## 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 27

All the

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

All the

**radii**of the same or equal spheres are equal. And spheres that have equal**radii**, are equal. * Constr. For all the points in the surface are” equidistant from thecentre ; wherefore (by Cor. 3 above) the straight lines from the centre to any ...

Side 28

Henceforward, mention will never be made of distances, but See Notc. always of

straight lines; nor of central distances, but always of

to be farther or nearer than some other, it shall always be understood that the ...

Henceforward, mention will never be made of distances, but See Notc. always of

straight lines; nor of central distances, but always of

**radii**. And if one point be saidto be farther or nearer than some other, it shall always be understood that the ...

Side 30

Let now the sphere whose centre is B, be turned about the point G, till its centre B

is applied to the centre A of the other sphere (which can be done inasmuch as

the

Let now the sphere whose centre is B, be turned about the point G, till its centre B

is applied to the centre A of the other sphere (which can be done inasmuch as

the

**radii**of these equal spheres are" equal); whereupon the surfaces of the two ... Side 33

About B as a centre, with the

spheres. In BC take any point as E, between B and the surfaces of both these

concentric spheres on the side of B which is towards C; and about B as a centre,

...

About B as a centre, with the

**radii**BC and BD respectively, describe" concentricspheres. In BC take any point as E, between B and the surfaces of both these

concentric spheres on the side of B which is towards C; and about B as a centre,

...

Side 38

... the straight line BA after the transposition will coincide with and occupy the

same place as AB did before, for if not, between the same two points there would

be +INTERc.10. two different straight lines, which cannott be; and because the

... the straight line BA after the transposition will coincide with and occupy the

same place as AB did before, for if not, between the same two points there would

be +INTERc.10. two different straight lines, which cannott be; and because the

**radii**...### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### Andre utgaver - Vis alle

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.