An elementary course of mathematics, Τόμος 2 |
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Αποτελέσματα 1 - 5 από τα 38.
Σελίδα 5
... common to the two triangles KRA , KRB , the angle KRA is equal to the angle KRB ; and the angle BRK is half the ... common , RK is equal to RL . In like manner , it may be shown that RM , RN , RO , & c . are all equal ; and there- fore a ...
... common to the two triangles KRA , KRB , the angle KRA is equal to the angle KRB ; and the angle BRK is half the ... common , RK is equal to RL . In like manner , it may be shown that RM , RN , RO , & c . are all equal ; and there- fore a ...
Σελίδα 4
... common segment AB ; which is impossible ( I. 11. Cor . ) . Therefore one part of a straight line , & c .: which was to be proved . PROP . II . THEOR . Two straight lines which cut one another are in one plane , and three straight lines ...
... common segment AB ; which is impossible ( I. 11. Cor . ) . Therefore one part of a straight line , & c .: which was to be proved . PROP . II . THEOR . Two straight lines which cut one another are in one plane , and three straight lines ...
Σελίδα 5
... common section is a straight line . Let two planes , AB , BC ( fig . 10 ) , cut one another , and let the line DB be their common section : DB shall be a straight line . If it be not , from the point D to B draw , in the plane AB , the ...
... common section is a straight line . Let two planes , AB , BC ( fig . 10 ) , cut one another , and let the line DB be their common section : DB shall be a straight line . If it be not , from the point D to B draw , in the plane AB , the ...
Σελίδα 6
... common ; therefore GE , EF are equal to HE , EF , each to each ; and the base GF is equal to the base FH ; therefore the angle GEF is equal to the angle HEF ( I. 8 ) ; and consequently each of these angles is a right angle ( I. Def . 10 ) ...
... common ; therefore GE , EF are equal to HE , EF , each to each ; and the base GF is equal to the base FH ; therefore the angle GEF is equal to the angle HEF ( I. 8 ) ; and consequently each of these angles is a right angle ( I. Def . 10 ) ...
Σελίδα 8
... common section of the plane pass- ing through BA and CA be the straight line DAE ( Prop . 3 ) ; so that BĂ , CA and DAE are in one plane . And because BA is perpen- dicular to the plane MN , and EA meets it in that plane , the angle BAE ...
... common section of the plane pass- ing through BA and CA be the straight line DAE ( Prop . 3 ) ; so that BĂ , CA and DAE are in one plane . And because BA is perpen- dicular to the plane MN , and EA meets it in that plane , the angle BAE ...
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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.