## 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 38

Side 14

Spheres are said to touch one another, which

Spheres described about the same centre, are called concentric. CoR. 2. A

sphere may be described about any centre, and with a central distance equal to

the ...

Spheres are said to touch one another, which

**meet**but do not cut one another.Spheres described about the same centre, are called concentric. CoR. 2. A

sphere may be described about any centre, and with a central distance equal to

the ...

Side 23

III); wherefore they

in ... Wherefore because it always

cut it, it always touchest it. And Nom. because the spheres A and BF touch one ...

III); wherefore they

**meet**. Also it does at no time cut the sphere BF; for if any pointin ... Wherefore because it always

**meets**; INTERc.3, the sphere BF but does notcut it, it always touchest it. And Nom. because the spheres A and BF touch one ...

Side 25

Wherefore if one of the spheres that touch one another, as BF, be imagined to

increase in magnitude and the other to decrease, till the sphere BF

point A, and vice versd, (the spheres during such process remaining ever in

contact); ...

Wherefore if one of the spheres that touch one another, as BF, be imagined to

increase in magnitude and the other to decrease, till the sphere BF

**meets**thepoint A, and vice versd, (the spheres during such process remaining ever in

contact); ...

Side 29

Because the spheres cut one another, the coincidence of their surfaces is not in a

point only; for if it was in a point only, the spheres would

another. And because the coincidence of the surfaces is not in a point, it is in a ...

Because the spheres cut one another, the coincidence of their surfaces is not in a

point only; for if it was in a point only, the spheres would

**meet**but not cut oneanother. And because the coincidence of the surfaces is not in a point, it is in a ...

Side 41

... they could

no where but in that point), and if they were less they could not

Wherefore the sphere described about the centre A with the radius AR, will bet

greater ...

... they could

**meet**in no point but C (inasmuch as the spheres AC and BC**meet**no where but in that point), and if they were less they could not

**meet**at all.Wherefore the sphere described about the centre A with the radius AR, will bet

greater ...

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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.