The geometry, by T. S. Davies. Conic sections, by Stephen FenwickJ. Weale, 1853 |
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Resultat 1-5 av 46
Side 142
... plane MN , the point E is in that plane ; and similarly , E being in the line CD , it is also in the plane PQ . The planes MN , PQ therefore meet in E , which is impossible ( Def . 1. ) since they are by hypothesis parallel to one ...
... plane MN , the point E is in that plane ; and similarly , E being in the line CD , it is also in the plane PQ . The planes MN , PQ therefore meet in E , which is impossible ( Def . 1. ) since they are by hypothesis parallel to one ...
Side 144
... plane , draw a plane through AB and E to cut the plane CF in EF ' . Then since through AB and CD the planes AF ... PQ through the latter pair . For if not , let the plane MN cut PQ in some line , as GH . Then , since AB is parallel to a ...
... plane , draw a plane through AB and E to cut the plane CF in EF ' . Then since through AB and CD the planes AF ... PQ through the latter pair . For if not , let the plane MN cut PQ in some line , as GH . Then , since AB is parallel to a ...
Side 145
... plane PQ ; and the plane MN cuts the plane PQ in a line GH parallel to BC , and therefore to EF . The line GH is therefore parallel to each of two straight lines DE , EF which meet ; but this is impossible , and hence the planes MN , PQ ...
... plane PQ ; and the plane MN cuts the plane PQ in a line GH parallel to BC , and therefore to EF . The line GH is therefore parallel to each of two straight lines DE , EF which meet ; but this is impossible , and hence the planes MN , PQ ...
Side 146
... plane ABC , which is impossible ; wherefore only one plane can be drawn through A parallel to MN . ( 3. ) All lines drawn through A parallel to the plane MN lie in the plane PQ parallel to MN . For if it be possible , let AD ' not in the ...
... plane ABC , which is impossible ; wherefore only one plane can be drawn through A parallel to MN . ( 3. ) All lines drawn through A parallel to the plane MN lie in the plane PQ parallel to MN . For if it be possible , let AD ' not in the ...
Side 147
... plane ABP with MN ( Prop . 11. ) ; and , similarly , AB is parallel to PF . Whence the two lines PE , PF in the ... PQ . PROPOSITION X. If a plane be parallel to one of two parallel lines , or to one of two parallel planes , it will be ...
... plane ABP with MN ( Prop . 11. ) ; and , similarly , AB is parallel to PF . Whence the two lines PE , PF in the ... PQ . PROPOSITION X. If a plane be parallel to one of two parallel lines , or to one of two parallel planes , it will be ...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick Royal Military Academy, Woolwich Uten tilgangsbegrensning - 1853 |
Vanlige uttrykk og setninger
ABCD axis base bisected called centre circle circumference coincide common cone construction contained coordinate curve described diameter difference dihedral angles direction distance divided double draw drawn edges ellipse equal equal angles equimultiples extremities faces figure formed four fourth given line given point greater hence horizontal inclination intersection join less likewise magnitudes manner meet method multiple opposite parallel parallelogram pass perpendicular perspective picture plane MN plane of projection position preceding prisms problem produced projector Prop proportional PROPOSITION proved ratio reason rectangle remaining respectively right angles SCHOLIUM segment shown sides similar sphere square straight line surface taken tangent THEOR third touch trace transverse triangle triangle ABC trihedral vertex vertical Whence Wherefore whole
Populære avsnitt
Side 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.
Side 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.
Side 4 - AB; but things which are equal to the same are equal to one another...
Side 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.
Side 8 - If two triangles have two sides of the one equal to two sides of the...
Side 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...
Side 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.
Side 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.
Side 4 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.
Side 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.