## Geometry Without Axioms; Or the First Book of Euclid's Elements. With Alterations and Familiar Notes; and an Intercalary Book in which the Straight Line and Plane are Derived from Properties of the Sphere ...: To which is Added an Appendix ... |

### Inni boken

Resultat 1-5 av 33

Side vi

A sphere may be turned in any manner whatsoever about its

change of place . ... they touch only in a point ; and if they are turned as one body

about the two

.

A sphere may be turned in any manner whatsoever about its

**centre**, withoutchange of place . ... they touch only in a point ; and if they are turned as one body

about the two

**centres**which remain at rest , the point of contact remains unmoved.

Side 14

And such point within , is called the

to every point in the surface , is called the central distance . Spheres are said to

touch one another , which meet but do not cut one another . Spheres described ...

And such point within , is called the

**centre**of the sphere ; and the distance from itto every point in the surface , is called the central distance . Spheres are said to

touch one another , which meet but do not cut one another . Spheres described ...

Side 15

If the

surfaces will coincide throughout . And if their central distances are not equal ,

their surfaces will not coincide at all , but one be interior to the other . For ( by Cor

...

If the

**centres**of two spheres coincide , and their central distances are equal ; theirsurfaces will coincide throughout . And if their central distances are not equal ,

their surfaces will not coincide at all , but one be interior to the other . For ( by Cor

...

Side 17

1 either or both of the spheres may be turned in any manner whatsoever about its

and not elsewhere . For each of them will be * without change of place ...

1 either or both of the spheres may be turned in any manner whatsoever about its

**centre**, and they must still always coincide in the surface in fixed space CEGDHFand not elsewhere . For each of them will be * without change of place ...

Side 18

But if So , it may be shown as before , that they must continue to coincide in the

same line in fixed space CEGDHF and not elsewhere , in whatsoever manner

they may be turned about their respective

But if So , it may be shown as before , that they must continue to coincide in the

same line in fixed space CEGDHF and not elsewhere , in whatsoever manner

they may be turned about their respective

**centres**. Let then the sphere whose**centre**...### Hva folk mener - Skriv en omtale

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### Andre utgaver - Vis alle

Geometry Without Axioms; Or the First Book of Euclid's Elements. With ... Thomas Perronet Thompson Uten tilgangsbegrensning - 1833 |

Geometry Without Axioms; Or the First Book of Euclid's Elements. with ... Thomas Perronet Thompson Ingen forhåndsvisning tilgjengelig - 2015 |

### Vanlige uttrykk og setninger

ABCD added alternate angle ABC angle BAC applied aret assigned axis base bisected body Book called centre change of place circle coincide common consequently Constr continually demonstrated described distance double drawn equal Euclid exterior angle extremities fall figure follows formed four right angles Geometry given straight line greater half impossible instance INTERC interior join kind less magnitude manner meet moved Note opposite parallel parallelogram parity of reasoning pass perpendicular plane portion prolonged proof Prop PROPOSITION proved radius remaining angle respectively rest right angles Second self-rejoining line shown situation space sphere sphere whose centre square straight line succession surface taken terminated thing third side touch triangle triangle ABC true turned unequal universally Wherefore whole

### Populære avsnitt

Side 51 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.

Side 109 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...

Side 111 - Parallelograms upon the same base and between the same parallels, are equal to one another.

Side 120 - If the square described on one of the sides of a triangle be equal to the squares described on the other two sides of it, the angle contained by these two sides is a right angle.

Side 72 - Any two sides of a triangle are together greater than the third side.

Side 55 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.

Side 70 - Any two angles of a triangle are together less than two right angles.

Side 138 - ... the exterior angle equal to the interior and opposite on the same side of the line ; and likewise the two interior angles on the same side of the line together equal to two right angles.

Side 106 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.