## 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 ... |

### Inni boken

Resultat 6-10 av 21

Side 46

COR . 2 . - Hence any plane passing through the centre of the sphere , divides it

into two equal parts , which are therefore called hemispheres . COR . 3 . - If a

point in the

COR . 2 . - Hence any plane passing through the centre of the sphere , divides it

into two equal parts , which are therefore called hemispheres . COR . 3 . - If a

point in the

**surface**of the sphere be at the distance of a quadrant from other ... Side 76

... reference to its projection . • 7 . A straight line drawn from the point of sight to

any original point , is called a projecting line . 8 . The

projecting lines of all the points of any original line , is called a projecting

.

... reference to its projection . • 7 . A straight line drawn from the point of sight to

any original point , is called a projecting line . 8 . The

**surface**, which contains theprojecting lines of all the points of any original line , is called a projecting

**surface**.

Side 78

The stereographic projection of any point in the

from the centre of the primitive , by the semi - tangent of that point ' s distance

from the pole opposite to the projecting point . PROPOSITION II . Every circle on

the ...

The stereographic projection of any point in the

**surface**of the sphere is distantfrom the centre of the primitive , by the semi - tangent of that point ' s distance

from the pole opposite to the projecting point . PROPOSITION II . Every circle on

the ...

Side 79

Thus , the conic

is cut by the primitive in a sub - contrary position ( Conic Sections ) ; therefore the

section mn is , in this case , likewise a circle . Cor . 1 . - The centres , and poles ...

Thus , the conic

**surface**, described by the revolution of AM , about the circle MN ,is cut by the primitive in a sub - contrary position ( Conic Sections ) ; therefore the

section mn is , in this case , likewise a circle . Cor . 1 . - The centres , and poles ...

Side 80

An angle , formed by two tangents , at the same point , in the

sphere , is equal to the angle formed by their projections . Let FGI and GH be the

two tangents , and A the projecting point ; let the plane AGF cut the sphere in the

circle ...

An angle , formed by two tangents , at the same point , in the

**surface**of thesphere , is equal to the angle formed by their projections . Let FGI and GH be the

two tangents , and A the projecting point ; let the plane AGF cut the sphere in the

circle ...

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### Andre utgaver - Vis alle

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...