An elementary course of mathematics, Volum 2 |
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Side iv
... third book . of the Supplement to his Elements of Geometry . I have therefore here followed his method though I have not always adhered to the form of his demonstrations . Little that is original can be expected in any elemen- iv PREFACE .
... third book . of the Supplement to his Elements of Geometry . I have therefore here followed his method though I have not always adhered to the form of his demonstrations . Little that is original can be expected in any elemen- iv PREFACE .
Side 19
... third plane , their common section shall be perpendicular to the same plane . Let two planes AB , BC ( fig . 38 ) be each of them perpendicular to a third plane MN , and let BD be the common section of the first two : BD shall be ...
... third plane , their common section shall be perpendicular to the same plane . Let two planes AB , BC ( fig . 38 ) be each of them perpendicular to a third plane MN , and let BD be the common section of the first two : BD shall be ...
Side 20
... third plane , upon the same side of it , which is impossible ( Prop . 8 ) : therefore , from the point D there cannot be any straight line at right angles to the plane MN , except BD the common section of the planes AB , BC : therefore ...
... third plane , upon the same side of it , which is impossible ( Prop . 8 ) : therefore , from the point D there cannot be any straight line at right angles to the plane MN , except BD the common section of the planes AB , BC : therefore ...
Side 23
... third the angle MAN and the dihedral angle MABN , any equimultiples what- ever have been taken , namely , the angle MAS and the dihedral angle MABS ; and of the second and fourth , the angle PCQ and the dihedral angle PCDQ , any ...
... third the angle MAN and the dihedral angle MABN , any equimultiples what- ever have been taken , namely , the angle MAS and the dihedral angle MABS ; and of the second and fourth , the angle PCQ and the dihedral angle PCDQ , any ...
Side 24
... third plane , the corresponding dihedral angles are equal . Let the two parallel planes MN , PQ ( fig . 44 ) be cut by the plane RS ; the dihedral angles MABR , PCDR are equal . Through A draw a plane perpendicular to AB ( Prop . 10 ) ...
... third plane , the corresponding dihedral angles are equal . Let the two parallel planes MN , PQ ( fig . 44 ) be cut by the plane RS ; the dihedral angles MABR , PCDR are equal . Through A draw a plane perpendicular to AB ( Prop . 10 ) ...
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Vanlige uttrykk og setninger
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.