Properties of the Plane
two distinct planes cannot meet in one point only
Taught in: Properties of the Plane
two similar triangles may be placed with a center of similitude
Taught in: SIMILAR SOLIDS
two tetrahedrons are similar if three faces are similar and similarly placed
Taught in: SIMILAR SOLIDS
unequally distant circles on a sphere
Taught in: The Sphere
volume of a cone
Taught in: Pyramids and Cones
volume of a cylinder
Taught in: Prisms and Cylinders, VARIABLES. LIMITS
Also in: Calculus Made Easy
volume of a frustum of a cone
Taught in: Pyramids and Cones
volume of a frustum of a pyramid
Taught in: Pyramids and Cones
volume of a parallelepiped
Taught in: Prisms and Cylinders
Also in: Spherical Trigonometry, for the Use of Colleges and Schools, Vector Analysis and Quaternions
volume of a prism
Taught in: Prisms and Cylinders
volume of a pyramid
Taught in: Pyramids and Cones
volume of a pyramid lies between inscribed and circumscribed prisms
Taught in: Pyramids and Cones
volume of a rectangular parallelepiped
Taught in: Prisms and Cylinders, VARIABLES. LIMITS
volume of a sphere
Taught in: The Sphere, VARIABLES. LIMITS
Also in: Calculus Made Easy
volume of a spherical cone
Taught in: The Sphere
volume of a spherical sector
Taught in: The Sphere
volume of a spherical segment
Taught in: The Sphere
volume of a triangular prism
Taught in: Prisms and Cylinders
volume of an oblique prism
Taught in: Prisms and Cylinders
volumes of similar polyhedrons
Taught in: SIMILAR SOLIDS
volumes of similar solids
Taught in: SIMILAR SOLIDS
volumes of similar tetrahedrons
Taught in: SIMILAR SOLIDS
volumes of tetrahedrons with equal trihedral angles
Taught in: SIMILAR SOLIDS

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Methods (15)

approximating the area and volume of a cylinder by prisms
Taught in: Prisms and Cylinders
approximating the lateral area of a cone by inscribed and circumscribed pyramids
Taught in: Pyramids and Cones
approximating the volume of a cone by inscribed and circumscribed prisms
Taught in: Pyramids and Cones
approximating the volume of a sphere by pyramids
Taught in: The Sphere
constructing a common perpendicular to two skew lines
Taught in: Properties of the Plane
constructing a line perpendicular to a plane
Taught in: Properties of the Plane
constructing a plane parallel to a line
Taught in: Properties of the Plane
constructing a plane perpendicular to a line
Taught in: Properties of the Plane
constructing a regular octahedron
Taught in: Regular Polyhedrons
constructing a regular tetrahedron
Taught in: Regular Polyhedrons
constructing a spherical triangle from its angles
Taught in: The Sphere
constructing a spherical triangle from its sides
Taught in: The Sphere
finding the diameter of a sphere
Taught in: The Sphere
inscribing a sphere in a tetrahedron
Taught in: The Sphere
interpolating in logarithmic tables
Taught in: PROJECTION OF LINE-SEGMENTS
Also in: Elements of Plane Trigonometry, First Course in the Theory of Equations

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Quantities (12)

altitude of a spherical zone
Taught in: The Sphere
angle
Taught in: Properties of the Plane
Also in: An Introduction to Mathematics, Calculus Made Easy, Elementary Illustrations of the Differential and Integral Calculus, Elements of Plane Trigonometry, Mathematical Recreations and Essays, Plane Geometry, Vector Analysis and Quaternions
area
Taught in: Prisms and Cylinders, VARIABLES. LIMITS
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Elements of Plane Trigonometry, Mathematical Recreations and Essays, Plane Geometry
circumference
Taught in: VARIABLES. LIMITS
Also in: An Introduction to Mathematics, Elementary Illustrations of the Differential and Integral Calculus, Elements of Plane Trigonometry, Mathematical Recreations and Essays, Plane Geometry
lateral area
Taught in: Prisms and Cylinders, Pyramids and Cones, VARIABLES. LIMITS
perimeter
Taught in: Prisms and Cylinders
Also in: Plane Geometry
pi
Taught in: Prisms and Cylinders
Also in: A Course of Pure Mathematics, Elements of Plane Trigonometry
radius
Taught in: The Sphere
Also in: An Introduction to Mathematics, Elementary Illustrations of the Differential and Integral Calculus, Elements of Plane Trigonometry, Plane Geometry, Spherical Trigonometry, for the Use of Colleges and Schools
right angle
Taught in: Properties of the Plane
Also in: Elements of Plane Trigonometry
spherical excess
Taught in: The Sphere
Also in: Spherical Trigonometry, for the Use of Colleges and Schools
total area
Taught in: Prisms and Cylinders
volume
Taught in: Prisms and Cylinders, Pyramids and Cones, VARIABLES. LIMITS
Also in: An Introduction to Mathematics, Mathematical Recreations and Essays, Spherical Trigonometry, for the Use of Colleges and Schools, Treatise on Thermodynamics, Vector Analysis and Quaternions

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Units (1)

spherical degree
Taught in: The Sphere

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Instruments (1)

pantograph
Taught in: SIMILAR SOLIDS

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People (2)

Adrien Marie Legendre
Taught in: The Sphere
Also in: Mathematical Recreations and Essays, Spherical Trigonometry, for the Use of Colleges and Schools
Cavalieri
Taught in: The Sphere, VARIABLES. LIMITS

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