## 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 46

Side 33

About B as a centre, with the radii

spheres. In

concentric spheres on the

...

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 theseconcentric spheres on the

**side**of B which is towards C; and about B as a centre,...

Side 36

... and no point in any one

the sphere whose centre is A, from any point outside as D let a straight line of D ...

... and no point in any one

**side**, shall coincide with any point in either of the other**sides**, except the points which were joined. ... For if**BC**be any straight line withinthe sphere whose centre is A, from any point outside as D let a straight line of D ...

Side 53

But it has been shown that AC is equal to AB; therefore AC and

them equal to AB. And things ... There might, therefore, for all that has yet been

proved, be more equilateral triangles than one, describable on the same

AB.

But it has been shown that AC is equal to AB; therefore AC and

**BC**are each ofthem equal to AB. And things ... There might, therefore, for all that has yet been

proved, be more equilateral triangles than one, describable on the same

**side**ofAB.

Side 55

Wherefore from the point B. a straight line has been drawn, equal to

U.M.–It has not yet been proved, that there might not be more equilateral

triangles than one, described upon AB on the same

prolongations of ...

Wherefore from the point B. a straight line has been drawn, equal to

**BC**. ... SchollU.M.–It has not yet been proved, that there might not be more equilateral

triangles than one, described upon AB on the same

**side**, and that theprolongations of ...

Side 56

Let BAC, EDF be two triangles, which A. D have the two sides AB, AC of the one,

equal to the two sides DE, DF of the other respectively, viz. AB to DE, and AC to

DF; and the angle BAC equal to the angle EDF. The third

...

Let BAC, EDF be two triangles, which A. D have the two sides AB, AC of the one,

equal to the two sides DE, DF of the other respectively, viz. AB to DE, and AC to

DF; and the angle BAC equal to the angle EDF. The third

**side BC**shall be equal...

### 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.