## 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 34

Side ix

If a tessera ( or quadrilateral rectilinear plane figure of which two of the opposite

sides are equal to one another and make equal

between them which shall be called the base ] has the angles at the base less

than ...

If a tessera ( or quadrilateral rectilinear plane figure of which two of the opposite

sides are equal to one another and make equal

**interior**angles with a sidebetween them which shall be called the base ] has the angles at the base less

than ...

Side 14

be let the turning be continued in various directions as called for , until the line

AC shall have been applied to the entire surface of a solid ( as would be done if it

were employed to scoop out a hollow figure from the

be let the turning be continued in various directions as called for , until the line

AC shall have been applied to the entire surface of a solid ( as would be done if it

were employed to scoop out a hollow figure from the

**interior**of some yielding ... Side 15

And if their central distances are not equal , their surfaces will not coincide at all ,

but one be

coincide throughout or not at all . But if their central distances are equal , then two

...

And if their central distances are not equal , their surfaces will not coincide at all ,

but one be

**interior**to the other . For ( by Cor . 4 above ) their surfaces eithercoincide throughout or not at all . But if their central distances are equal , then two

...

Side 23

... traced by it a concentric sphere

Wherefore because it always meets INTERC . 3. the sphere BF but does not cut it

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

another ...

... traced by it a concentric sphere

**interior**to the sphere BF , and there is not .Wherefore because it always meets INTERC . 3. the sphere BF but does not cut it

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

another ...

Side 41

... the surfaces would ; coincide throughout and the spheres be Cor . 4 . equal ;

and if it did not coincide but was

cannot be , for it is the greater . And because C is a point within the sphere

described ...

... the surfaces would ; coincide throughout and the spheres be Cor . 4 . equal ;

and if it did not coincide but was

**interior**, the sphere would be the less , whichcannot be , for it is the greater . And because C is a point within the sphere

described ...

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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ... Thomas Perronet Thompson 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 added alternate angle ABC angle BAC applied aret assigned axis base bisected body Book called centre change of place circle coincide common consequently Constr continually demonstrated described distance double drawn equal Euclid exterior angle extremities fall figure follows formed four right angles Geometry given straight line greater half impossible instance INTERC interior join kind less magnitude manner meet moved Note opposite parallel parallelogram parity of reasoning pass perpendicular plane portion prolonged proof Prop PROPOSITION proved radius remaining angle respectively rest right angles Second self-rejoining line shown situation space sphere sphere whose centre square straight line succession surface taken terminated thing third side touch triangle triangle ABC true turned unequal universally Wherefore whole

### 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.