## 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

Side 1

The

straight line , and another drawn from the point in which the first line meets the

plane , to the point in which a perpendicular to the plane drawn from any point of

the ...

The

**inclination**of a straight line to a plane is the acute angle contained by thatstraight line , and another drawn from the point in which the first line meets the

plane , to the point in which a perpendicular to the plane drawn from any point of

the ...

Side 10

If two parallel planes be cut by a third plane , they have the same

that plane . Let AB and CD be two parallel planes , and EH a third plane cutting

them . The planes AB and CD are equally

...

If two parallel planes be cut by a third plane , they have the same

**inclination**tothat plane . Let AB and CD be two parallel planes , and EH a third plane cutting

them . The planes AB and CD are equally

**inclined**to EH . Let the straight lines EF...

Side 11

Therefore , since LM and LO are at right angles to LG , the common section of the

two planes CD and EH , the angle OLM is the

plane EH ( I . Def , 4 ) . For the same reason the angle MKN is the

Therefore , since LM and LO are at right angles to LG , the common section of the

two planes CD and EH , the angle OLM is the

**inclination**of the plane CD to theplane EH ( I . Def , 4 ) . For the same reason the angle MKN is the

**inclination**of ... Side 17

... solids be contained by the same number of equal and similar planes , similarly

situated , and if the

SECOND BOOK 17.

... solids be contained by the same number of equal and similar planes , similarly

situated , and if the

**inclination**of any two contiguous planes in the one solid beSECOND BOOK 17.

Side 18

Being a Treatise on the Higher Branches of Synthetical Geometry, Containing the

Solid and Spherical Geometry of Playfair ... A. Bell. of any two contiguous planes

in the one solid be the same with the

Being a Treatise on the Higher Branches of Synthetical Geometry, Containing the

Solid and Spherical Geometry of Playfair ... A. Bell. of any two contiguous planes

in the one solid be the same with the

**inclination**of the two equal , and similarly ...### Hva folk mener - Skriv en omtale

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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 Let ABC 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...