## 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

This , however , is not attempted by introducing a mode of reasoning looser or

even for the time that might thereby be saved ; but it is done chiefly by laying

aside a ...

This , however , is not attempted by introducing a mode of reasoning looser or

**less**rigorous than that of the Greek geometer ; for this would be to pay too deareven for the time that might thereby be saved ; but it is done chiefly by laying

aside a ...

Side 4

The perpendicular PO is

measures the shortest distance from the point P to the plane . PROPOSITION V .

THEOREM . If three straight lines meet all in one point , and a straight line stand

at right ...

The perpendicular PO is

**less**than any oblique line as PB , and therefore itmeasures the shortest distance from the point P to the plane . PROPOSITION V .

THEOREM . If three straight lines meet all in one point , and a straight line stand

at right ...

Side 15

But if they are not , let BAC be that angle which is not

two , and is greater than one of them DAB ; and at the point A in the straight line

AB , make , in the plane which passes B through BA , AC , the angle BAE equal ...

But if they are not , let BAC be that angle which is not

**less**than either of the othertwo , and is greater than one of them DAB ; and at the point A in the straight line

AB , make , in the plane which passes B through BA , AC , the angle BAE equal ...

Side 16

I . 25 ) than the angle EAC ; and , by the construction , the angle DAB is equal to

the angle BAE ; wherefore the angles DAB , DAC , are together greater than BAE

, EAC , that is , than the angle BAC . But BAC is not

...

I . 25 ) than the angle EAC ; and , by the construction , the angle DAB is equal to

the angle BAE ; wherefore the angles DAB , DAC , are together greater than BAE

, EAC , that is , than the angle BAC . But BAC is not

**less**than either of the angles...

Side 17

Of these , the six angles CBA , ACB , ACD , CDA , ADB , DBA , are greater than

two right angles ; therefore the remaining three angles BAC , DAC , BAD , which

contain the solid angle at A , are

Of these , the six angles CBA , ACB , ACD , CDA , ADB , DBA , are greater than

two right angles ; therefore the remaining three angles BAC , DAC , BAD , which

contain the solid angle at A , are

**less**than four right angles . Next , let the solid ...### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### 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...