The geometry, by T. S. Davies. Conic sections, by Stephen FenwickJ. Weale, 1853 |
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Página 147
... planes MN , PQ . PROPOSITION X. If a plane be parallel to one of two parallel lines , or to one of two parallel planes , it will be parallel to the other . ( 1. ) Let the plane MN be parallel to AB , one of the two parallel lines AB ...
... planes MN , PQ . PROPOSITION X. If a plane be parallel to one of two parallel lines , or to one of two parallel planes , it will be parallel to the other . ( 1. ) Let the plane MN be parallel to AB , one of the two parallel lines AB ...
Página 148
... plane ; viz . , the plane which passes through AB and any one of them CD . M C D E C H N ( 2. ) Also since this plane cuts MN in a line DH parallel to AB ( Prop . 11. ) , the figure CDFE is a parallelogram , and hence the oppo- site ...
... plane ; viz . , the plane which passes through AB and any one of them CD . M C D E C H N ( 2. ) Also since this plane cuts MN in a line DH parallel to AB ( Prop . 11. ) , the figure CDFE is a parallelogram , and hence the oppo- site ...
Página 149
... planes , then every plane drawn through this line to cut them , will cut them in parallel lines . Let the line AB be parallel to each of the planes MN , PQ ; and any plane RS be drawn through AB to cut them in PR , SN ; then PR will be ...
... planes , then every plane drawn through this line to cut them , will cut them in parallel lines . Let the line AB be parallel to each of the planes MN , PQ ; and any plane RS be drawn through AB to cut them in PR , SN ; then PR will be ...
Página 151
... plane Whence one plane can be drawn as enun- B K ' A H ' F ( 2. ) There can be only one plane drawn through E ... MN . S Then since the line AB without the plane MN is parallel to FG in the plane , the line AB is parallel to the plane MN ...
... plane Whence one plane can be drawn as enun- B K ' A H ' F ( 2. ) There can be only one plane drawn through E ... MN . S Then since the line AB without the plane MN is parallel to FG in the plane , the line AB is parallel to the plane MN ...
Página 156
... plane in abc ; then abc is a circle . For draw the planes SEA , SEB , etc. , cutting ABC in AE , BE , etc. , and abc ... MN in A and B , C and D , etc .: then AB , CD , etc. , will always pass through the same point in the plane , viz ...
... plane in abc ; then abc is a circle . For draw the planes SEA , SEB , etc. , cutting ABC in AE , BE , etc. , and abc ... MN in A and B , C and D , etc .: then AB , CD , etc. , will always pass through the same point in the plane , viz ...
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 4 - AB; but things which are equal to the same are equal to one another...
Página 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.
Página 8 - If two triangles have two sides of the one equal to two sides of the...
Página 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...
Página 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.
Página 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.
Página 4 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.
Página 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.