An elementary course of mathematics, Volumen2 |
Dentro del libro
Resultados 1-5 de 9
Página v
... works to which I have referred , and to pursue it to any extent that circumstances may render necessary . In the Geometry of Planes I have likewise followed nearly the order of the propositions in De Fourcy's introduction PREFACE .
... works to which I have referred , and to pursue it to any extent that circumstances may render necessary . In the Geometry of Planes I have likewise followed nearly the order of the propositions in De Fourcy's introduction PREFACE .
Página 32
... referred to that plane by a perpendi- cular let fall from it on the plane , and the foot of the perpendicular be referred to the fixed lines by perpendiculars , the position of the point in space will be determined when the lengths of ...
... referred to that plane by a perpendi- cular let fall from it on the plane , and the foot of the perpendicular be referred to the fixed lines by perpendiculars , the position of the point in space will be determined when the lengths of ...
Página 33
... referred , by a perpendicular , to the plane in which the two fixed straight lines are , which we will suppose to be the plane of the paper , and , for the sake of illus- tration , we will in the first instance consider this to be ...
... referred , by a perpendicular , to the plane in which the two fixed straight lines are , which we will suppose to be the plane of the paper , and , for the sake of illus- tration , we will in the first instance consider this to be ...
Página 34
... referred to this plane by a perpendicular to it from A , meeting the plane in a ; and the point A being referred , by a perpendicular , to the vertical plane , this plane be conceived to revolve about the horizontal line ay until it ...
... referred to this plane by a perpendicular to it from A , meeting the plane in a ; and the point A being referred , by a perpendicular , to the vertical plane , this plane be conceived to revolve about the horizontal line ay until it ...
Página 38
... referred to an ideal plane between it and the eye , by lines drawn from the eye through these points , and intersecting this plane , which is that of the picture : the intersections of these lines with the plane of the picture , are the ...
... referred to an ideal plane between it and the eye , by lines drawn from the eye through these points , and intersecting this plane , which is that of the picture : the intersections of these lines with the plane of the picture , are the ...
Otras ediciones - Ver todas
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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...
Página 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...
Página 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...
Página 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.
Página 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.