## 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 ... |

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Resultat 1-5 av 15

Side vi

Consequences deducible from this are , that if two spheres

externally , they

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

Hence ...

Consequences deducible from this are , that if two spheres

**touch**one anotherexternally , they

**touch**only in a point ; and if they are turned as one body aboutthe two centres which remain at rest , the point of contact remains unmoved .

Hence ...

Side xi

Anything that can be made the object of

whose particles are immoveable among themselves , at least by any force there

is question of employing ; is called a hard body . IV . That which has length ,

breadth ...

Anything that can be made the object of

**touch**, is called a body . III . A bodywhose particles are immoveable among themselves , at least by any force there

is question of employing ; is called a hard body . IV . That which has length ,

breadth ...

Side 1

The only way in which coincidence can actually be brought to pass , is when the

things

the surface of a cast and the surface of the mould which contains it . And in like ...

The only way in which coincidence can actually be brought to pass , is when the

things

**touch**one another or are in contact . Thus there is coincidence betweenthe surface of a cast and the surface of the mould which contains it . And in like ...

Side 14

Spheres are said to

Spheres described about the same centre , are called concentric . CoR . 2. A

sphere may be described about any centre , and with a central distance equal to

the ...

Spheres are said to

**touch**one another , which meet but do not cut one another .Spheres described about the same centre , are called concentric . CoR . 2. A

sphere may be described about any centre , and with a central distance equal to

the ...

Side 16

If two spheres

be two spheres whose centres are A and B , touching one another externally .

The one cannot

...

If two spheres

**touch**one another externally , they**touch**only in a point . Let therebe two spheres whose centres are A and B , touching one another externally .

The one cannot

**touch**the other in more than a single point at once . For if this be...

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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.