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 2
... produced ever so far both ways , do not meet , these straight lines are called parallels . 13. A plane figure is any portion of a plane surface which is included by a line or lines . The whole circuit of any figure , that is , the ...
... produced ever so far both ways , do not meet , these straight lines are called parallels . 13. A plane figure is any portion of a plane surface which is included by a line or lines . The whole circuit of any figure , that is , the ...
Page 7
... produced , shall bisect the base at right angles . For the straight line which bisects the base at right an- gles passes through the vertex of each . PROP . 7. ( EUc . i . 8. ) If two triangles have two sides of the one equal to two ...
... produced , shall bisect the base at right angles . For the straight line which bisects the base at right an- gles passes through the vertex of each . PROP . 7. ( EUc . i . 8. ) If two triangles have two sides of the one equal to two ...
Page 8
... produced to meet the side A B of the en- veloping triangle in E , BD and DC together will be less than B E and EC ... Produce B A to D , so that A D may be equal to A C , and join C D. Then , because A D is equal to A C , the angle ACD ...
... produced to meet the side A B of the en- veloping triangle in E , BD and DC together will be less than B E and EC ... Produce B A to D , so that A D may be equal to A C , and join C D. Then , because A D is equal to A C , the angle ACD ...
Page 9
... produced to H and K. Then , because DF is equal to DG , the angles H FG , KGF , upon the other side of the base of the isosceles triangle D FG , are equal to In the third case , let D F and D G be D G K one another ( 6. Cor . 2. ) . But ...
... produced to H and K. Then , because DF is equal to DG , the angles H FG , KGF , upon the other side of the base of the isosceles triangle D FG , are equal to In the third case , let D F and D G be D G K one another ( 6. Cor . 2. ) . But ...
Page 11
... produced ever so far both ways , that is ( def . 12. ) A B is parallel to CD . In the next place , let A B be parallel to CD , and from any point E of A Blet EF be drawn at right angles to CD : EF shall also be at right angles to AB ...
... produced ever so far both ways , that is ( def . 12. ) A B is parallel to CD . In the next place , let A B be parallel to CD , and from any point E of A Blet EF be drawn at right angles to CD : EF shall also be at right angles to AB ...
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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