An elementary course of mathematics, Τόμος 2 |
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Αποτελέσματα 1 - 5 από τα 35.
Σελίδα 4
... similar polygons inscribed in circles are to one an- other as the diameters of the circles ; and their areas are to one an- other as the squares of the diameters . Let ABCDEF , GHIKLM ( fig . 4 ) be two similar polygons in- scribed in ...
... similar polygons inscribed in circles are to one an- other as the diameters of the circles ; and their areas are to one an- other as the squares of the diameters . Let ABCDEF , GHIKLM ( fig . 4 ) be two similar polygons in- scribed in ...
Σελίδα 5
... similar polygons , & c .: which was to be proved . Cor . Since equilateral polygons inscribed in a circle are equi- angular ( IV . 11 , 15 , 16 ) , equilateral polygons , of the same number of sides , inscribed in circles , are similar ...
... similar polygons , & c .: which was to be proved . Cor . Since equilateral polygons inscribed in a circle are equi- angular ( IV . 11 , 15 , 16 ) , equilateral polygons , of the same number of sides , inscribed in circles , are similar ...
Σελίδα 6
... similar polygons inscribed in circles , their areas are to each other as the squares of the diameters of their circumscribing circles ( Prop . 4 ) , and therefore as the squares of their radii ; consequently the area of ABCD & c . is to ...
... similar polygons inscribed in circles , their areas are to each other as the squares of the diameters of their circumscribing circles ( Prop . 4 ) , and therefore as the squares of their radii ; consequently the area of ABCD & c . is to ...
Σελίδα 7
... similar inscribed polygon by I , then C is to I , as OM to OR ( Prop . 5 ) ; and therefore by conversion ( V. E ) , C is to its excess above I , as OM to MR , and therefore as eight times OM to eight times MR . And because the perimeter ...
... similar inscribed polygon by I , then C is to I , as OM to OR ( Prop . 5 ) ; and therefore by conversion ( V. E ) , C is to its excess above I , as OM to MR , and therefore as eight times OM to eight times MR . And because the perimeter ...
Σελίδα 8
... similar , and their perimeters are as the diameters of the circles in which they are inscribed ( Prop . 4 ) . Therefore AD is to GK as the peri- meter ABCDEF is to the perimeter GHIKLM ; but AD is to GK as the circumference ABE is to P ...
... similar , and their perimeters are as the diameters of the circles in which they are inscribed ( Prop . 4 ) . Therefore AD is to GK as the peri- meter ABCDEF is to the perimeter GHIKLM ; but AD is to GK as the circumference ABE is to P ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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...
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.