New Elementary Geometry: With Practical Applications ; a Shorter Course Upon the Basis of the Larger Work |
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Page 17
... intersection D. Hence the two triangles ABC , DEF coincide with each other , and are therefore equal ( 26 , Ax . 12 ) . 45. Cor . When , in two triangles , these three parts are equal , namely , the angle B equal to the angle E , the ...
... intersection D. Hence the two triangles ABC , DEF coincide with each other , and are therefore equal ( 26 , Ax . 12 ) . 45. Cor . When , in two triangles , these three parts are equal , namely , the angle B equal to the angle E , the ...
Page 25
... intersection of the two straight lines IK , GH , are equal ( Theo . III . ) ; and the triangles KOG , IOH have the two sides KO , OG and the included angle in the one equal to the two sides IO , O H and the included angle in the other ...
... intersection of the two straight lines IK , GH , are equal ( Theo . III . ) ; and the triangles KOG , IOH have the two sides KO , OG and the included angle in the one equal to the two sides IO , O H and the included angle in the other ...
Page 57
... intersection of two chords is measured by half the sum of the two intercepted arcs . Let the two chords AB , CD inter- sect each other at the point E ; then will the angle DEB , or its equal , A E C , be measured by half the sum of the ...
... intersection of two chords is measured by half the sum of the two intercepted arcs . Let the two chords AB , CD inter- sect each other at the point E ; then will the angle DEB , or its equal , A E C , be measured by half the sum of the ...
Page 67
... intersection . C A B A C D D B 7. At a point in a given straight line to make an angle equal to half a right angle . 8. To describe a square whose side shall be equal to a given straight line . BOOK IV . AREAS AND RELATIONS OF PLANE ...
... intersection . C A B A C D D B 7. At a point in a given straight line to make an angle equal to half a right angle . 8. To describe a square whose side shall be equal to a given straight line . BOOK IV . AREAS AND RELATIONS OF PLANE ...
Page 110
... intersection of two planes , and is measured by the inclination of two straight lines drawn from any point in the line of intersection , perpendicular to that line , one being drawn in each plane . A B M N The line of common section ...
... intersection of two planes , and is measured by the inclination of two straight lines drawn from any point in the line of intersection , perpendicular to that line , one being drawn in each plane . A B M N The line of common section ...
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Common terms and phrases
A B C A B equal ABCD ABCDEF adjacent angles allel alternate angles altitude angle ACD angle BAC antecedent base multiplied bases ABC bisect chord circumference cone consequently convex surface cylinder diagonal diameter divided draw the straight equal and parallel equal angles equal bases equal Theo equiangular equivalent feet formed four right angles frustum given straight line greater Greenleaf's half the sum homologous sides hypothenuse included angle inscribed angle inscribed circle interior angles intersection Let ABC line CD magnitudes mean proportional measured by half meet number of sides opposite parallelogram parallelopipedon perimeter perpendicular polyedron prism quadrilateral radii radius ratio rectangle regular polygon rhombus right angles Theo Scholium secant line side A B side BC slant hight Solid sphere square described tangent THEOREM third triangles ABC triangular triangular prism vertex volume
Popular passages
Page 23 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 29 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 83 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing these angles proportional, are similar.
Page 85 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Page 61 - At a point in a given straight line to make an angle equal to a given angle.
Page 57 - The angle formed by a tangent and a chord is measured by half the intercepted arc.
Page 62 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Page 117 - If two angles not in the same plane have their sides parallel and lying in the same direction, these angles will be equal, and their planes will be parallel. Let...
Page 100 - The circumferences of circles are to each other as their radii, and their areas are to each other as the squares of their radii. Let C denote the circumference of one of ^ the circles, R its radius OA, A its area; and let C...
Page 88 - Similar polygons may be divided into the same number of triangles similar each to each, and similarly situated.