## 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 23

Side vi

A surface of this

lines and planes may be inferred . If in this there is any novelty and truth , it is

surprising that a property which was the foundation of the Platonic notion of the ...

A surface of this

**kind**is called a plane . From these , all the relations of straightlines and planes may be inferred . If in this there is any novelty and truth , it is

surprising that a property which was the foundation of the Platonic notion of the ...

Side viii

It was therefore of evil example , that science of any

be founded on axioms ; and it is no answer to say , that in a particular case they

were true . The Second Book of Euclid would be true , if the First existed only in ...

It was therefore of evil example , that science of any

**kind**should be supposed tobe founded on axioms ; and it is no answer to say , that in a particular case they

were true . The Second Book of Euclid would be true , if the First existed only in ...

Side xii

Thus the extremity of a line in the black surface above , is a point ; which

manifestly has no dimensions of any

black scrawls , the point is in strictness the extremity of one of their edges . When

a point is ...

Thus the extremity of a line in the black surface above , is a point ; which

manifestly has no dimensions of any

**kind**. And if the lines are represented byblack scrawls , the point is in strictness the extremity of one of their edges . When

a point is ...

Side 1

Figures in general , as being things capable of being compared in point of

greatness with objects of their own

surfaces with surfaces , & c . ] , are called magnitudes . XIV . Magnitudes which if

their ...

Figures in general , as being things capable of being compared in point of

greatness with objects of their own

**kind**, [ that is to say , solids with solids ,surfaces with surfaces , & c . ] , are called magnitudes . XIV . Magnitudes which if

their ...

Side 5

What is called the contrary of a proposition is , when both the premises and the

conclusion are altered , not merely by the insertion of a negation , but by being

changed into something of a positively contrary

...

What is called the contrary of a proposition is , when both the premises and the

conclusion are altered , not merely by the insertion of a negation , but by being

changed into something of a positively contrary

**kind**. For example , if the original...

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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.