## 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 12

Side vi

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

Hence if about two assigned points be described a

touching one another , any number of intermediate points may be determined

that shall ...

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

Hence if about two assigned points be described a

**succession**of spherestouching one another , any number of intermediate points may be determined

that shall ...

Side vii

There may be places where it would be possible to evade the recognition of

continuous motion , by a forced and affected substitution of a

positions instead , with the effect of greatly reducing the distinctness of the whole

; as for ...

There may be places where it would be possible to evade the recognition of

continuous motion , by a forced and affected substitution of a

**succession**ofpositions instead , with the effect of greatly reducing the distinctness of the whole

; as for ...

Side viii

XXVIII D in the First Book , where the conclusion rests entirely on the impossibility

of a certain line ceasing to cut a series of other lines during a continuous motion ,

in a way incapable of being supplied by any

XXVIII D in the First Book , where the conclusion rests entirely on the impossibility

of a certain line ceasing to cut a series of other lines during a continuous motion ,

in a way incapable of being supplied by any

**succession**of insulated positions ... Side 20

Nom.26 . the face towards A , will be turned to all sides in

CD , which is not a self - rejoining line , must change its place ; for it cannot have

its face turned to all sides in

Nom.26 . the face towards A , will be turned to all sides in

**succession**; the lineCD , which is not a self - rejoining line , must change its place ; for it cannot have

its face turned to all sides in

**succession**and be without change of place . Side 28

4 , point ; nor any other point in the straight line ( as described by means of a

touching spheres . CoR . 9. A straight line from the centre of a sphere to a point

outside ...

4 , point ; nor any other point in the straight line ( as described by means of a

**succession**of concentric spheres in Prop . IX ) be in the surface of either of thetouching spheres . CoR . 9. A straight line from the centre of a sphere to a point

outside ...

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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.