Solid and Spherical Geometry and Conic Sections: Being a Treatise on the Higher Branches of Synthetical Geometry, Containing the Solid and Spherical Geometry of Playfair ... |
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Side 5
angle ABC , by the hypothesis , is also a right angle ; therefore the angle ABF is
equal to the angle ABC , and they are both in the same plane ; which is
impossible : therefore the straight line BC is not above the plane in which are BD
and BE .
angle ABC , by the hypothesis , is also a right angle ; therefore the angle ABF is
equal to the angle ABC , and they are both in the same plane ; which is
impossible : therefore the straight line BC is not above the plane in which are BD
and BE .
Side 7
plane with the first two , the first two and the other two shall contain equal angles .
Let the two straight lines AB , BC , which meet one another , be parallel to the two
straight lines DE , EF , that meet one another , and are not in the same plane ...
plane with the first two , the first two and the other two shall contain equal angles .
Let the two straight lines AB , BC , which meet one another , be parallel to the two
straight lines DE , EF , that meet one another , and are not in the same plane ...
Side 9
B is a right angle ; wherefore the angle CAE is equal to the angle BAE ; and they
are in one plane ; which is impossible . Also , from a point above a plane , there
can be but one per : pendicular to that plane ; for if there could be two , they ...
B is a right angle ; wherefore the angle CAE is equal to the angle BAE ; and they
are in one plane ; which is impossible . Also , from a point above a plane , there
can be but one per : pendicular to that plane ; for if there could be two , they ...
Side 10
And because BA is parallel ( I . 8 ) to GH ( for each of them is parallel to DE ) , the
angles ĜBA , BGH , are together equal ( Pl . Ge . I . 29 ) to two right angles . And
BGH is a right angle ; therefore also GBA is a right angle , and GB perpendicular
...
And because BA is parallel ( I . 8 ) to GH ( for each of them is parallel to DE ) , the
angles ĜBA , BGH , are together equal ( Pl . Ge . I . 29 ) to two right angles . And
BGH is a right angle ; therefore also GBA is a right angle , and GB perpendicular
...
Side 11
But because KN and LO are parallel , being the common sections of the parallel
planes AB and CD with a third plane , the interior angle NKM is equal to the
exterior angle OLM ; that is , the inclination of the plane AB to the plane EH , is
equal ...
But because KN and LO are parallel , being the common sections of the parallel
planes AB and CD with a third plane , the interior angle NKM is equal to the
exterior angle OLM ; that is , the inclination of the plane AB to the plane EH , is
equal ...
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Solid and Spherical Geometry and Conic Sections: Being a Treatise on the ... A. Bell Uten tilgangsbegrensning - 1837 |
Solid and Spherical Geometry and Conic Sections: Being a Treatise on the ... William Chambers,Robert Chambers,A Bell Ingen forhåndsvisning tilgjengelig - 2018 |
Solid and Spherical Geometry and Conic Sections: Being a Treatise on the ... William Chambers,Robert Chambers,A Bell Ingen forhåndsvisning tilgjengelig - 2015 |
Vanlige uttrykk og setninger
ABCD affection altitude angle ABC axis base bisects called centre circle common section cone conjugate consequently contained cord cosine curve cylinder described diameter difference distance divided draw drawn ellipse equal extremities fall figure foci focus fore given given point greater half Hence hyperbola inclination intercepted intersection join less line be drawn lines drawn manner measure meet namely opposite ordinate parabola parallel parallelogram pass perpendicular perspective plane point of contact pole primitive prism produced projection proportional PROPOSITION proved pyramid quadrant radius ratio reason rectangle right angles segments semi-ordinate sides similar sine small circle solid sphere spherical triangle square straight line surface tangent THEOREM third transverse triangle vertex vertical
Populære avsnitt
Side 50 - 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.
Side 15 - A cone is a solid figure described by the revolution of a right-angled triangle about one of the sides containing the right angle, which side remains fixed.
Side 25 - LR, the base of which is the parallelogram LQ, and of which LM is one of its insisting straight lines : therefore, because the parallelogram AB is equal to CD, as the base AB is to the base LQ, so is (7.
Side 17 - DAB, which contain the solid angle at A, are less than four right angles. Next, let the solid angle at A be contained by any number of plane angles BAC, CAD, DAE, EAF, FAB. These shall together be less than four right angles.
Side 27 - FC, as the solid HD to the solid DC. But the base HF is equal to the base AE, and the solid GK to the solid AB ; therefore, as the base AE to the base CF, so is the solid AB to the solid CD.
Side 53 - EM (2.) are ^quadrants, and FL, EM together, that is, FE and ML together, are equal to a semicircle. But since A is the pole of ML, ML is the measure of the angle BAC (3.), consequently FE is the supplement of the measure of the angle BAC.
Side 19 - And AB is parallel to CD ; therefore AC is a parallelogram. In like manner, it may be proved, that each of the figures CE, FG, GB, BF, AE is a parallelogram: Join AH, DF; and...
Side 5 - If two straight lines be at right angles to the same plane, they shall be parallel to one another. Let the straight lines AB, CD be at right angles to the same plane.
Side 9 - CA is at right angles to the given plane, it makes right angles with every straight line meeting it in that plane. But DAE, which is in that plane, meets CA : therefore CAE is a right angle. For the same reason BAE is a right angle. Wherefore the angle CAE is equal to the angle BAE ; and they are in one plane, which is impossible. Also, from a point above a plane, there can be but one perpendicular to that plane ; for if there could be two, they would be parallel (6.
Side 1 - The inclination of a straight line to a plane is the acute angle contained by that straight line, and another drawn from the point in which the first line meets the plane, to the point in which...
Bibliografisk informasjon
| Tittel | Solid and Spherical Geometry and Conic Sections: Being a Treatise on the Higher Branches of Synthetical Geometry, Containing the Solid and Spherical Geometry of Playfair ... Chambers's educational course Chambers's educational course,--ed. by W. and R. Chambers |
| Forfatter | A. Bell |
| Utgiver | William and Robert Chambers and sold by all booksellers, 1837 |
| Original fra | Oxford University |
| Digitalisert | 4. des 2006 |
| Lengde | 164 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |