An elementary course of mathematics, Volume 2 |
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Page 84
... measure of the plane's inclina- tion ; and the line aan ( the projection of a line of greatest inclina- tion on the plane ) having the indices of the equidistant points a1 , a2 , ag , a4 , & c . marked on it , is called the Scale of Slope ...
... measure of the plane's inclina- tion ; and the line aan ( the projection of a line of greatest inclina- tion on the plane ) having the indices of the equidistant points a1 , a2 , ag , a4 , & c . marked on it , is called the Scale of Slope ...
Page 85
... slope on which is in the direction of this line , and in which , therefore , the horizontal trace and all horizontal lines are perpendicular to the line a10 , a16 It is to be borne in ... index fixes the plane's SCALE OF SLOPE OF PLANES . 85.
... slope on which is in the direction of this line , and in which , therefore , the horizontal trace and all horizontal lines are perpendicular to the line a10 , a16 It is to be borne in ... index fixes the plane's SCALE OF SLOPE OF PLANES . 85.
Page 86
... index , must meet in the straight line which is the projec- tion of the intersection of the two planes . Thus let ab , cd ( fig . 7 ) be the scales of slope of two planes : produce ab , cd , and extend the scales so as to have the ...
... index , must meet in the straight line which is the projec- tion of the intersection of the two planes . Thus let ab , cd ( fig . 7 ) be the scales of slope of two planes : produce ab , cd , and extend the scales so as to have the ...
Page 87
... scale of slope on a limited portion of the surface . As the scale of slope on a plane is a perpendicular to the projection of a horizontal straight line in the plane , the scale of slope at any point on a surface is a perpendicular at ...
... scale of slope on a limited portion of the surface . As the scale of slope on a plane is a perpendicular to the projection of a horizontal straight line in the plane , the scale of slope at any point on a surface is a perpendicular at ...
Page 89
... scale of slope , be required , this slope is expressed by a fraction whose numerator is the difference of the indices of A and B , and the denominator is the projection of AB . If the converse of the former part of this problem were ...
... scale of slope , be required , this slope is expressed by a fraction whose numerator is the difference of the indices of A and B , and the denominator is the projection of AB . If the converse of the former part of this problem were ...
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Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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...
Page 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...
Page 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...
Page 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.
Page 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.