An elementary course of mathematics, Volumen2 |
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Página vi
... Horizontal Projection has been drawn up from M. Le Capitaine F. Noizet's " Mémoire sur la Géométrie appliquée au Dessin de la Fortification " ( Mémorial de l'Officier du Génie , No. 6 ) , a memoir that cannot be too strongly recommended ...
... Horizontal Projection has been drawn up from M. Le Capitaine F. Noizet's " Mémoire sur la Géométrie appliquée au Dessin de la Fortification " ( Mémorial de l'Officier du Génie , No. 6 ) , a memoir that cannot be too strongly recommended ...
Página vii
... . 56 Miscellaneous Problems 71 Cases of the Trihedral angle HORIZONTAL PROJECTION Problems . Straight lines and Planes . Surfaces 77 82 88 101 ISOMETRIC PERSPECTIVE 103 GEOMETRY OF SOLIDS . Page Propositions . Equal solids .
... . 56 Miscellaneous Problems 71 Cases of the Trihedral angle HORIZONTAL PROJECTION Problems . Straight lines and Planes . Surfaces 77 82 88 101 ISOMETRIC PERSPECTIVE 103 GEOMETRY OF SOLIDS . Page Propositions . Equal solids .
Página 32
... horizontal plane giving what is termed the Plan of the points in the body , and the perpendiculars giving the heights of these points above the plane . In this mode of representation , which is called Hori- zontal Projection , in order ...
... horizontal plane giving what is termed the Plan of the points in the body , and the perpendiculars giving the heights of these points above the plane . In this mode of representation , which is called Hori- zontal Projection , in order ...
Página 34
... horizontal planes , until it coincides with the latter , and the foot of the perpendicular Aa on the horizontal ... Projection of the original point . Thus the point a ( fig . 4 ) , where the perpendicular Aa , from the point A , to the plane ...
... horizontal planes , until it coincides with the latter , and the foot of the perpendicular Aa on the horizontal ... Projection of the original point . Thus the point a ( fig . 4 ) , where the perpendicular Aa , from the point A , to the plane ...
Página 39
... projection be made common to the two pictures , so that one is immediately ... projections will be given by the intersection of planes passing through ab , a ... horizontal and vertical planes as those usually employed in projections , we ...
... projection be made common to the two pictures , so that one is immediately ... projections will be given by the intersection of planes passing through ab , a ... horizontal and vertical planes as those usually employed in projections , we ...
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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.