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 95
In a projected great circle , the semi - conjugate axis is the cosine of the great
circle ' s inclination to the primitive . COR . 2 . – Perpendiculars to the transverse
axis intercept corresponding arcs of the projection and the primitive . Cor . 3 .
In a projected great circle , the semi - conjugate axis is the cosine of the great
circle ' s inclination to the primitive . COR . 2 . – Perpendiculars to the transverse
axis intercept corresponding arcs of the projection and the primitive . Cor . 3 .
Side 96
The transverse axis is to the conjugate , as radius to the cosine of the circle ' s
inclination to the primitive . · Cor . 2 . - Half the transverse axis is the cosine of half
the sum of the greatest and least distances of the small circle from the primitive .
The transverse axis is to the conjugate , as radius to the cosine of the circle ' s
inclination to the primitive . · Cor . 2 . - Half the transverse axis is the cosine of half
the sum of the greatest and least distances of the small circle from the primitive .
Side 97
The centre of the primitive , the centre of projection , the projected poles , ? and
the extremities of the conjugate axis , are all in Bil one and the same straight line .
- - Cor . 2 . - - As radius is to the sine of a small circle ' s ind - - clination to the ...
The centre of the primitive , the centre of projection , the projected poles , ? and
the extremities of the conjugate axis , are all in Bil one and the same straight line .
- - Cor . 2 . - - As radius is to the sine of a small circle ' s ind - - clination to the ...
Side 101
Hence the projection is an ellipse , of which the transverse axis is equal to the
diameter of the circle , and its conjugate less in the preceding ratio . Cor . 3 . - -
The projection of a sphere is a circle of equal diameter . FOURTH BOOK .
Hence the projection is an ellipse , of which the transverse axis is equal to the
diameter of the circle , and its conjugate less in the preceding ratio . Cor . 3 . - -
The projection of a sphere is a circle of equal diameter . FOURTH BOOK .
Side 122
Two diameters are said to be conjugate to one another when each is parallel to
the ordinates of the other . 8 . The parameter of a diameter is a third proportional
to that diameter and its conjugate . PROPOSITION I . If from any point in an
ellipse ...
Two diameters are said to be conjugate to one another when each is parallel to
the ordinates of the other . 8 . The parameter of a diameter is a third proportional
to that diameter and its conjugate . PROPOSITION I . If from any point in an
ellipse ...
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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 |