## 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 33

Side viii

The Second Book of Euclid would be

the heads of the Propositions under the title of Axioms ; but this would make a

most lame and imperfect specimen of reasoning . The ways in which the Axioms

...

The Second Book of Euclid would be

**true**, if the First existed only in the shape ofthe heads of the Propositions under the title of Axioms ; but this would make a

most lame and imperfect specimen of reasoning . The ways in which the Axioms

...

Side 2

An assertion which it is proposed to show to be

operation which it is proposed to show how to perform , is called a Problem . And

both are called by the title of Propositions . XIX . A Proposition dependent on

some ...

An assertion which it is proposed to show to be

**true**, is called a Theorem . Anoperation which it is proposed to show how to perform , is called a Problem . And

both are called by the title of Propositions . XIX . A Proposition dependent on

some ...

Side 3

When a thing is said to be so and so by parity of reasoning , the meaning is , that

what has been shown to be

same steps be shown to be

...

When a thing is said to be so and so by parity of reasoning , the meaning is , that

what has been shown to be

**true**in some previous instance , may by taking thesame steps be shown to be

**true**in this . Thus , if it has been shown that because...

Side 4

propositions as are only known to be

has actually been made . For example , a cooper knows that in every instance

where he has tried it , the distance that went exactly round the rim of his cask at

six ...

propositions as are only known to be

**true**in the instances in which experimenthas actually been made . For example , a cooper knows that in every instance

where he has tried it , the distance that went exactly round the rim of his cask at

six ...

Side 5

Neither the converse , the negative , nor the contrary of any proposition , is to be

admitted to be

this be done , it is impossible to know whether it is

Neither the converse , the negative , nor the contrary of any proposition , is to be

admitted to be

**true**, till it has been demonstrated as a distinct proposition . For tillthis be done , it is impossible to know whether it is

**true**or not . For example , it is ...### Hva folk mener - Skriv en omtale

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### Andre utgaver - Vis alle

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.