## 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 56

Side 22

But

BE would also bef equal to AC, and it is not. And because

the point B is not equidistant from all the points in the surface of the sphere. And

in ...

But

**BC**ist equal to AC ; wherefore**BC**is not equal to BE; for if they were equal,BE would also bef equal to AC, and it is not. And because

**BC**is not equal to BE,the point B is not equidistant from all the points in the surface of the sphere. And

in ...

Side 33

For if this be disputed, let it be assumed that ABD is also a

as a centre, with the radii

In

For if this be disputed, let it be assumed that ABD is also a

**straight line**. About Bas a centre, with the radii

**BC**and BD respectively, describe" concentric spheres.In

**BC**take any point as E, between B and the surfaces of both these concentric ... Side 36

5 above) it may be multiplied [that is to say,

added one to another] any number of times, and ... For if

within the sphere whose centre is A, from any point outside as D let a

of D ...

5 above) it may be multiplied [that is to say,

**straight lines**equal to it may beadded one to another] any number of times, and ... For if

**BC**be any**straight line**within the sphere whose centre is A, from any point outside as D let a

**straight line**of D ...

Side 37

4, about the centre is” without change of place, the straight line BCG which cuts

the surface of the sphere after the last turning, cuts also the surface as it was

before the first turning. That is to say, the

the ...

4, about the centre is” without change of place, the straight line BCG which cuts

the surface of the sphere after the last turning, cuts also the surface as it was

before the first turning. That is to say, the

**straight line BC**being prolonged beforethe ...

Side 41

... self-rejoining line in which is the point A, and that if the figure MBQ was turned

round the

necessarily each greater than AC or

... self-rejoining line in which is the point A, and that if the figure MBQ was turned

round the

**straight line**MQ, the point B ... Because AR and BR are equal, they arenecessarily each greater than AC or

**BC**(unless the point R coincides with C, ...### Hva folk mener - Skriv en omtale

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### 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.