The geometry, by T. S. Davies. Conic sections, by Stephen FenwickJ. Weale, 1853 |
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Ergebnisse 6-10 von 28
Seite 169
... dihedral angles with them . Let the plane MN cut the parallel planes PQ , RS in MQ , DS ; the di- hedral angles PMQN , RDSN will be equal . For since the planes PQ , RS are parallel , the edges MQ , DS of the dihedral angles are ...
... dihedral angles with them . Let the plane MN cut the parallel planes PQ , RS in MQ , DS ; the di- hedral angles PMQN , RDSN will be equal . For since the planes PQ , RS are parallel , the edges MQ , DS of the dihedral angles are ...
Seite 170
... angle of the dihedral angle PQBN ( Def . 4 ) .間 P Ο But AB being perpendicular to MN , ABC is a right angle ( Prop . II . ) ; and the profile angle of the planes being a right angle , then the dihedral angle is a right angle ( Def . 4 ) ...
... angle of the dihedral angle PQBN ( Def . 4 ) .間 P Ο But AB being perpendicular to MN , ABC is a right angle ( Prop . II . ) ; and the profile angle of the planes being a right angle , then the dihedral angle is a right angle ( Def . 4 ) ...
Seite 172
... angle equal or supplementary to the profile angle of the planes . P Let the planes PQ , RS ... dihedral angle PQRS ; and BDC is the profile angle . Now the four angles of the quadrilateral figure ABDC are 172 GEOMETRY OF PLANES AND SOLIDS .
... angle equal or supplementary to the profile angle of the planes . P Let the planes PQ , RS ... dihedral angle PQRS ; and BDC is the profile angle . Now the four angles of the quadrilateral figure ABDC are 172 GEOMETRY OF PLANES AND SOLIDS .
Seite 173
... angle BAC turned towards the dihedral edge , is that specified . But when the point A is not between the planes PQ , RS as in the preceding figure ; but without the dihedral angle , the profile angle BDC is equal to the angle BAC formed ...
... angle BAC turned towards the dihedral edge , is that specified . But when the point A is not between the planes PQ , RS as in the preceding figure ; but without the dihedral angle , the profile angle BDC is equal to the angle BAC formed ...
Seite 177
... dihedral angles with it : then , ( 1. ) That formed when the trace of the revolving plane is perpendicu- lar to the line itself , is the least ; ( 2. ) As the plane revolves from this position towards coincidence ( either way ) with the ...
... dihedral angles with it : then , ( 1. ) That formed when the trace of the revolving plane is perpendicu- lar to the line itself , is the least ; ( 2. ) As the plane revolves from this position towards coincidence ( either way ) with the ...
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ABC is equal ABCD angle ABC angle BAC axis bisected centre circle ABC circumference coincide cone conic section construction coordinate planes curve described Descriptive Geometry dicular dihedral angles directrix distance draw edges ellipse equal angles equiangular equimultiples given line given point given straight line greater hence inclination intersection join less Let ABC Let the plane line BC lines drawn magnitudes meet multiple opposite orthograph parabola parallel planes parallelogram parallelopiped perpen perpendicular plane MN plane of projection plane parallel plane PQ prisms profile angles profile plane projecting plane projector Prop Q. E. D. PROPOSITION ratio rectangle rectangle contained rectilineal figure remaining angle respectively right angles SCHOLIUM segment sides six right sphere spherical spherical angle tangent THEOR trace triangle ABC trihedral vertex vertical plane Whence Wherefore
Beliebte Passagen
Seite 19 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Seite 35 - If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Seite 4 - AB; but things which are equal to the same are equal to one another...
Seite 128 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.* Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG : the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. Let BG, CG, be placed in a straight line ; therefore DC and CE are also in a straight line (14.
Seite 8 - If two triangles have two sides of the one equal to two sides of the...
Seite 36 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced...
Seite 21 - BCD, and the other angles to the other angles, (4. 1.) each to each, to which the equal sides are opposite : therefore the angle ACB is equal to the angle CBD ; and because the straight line BC meets the two straight lines AC, BD, and makes the alternate angles ACB, CBD equal to one another, AC is parallel (27. 1 .) to DB ; and it was shown to be equal to it. Therefore straight lines, &c.
Seite 65 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles which this line makes with the line touching the circle shall be equal to the angles which are in the alternate segments of the circle.
Seite 4 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.
Seite 116 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.