Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce Morton] 1830. Elements of trigonometry, by W. Hopkins. 1833. Elements of spherical trigonometry, by A. De Morgan. A treatise on algebraical geometry, by S.W. Waud. 1835Baldwin & Craddock, 1835 - Mathematics |
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Page 119
- " lar faces similarly situated , and forming equal dihedral and. Much as each of the foregoing pro- blems may be varied in appearance by the consideration of internal contact , they admit of being varied yet further by supposing , when ...
- " lar faces similarly situated , and forming equal dihedral and. Much as each of the foregoing pro- blems may be varied in appearance by the consideration of internal contact , they admit of being varied yet further by supposing , when ...
Page 125
... face common to both , unless they coincide altogether . ( See Prop . 1. ) Therefore a straight line cuts a plane in a point ; and a plane cuts a plane in a line , which line ( see Prop . 2. ) is a straight line . said to form at that ...
... face common to both , unless they coincide altogether . ( See Prop . 1. ) Therefore a straight line cuts a plane in a point ; and a plane cuts a plane in a line , which line ( see Prop . 2. ) is a straight line . said to form at that ...
Page 126
lar faces similarly situated , and forming equal dihedral and solid angles . † The Greek word for " seat " being in all cases annexed to the Greek numeral which indicates the number of seats , or faces , on which the figure may be ...
lar faces similarly situated , and forming equal dihedral and solid angles . † The Greek word for " seat " being in all cases annexed to the Greek numeral which indicates the number of seats , or faces , on which the figure may be ...
Page 127
... faces , one of which is a triangle or other rectilineal figure , and the rest triangles which have a common vertex , and for their bases the sides of the first triangle or rectilineal figure . Such a figure may be formed by drawing ...
... faces , one of which is a triangle or other rectilineal figure , and the rest triangles which have a common vertex , and for their bases the sides of the first triangle or rectilineal figure . Such a figure may be formed by drawing ...
Page 138
... faces are equilateral triangles . Again , three an- gles of squares may be taken to form a solid angle ; but four angles of squares are equal to four right angles ( 1. def . 20. ) . ↑ Lastly , three angles of regular pentagons may be ...
... faces are equilateral triangles . Again , three an- gles of squares may be taken to form a solid angle ; but four angles of squares are equal to four right angles ( 1. def . 20. ) . ↑ Lastly , three angles of regular pentagons may be ...
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Common terms and phrases
A B C ABCD adjacent angles altitude apothem base BC bisect centre chord circum circumference circumscribed coincide common measure common section compounded cone conic section contained convex surface cylinder describe a circle diameter dihedral angle divided draw drawn edges equal angles equimultiples ference fore four magnitudes frustum given point given straight line gles harmonical harmonical mean Hence hyperbola hypotenuse inscribed join likewise locus meet parallel parallelogram parallelopiped pass pendicular pentagon perimeter perpendicular plane prism Prob produced PROP proposition pyramid quadrilateral radii radius rallel rectangle rectilineal figure regular polygon respectively right angles Scholium scribed segment sides A B similar solid angles sphere spherical angle square of A B straight lines A B tangent third three sides touch triangle ABC vertex vertical