## 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 25

Side 26

A body or figure which is turned about two points in it that are also the

of a straight line, (inasmuch as the whole of the straight line remains without

change of place) is said to be turned round such straight line. When from any

point ...

A body or figure which is turned about two points in it that are also the

**extremities**of a straight line, (inasmuch as the whole of the straight line remains without

change of place) is said to be turned round such straight line. When from any

point ...

Side 27

someo. of place, and consequently is a” straight line. Oln. CoR. 3. The straight

lines between equidistant points, are equal. And the

lines are equidistant. +I.Nom ...

someo. of place, and consequently is a” straight line. Oln. CoR. 3. The straight

lines between equidistant points, are equal. And the

**extremities**of equal straightlines are equidistant. +I.Nom ...

Side 28

For it has been shown” how it may be described with a central " " distance equal

to the distance between any two points; therefore it may be described with a

central distance equal to the distance between the

radius.

For it has been shown” how it may be described with a central " " distance equal

to the distance between any two points; therefore it may be described with a

central distance equal to the distance between the

**extremities**of the proposedradius.

Side 33

... these concentric spheres on the side of B which is towards C; and about B as a

centre, with the radius BE, describe a sphere, whose surface (because it lies

within the surfaces which pass through the

BD.

... these concentric spheres on the side of B which is towards C; and about B as a

centre, with the radius BE, describe a sphere, whose surface (because it lies

within the surfaces which pass through the

**extremities**C and D) will cut BC andBD.

Side 35

Thirdly; If there be two straight lines A __B as AB and CD, and their

and C are made to coincide each with a several * D point between the

of the other A B line; the whole AD shall be a straight line. C D For if the line ...

Thirdly; If there be two straight lines A __B as AB and CD, and their

**extremities**Band C are made to coincide each with a several * D point between the

**extremities**of the other A B line; the whole AD shall be a straight line. C D For if the line ...

### 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.