## 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 35

Side vi

If two equal spheres be placed touching one another externally , and about the

centre of each a sphere be described passing through the centre of the other ,

and a straight line of unlimited length be

two ...

If two equal spheres be placed touching one another externally , and about the

centre of each a sphere be described passing through the centre of the other ,

and a straight line of unlimited length be

**drawn**from the point of contact of thetwo ...

Side vii

... by a forced and affected substitution of a succession of positions instead , with

the effect of greatly reducing the distinctness of the whole ; as for instance in the

conclusions

...

... by a forced and affected substitution of a succession of positions instead , with

the effect of greatly reducing the distinctness of the whole ; as for instance in the

conclusions

**drawn**with respect to the sphere and straight line from turning them...

Side 26

A straight line

, is called a diameter of the sphere . Cor . A straight line may be described or

made to pass from any one point to any other point . For it may be done by Prop .

A straight line

**drawn**through the centre and terminated both ways by the surface, is called a diameter of the sphere . Cor . A straight line may be described or

made to pass from any one point to any other point . For it may be done by Prop .

Side 28

... of central distances , but always of radii . And if one point be said to be farther

or nearer than some other , it shall always be understood that the straight line

XI .

... of central distances , but always of radii . And if one point be said to be farther

or nearer than some other , it shall always be understood that the straight line

**drawn**to it is greater or less than the straight line**drawn**to the other . one PROP ,XI .

Side 41

AR , the straight line of unlimited length CL

surface of such sphere and be cut by it . Let it be met in S ; and Soe Note 1. join

AS , BS . Because S is a point in CL , it may be shown as has been done before ,

that ...

AR , the straight line of unlimited length CL

**drawn**from it will * cut Cor . 8 . thesurface of such sphere and be cut by it . Let it be met in S ; and Soe Note 1. join

AS , BS . Because S is a point in CL , it may be shown as has been done before ,

that ...

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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.