## 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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Side vi

Consequences deducible from this are , that if two spheres touch one another

externally , they touch only in a point ; and if they are turned as one

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 another

externally , 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 touch , is called a

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

is question of employing ; is called a hard

breadth ...

Anything that can be made the object of touch , is called a

**body**. III . A**body**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 ...

Side xii

Figures of all kinds , lines , and points , will always be considered as ex . hibited

on a hard

points to be fixed with relation to one another ; and will , on occasion , be

supposed ...

Figures of all kinds , lines , and points , will always be considered as ex . hibited

on a hard

**body**of some kind , which causes the position of the several parts orpoints to be fixed with relation to one another ; and will , on occasion , be

supposed ...

Side 12

A hard

such point or points remaining unmoved . Let A be a hard

A hard

**body**may be turned about any one point , or about any two points , in it ;such point or points remaining unmoved . Let A be a hard

**body**. First Case ; the**body**A may be turned about any one point in it , as B , such point remaining ... Side 13

situation , as M , such that the points B and C respectively occupy the same

places in fixed space as they did when the

the same reason , between the situations A and M the

other ...

situation , as M , such that the points B and C respectively occupy the same

places in fixed space as they did when the

**body**was in the situation A. And forthe same reason , between the situations A and M the

**body**may be placed inother ...

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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.