An elementary course of mathematics, Volum 2 |
Inni boken
Resultat 1-5 av 47
Side 1
... angles to the line AB . Straight lines which meet a plane and are not perpendicular to it are called oblique . 4. The inclination of a straight line to a plane , is the acute angle contained by that straight line , and another drawn ...
... angles to the line AB . Straight lines which meet a plane and are not perpendicular to it are called oblique . 4. The inclination of a straight line to a plane , is the acute angle contained by that straight line , and another drawn ...
Side 2
... inclination of a plane to a plane is the acute angle con- tained by two straight lines drawn from any , the same point in the line of intersection of the planes , at right angles to it , one upon one plane , and the other upon the other ...
... inclination of a plane to a plane is the acute angle con- tained by two straight lines drawn from any , the same point in the line of intersection of the planes , at right angles to it , one upon one plane , and the other upon the other ...
Side 11
... angles CBA , DBA , and the angles CBA , DBA are right angles , AC is equal AD ( I. 4 ) ... angle with the line joining the intersections than with any other line ... inclination of the straight line AB to the plane MN . PROP . XVI . THEOR ...
... angles CBA , DBA , and the angles CBA , DBA are right angles , AC is equal AD ( I. 4 ) ... angle with the line joining the intersections than with any other line ... inclination of the straight line AB to the plane MN . PROP . XVI . THEOR ...
Side 21
... inclination to each other is everywhere the same ; that is from whatever point in the common intersection of two planes , straight lines be drawn perpendicular to it , one in each plane , the angle contained by these lines will be the ...
... inclination to each other is everywhere the same ; that is from whatever point in the common intersection of two planes , straight lines be drawn perpendicular to it , one in each plane , the angle contained by these lines will be the ...
Side 22
... angles formed by faces or planes whose angles of inclination to each other are the same , are equal to one another : and conversely , if two dihedral angles are equal , the angles of inclination of their faces are equal . Let MABN ...
... angles formed by faces or planes whose angles of inclination to each other are the same , are equal to one another : and conversely , if two dihedral angles are equal , the angles of inclination of their faces are equal . Let MABN ...
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ABCD allel altitude angle formed angle of inclination auxiliary plane circle described circumference circumscribed coincide cone consequently construction Descriptive Geometry determined diameter dicular dihedral angle contained distance ellipse equal and similar equal bases equilateral polygon faces ASB figure given angle given plane given point given straight line greater hemisphere horizontal plane horizontal projection horizontal trace inscribed isometric line joining line of level line parallel meets the plane parallel planes parallel to xy parallelepiped parallelogram pendicular perimeter perpen perpendicular to xy plane angles plane MN plane passing plane Prop planes BM planes of projection point of intersection prism Prob PROBLEM projecting plane pyramid rectangle right angles right-angled triangle scale of slope series of cylinders sides solid angle space straight line drawn THEOR third face trihedral vertical plane vertical projection vertical trace Wherefore
Populære avsnitt
Side 5 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Side 18 - FD. Join AC, BD, AD, and let AD meet the plane KL in the point X; and join EX, XF. Because the two parallel planes KL, MN are cut by the plane EBDX, the common sections EX, BD are parallel (Prop.
Side 13 - For the same reason, CD is likewise at right angles to the plane HGK. Therefore AB, CD are each of them at right angles to the plane HGK.
Side 4 - BC above it : and since the straight line AB is in the plane, it can be produced in that plane : let it be produced to D ; and let any plane pass through the straight line AD, and be turned about it until it pass through the point C; and because the points B, C, are in this plane, the straight line* BC is in it: »7Def.1.
Side 9 - Note. (3. 11.) line; let this be BF: therefore the three straight lines AB, BC, BF are all in one plane, viz. that which passes through AB, BC : and because AB stands at right angles to each of the straight lines BD, BE, it is also at right angles (4. 1 1.) to the plane passing through them; and therefore makes right angles (3.
Side 16 - BGH are together equal* to two right angles: and BGH is a right angle; therefore also GBA is a right angle, and GB perpendicular to BA. For the same reason GB is perpendicular to BC. Since therefore the straight line GB stands at right angles to the two straight lines BA, BC, that cut one another in B, GB is perpendicular...
Side 9 - If three straight lines meet all in one point, and a straight line stand at right angles to each of them in that point ; these three straight lines are in one and the same plane. Let the straight line AB stand at right angles to each of the straight lines BC, BD, BE, in B, the point where they meet ; BC, BD, BE are in one and the same plane. If not, let...
Side 1 - A plane is perpendicular to a plane, when the straight lines drawn in one of the planes perpendicular to the common section of the two planes, are perpendicular to the other plane. 5. The inclination of a straight line to a plane...
Side 28 - Cor. 1.) therefore all the angles of the triangles are equal to all the angles of the polygon together with four right angles : (i. ax. 1.) but all the angles at the bases of the triangles are greater than all the angles of the polygon, as has been proved ; wherefore the remaining angles of the triangles, viz. those of the vertex, which contain the solid angle at A, are less than four right angles.
Side 5 - If a straight line stand at right angles to each of two straight lines in the point of their intersection, it will also be at right angles to the plane in which these lines are.