## 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 36

Side vi

A solid may be

from a given point within ; such a solid is called a sphere . A sphere may be

turned in any manner whatsoever about its centre , without change of place .

A solid may be

**described**, all the points in whose surface shall be equidistantfrom a given point within ; such a solid is called a sphere . A sphere may be

turned in any manner whatsoever about its centre , without change of place .

Side 14

There shall be

at rest , the point A can struction . applied to every point in the line AC , in any of

its situations . + Constr . Also every point in the surface of the

There shall be

**described**the solid required . • By Con For , the point B remainingat rest , the point A can struction . applied to every point in the line AC , in any of

its situations . + Constr . Also every point in the surface of the

**described**solid ... Side 21

B в Let there be a sphere

also be E a centre ( that is , can also be equidistant from all the points in the

surface of the sphere . ] In the surface of the sphere

...

B в Let there be a sphere

**described**about the centre A. No other point , as B , canalso be E a centre ( that is , can also be equidistant from all the points in the

surface of the sphere . ] In the surface of the sphere

**described**about A , take any...

Side 22

5. to the sphere whose centre is C , in such manner $ that they shall Cor . touch in

the point A. Whereupon the point D in this last -

the surface of the sphere whose centre is A ; for if not , their central distances ...

5. to the sphere whose centre is C , in such manner $ that they shall Cor . touch in

the point A. Whereupon the point D in this last -

**described**sphere will be found inthe surface of the sphere whose centre is A ; for if not , their central distances ...

Side 23

In the surface of the sphere A , in that portion of it which is within the sphere so

process of describing a sphere about B as above ) was made to

the ...

In the surface of the sphere A , in that portion of it which is within the sphere so

**described**about B , let any point be taken , as D. But when the point A ( in theprocess of describing a sphere about B as above ) was made to

**describe**a line ,the ...

### Hva folk mener - Skriv en omtale

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

### 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.