## 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 iii

Being an attempt to get rid of Axioms and Postulates ; and particularly to establish

the Theory of

previous demonstration . In the present Edition the part relating to

Being an attempt to get rid of Axioms and Postulates ; and particularly to establish

the Theory of

**Parallel**Lines without recourse to any principle not grounded onprevious demonstration . In the present Edition the part relating to

**Parallel**Lines ... Side v

In the preceding Editions endeavour had been made to get rid of Axioms , and

particularly to establish the Theory of

principle not grounded on previous demonstration . On showing the results to

some of ...

In the preceding Editions endeavour had been made to get rid of Axioms , and

particularly to establish the Theory of

**Parallel**Lines without recourse to anyprinciple not grounded on previous demonstration . On showing the results to

some of ...

Side vii

But there are others where the reasoning depends altogether on the supposition

of a continuity of motion ; as , notably , in the very pinch and nip of the argument

on

But there are others where the reasoning depends altogether on the supposition

of a continuity of motion ; as , notably , in the very pinch and nip of the argument

on

**Parallel**Lines in Prop . XXVIII D in the First Book , where the conclusion ... Side ix

In the present Edition , the part relating to the disputed principle of

has been reduced in bulk to one half , and in substance to the following . If a

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

sides ...

In the present Edition , the part relating to the disputed principle of

**Parallel**Lineshas been reduced in bulk to one half , and in substance to the following . If a

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

sides ...

Side 82

Straight lines which are in the same plane , and which being prolonged ever so

far both ways do not meet , are called

upon two other straight lines which are both in the same plane , makes the

alternate ...

Straight lines which are in the same plane , and which being prolonged ever so

far both ways do not meet , are called

**parallel**. CoR . 1. If a straight line fallingupon two other straight lines which are both in the same plane , makes the

alternate ...

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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.