## 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 31

Side 1

Things which occupy the same place, are said to coincide. The only way in which

coincidence can actually be brought to

another or are in contact. Thus there is coincidence between the surface of a cast

and ...

Things which occupy the same place, are said to coincide. The only way in which

coincidence can actually be brought to

**pass**, is when the things touch oneanother or are in contact. Thus there is coincidence between the surface of a cast

and ...

Side 10

But if so, either MN is the smallest magnitude which they cannot

And if it is not, then there is some magnitude which may be cut off from it, and the

remainder be a magnitude which they cannot

But if so, either MN is the smallest magnitude which they cannot

**pass**, or it is not.And if it is not, then there is some magnitude which may be cut off from it, and the

remainder be a magnitude which they cannot

**pass**. Wherefore there will be ... Side 11

For if not, there would be a magnitude which they cannot

(by Cor. 16) the magnitudes would not be all equal to one another. Which cannot

be, for they are equal. The assumptiont therefore cannot be true; or there is not ...

For if not, there would be a magnitude which they cannot

**pass**; and consequently(by Cor. 16) the magnitudes would not be all equal to one another. Which cannot

be, for they are equal. The assumptiont therefore cannot be true; or there is not ...

Side 24

For if it did not, the surfaces of the spheres would at one instant coincide in some

point in fixed space and both of them

would not; which cannot be without one or both of the spheres having suffered ...

For if it did not, the surfaces of the spheres would at one instant coincide in some

point in fixed space and both of them

**pass**through it, and at another instant theywould not; which cannot be without one or both of the spheres having suffered ...

Side 26

When from any point to any other point, a straight line is described or made to

either end, in such manner that the whole continues to be a straight line, the

original ...

When from any point to any other point, a straight line is described or made to

**pass**; the two points are said to be joined. If to a straight line addition is made ateither end, in such manner that the whole continues to be a straight line, the

original ...

### 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.