## 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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Resultat 1-5 av 21

Side 33

... point B, are turned about their centres which remain at rest, and consequently

the spheres

straight line; about F as a centre, with a radius

sphere.

... point B, are turned about their centres which remain at rest, and consequently

the spheres

**aret**without change of place; and if these ... If then ABD is also astraight line; about F as a centre, with a radius

**equal**to FB or EB, describet asphere.

Side 54

And DA, DB, parts of them,

equal to the remainder B.G. Cor. 7. But it has been shown that BC is equal to BG ;

wherefore AL and BC are each of them equal to BG. And things which are ...

And DA, DB, parts of them,

**aret equal**; f INTERC. I. therefore the remainder AL istequal to the remainder B.G. Cor. 7. But it has been shown that BC is equal to BG ;

wherefore AL and BC are each of them equal to BG. And things which are ...

Side 56

If two triangles have two sides of the one, equal to two sides of the other

respectively; and have also the angles belneen ... to both ; for if it did not, the

angle BAC would be either greater or less than EDF, which is impossible, for they

If two triangles have two sides of the one, equal to two sides of the other

respectively; and have also the angles belneen ... to both ; for if it did not, the

angle BAC would be either greater or less than EDF, which is impossible, for they

**aret equal**. Side 58

BCF and CBG, are also equal; it follows that the remainders are” equal, viz. the

angle ACB equal to the angle ABC. ... equal to the angle B. But the angle A also

was equal to the angle B; therefore the angles A and C

BCF and CBG, are also equal; it follows that the remainders are” equal, viz. the

angle ACB equal to the angle ABC. ... equal to the angle B. But the angle A also

was equal to the angle B; therefore the angles A and C

**aret equal**to one another. Side 63

All right angles are equal to one another. Let ABC, DEF be two right A DI angles.

They are equal to one another. Prolongs CB to G, and FE C B G F E H to H; and

because ABC is a right angle, ABC and ABG

All right angles are equal to one another. Let ABC, DEF be two right A DI angles.

They are equal to one another. Prolongs CB to G, and FE C B G F E H to H; and

because ABC is a right angle, ABC and ABG

**aret equal**to one another; and in ...### Hva folk mener - Skriv en omtale

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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.