## 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 body about

the two centres which remain at rest, the point of contact

Hence if ...

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 about

the two centres which remain at rest, the point of contact

**remains unmoved**.Hence if ...

Side 15

Let the substantial sphere whose centre is B, bef turned in any manner

whatsoever about the centre B which remains at rest. The sphere shall be without

change of place. For if its” reciprocal be supposed to

particular ...

Let the substantial sphere whose centre is B, bef turned in any manner

whatsoever about the centre B which remains at rest. The sphere shall be without

change of place. For if its” reciprocal be supposed to

**remain unmoved**, anyparticular ...

Side 16

So also of the hollow sphere, if it be turned while the substantial one which is its

reciprocal

of every other sphere. Wherefore, universally, if a sphere be turned &c.

So also of the hollow sphere, if it be turned while the substantial one which is its

reciprocal

**remains unmoved**. And by parity of reasoning, the like may be provedof every other sphere. Wherefore, universally, if a sphere be turned &c.

Side 24

Their point of contact C shall

sphere remains at rest, each sphere is turned about its own centre; wherefore

each sphere willt be without change of place. Hence their point of contact will at

all times ...

Their point of contact C shall

**remain unmoved**. Because the centre of eachsphere remains at rest, each sphere is turned about its own centre; wherefore

each sphere willt be without change of place. Hence their point of contact will at

all times ...

Side 25

... If then the hard body in which are all the spheres, be turned” about the points A

and B; the point of contact F willf

centre A, in the same hard body be described other spheres successively less ...

... If then the hard body in which are all the spheres, be turned” about the points A

and B; the point of contact F willf

**remain unmoved**. And in like manner if about thecentre A, in the same hard body be described other spheres successively less ...

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Geometry Without Axioms Or the First Book Euclid's Elements: With ... 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 adjacent angles alternate angles angle ABC angle ACB angle BAC angular points aret equal assigned point axis base BC bisected called CEGDHF central distances change of place circle coincide throughout Constr demonstrated double equal straight lines equal to AC equal to EF equilateral triangle Euclid exterior angle extremities four right angles Geometry given straight line greater hard body inclose a space instance INTERC Intercalary Book ist equal join line AC magnitude manner meet opposite angles parallelogram parity of reasoning pass perpendicular prolonged Prop PROPOSITION proved quadrilateral radii radius rectilinear figure remain unmoved remaining angle remains at rest respectively Scholium self-rejoining line shown side BC side opposite situation sphere whose centre straight line BC tessera THEOREM.–If third side triangle ABC tryo turned unlimited length Wherefore willf

### 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.