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 |
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Σελίδα 134
... plane C D E. Therefore , & c . Cor . 1. Through any given point a plane may be drawn , and one only , which shall be parallel to a given plane . For a perpendicular A B may be drawn from the given point A to the given plane F G H ( 7 ...
... plane C D E. Therefore , & c . Cor . 1. Through any given point a plane may be drawn , and one only , which shall be parallel to a given plane . For a perpendicular A B may be drawn from the given point A to the given plane F G H ( 7 ...
Σελίδα 135
... plane BAC shall be pa- rallel to the plane EDF . D F In the straight lines AB , AC take any points B , C : make D E equal to AB and DF equal to AC , and join BC , EF , AD , BE , CF. Then , because the straight lines AB , DE are equal ...
... plane BAC shall be pa- rallel to the plane EDF . D F In the straight lines AB , AC take any points B , C : make D E equal to AB and DF equal to AC , and join BC , EF , AD , BE , CF. Then , because the straight lines AB , DE are equal ...
Σελίδα 136
CBD coincides with the plane GFH . And , because the planes A B C , DBC coincide with the planes E F G , HFG respectively , the dihedral angle ABCD coincides with the dihedral angle EF GH , and is equal to it . Therefore , & c PROP . 17 ...
CBD coincides with the plane GFH . And , because the planes A B C , DBC coincide with the planes E F G , HFG respectively , the dihedral angle ABCD coincides with the dihedral angle EF GH , and is equal to it . Therefore , & c PROP . 17 ...
Σελίδα 137
... plane D B C. From the point B , in the plane DB C , let BD be drawn at right angles to BC . Then , because the planes are at right angles to one ano- ther , the angle ABD is a right angle ( 17. Cor . ) : but ABC is likewise a right ...
... plane D B C. From the point B , in the plane DB C , let BD be drawn at right angles to BC . Then , because the planes are at right angles to one ano- ther , the angle ABD is a right angle ( 17. Cor . ) : but ABC is likewise a right ...
Σελίδα 138
... plane angles , any two of which are ( 19. ) together greater than the third , the pairs of an gles at B , C , D , & c . are together greater than the angles of the figure B CDEF . Therefore , the angles at A are together less than four ...
... plane angles , any two of which are ( 19. ) together greater than the third , the pairs of an gles at B , C , D , & c . are together greater than the angles of the figure B CDEF . Therefore , the angles at A are together less than four ...
Άλλες εκδόσεις - Προβολή όλων
Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ... Πλήρης προβολή - 1835 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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