## 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

Side 14

+

point in the line AC applied to it . Wherefore the point A can be applied to every

point in the described surface , the point B remaining at rest ; consequently each

...

+

**Constr**. Also every point in the surface of the described solid , hast had somepoint in the line AC applied to it . Wherefore the point A can be applied to every

point in the described surface , the point B remaining at rest ; consequently each

...

Side 15

3 . posed to remain unmoved , any par+

substantial sphere as A , willt at all times be coincident with some point or other in

the reciprocal ; because they are equally distant from the centre . And in like ...

3 . posed to remain unmoved , any par+

**Constr**. ticular point in the surface of thesubstantial sphere as A , willt at all times be coincident with some point or other in

the reciprocal ; because they are equally distant from the centre . And in like ...

Side 22

... wherefore the distance BE is not +

But BC ist equal to AC ; wherefore BC is not equal to BE ; for if they were equal ,

BE INTERC . 1. would also be f equal to AC , and it is not . And because BC is

Cor .

... wherefore the distance BE is not +

**Constr**. equal to the distance AE , or AC .But BC ist equal to AC ; wherefore BC is not equal to BE ; for if they were equal ,

BE INTERC . 1. would also be f equal to AC , and it is not . And because BC is

Cor .

Side 27

wherefore ( by Cor . 3 above ) the straight lines from the centre to any points in

the surface are equal . And if two spheres have equal radii , the extremities of the

radii ( by ...

**Constr**. For all the points in the surface are * equidistant from the centre ;wherefore ( by Cor . 3 above ) the straight lines from the centre to any points in

the surface are equal . And if two spheres have equal radii , the extremities of the

radii ( by ...

Side 33

9 . INTERC.10 . wherefore BE , BF aref equal . About E as a centre , with the Cor .

4 . radius EB , describe a sphere ; and about A as a centre , with the radius AB ,

describe another sphere . •

9 . INTERC.10 . wherefore BE , BF aref equal . About E as a centre , with the Cor .

4 . radius EB , describe a sphere ; and about A as a centre , with the radius AB ,

describe another sphere . •

**Constr**. Because the surfaces of these two spheres ...### Hva folk mener - Skriv en omtale

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### 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.