## 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 39

Side vi

A solid may be described , all the points in whose

from a given point within ; such a solid is called a sphere . A sphere may be

turned in any manner whatsoever about its centre , without change of place .

A solid may be described , all the points in whose

**surface**shall be equidistantfrom a given point within ; such a solid is called a sphere . A sphere may be

turned in any manner whatsoever about its centre , without change of place .

Side x

The latest innovation has been the assertion , that an angle ( or the thing spoken

of under that term by geometers whether they knew it or not , ) is a plane

an alteration which will probably be considered as among the most violent in ...

The latest innovation has been the assertion , that an angle ( or the thing spoken

of under that term by geometers whether they knew it or not , ) is a plane

**surface**;an alteration which will probably be considered as among the most violent in ...

Side xii

V. That which bounds a solid , is called a

length and breadth , but not thickness . For if it had thickness , it would not be the

boundary , but part of the solid . VI . That which bounds a

V. That which bounds a solid , is called a

**surface**. A**surface**, consequently , haslength and breadth , but not thickness . For if it had thickness , it would not be the

boundary , but part of the solid . VI . That which bounds a

**surface**, is called a ... Side 1

Thus there is coincidence between the

mould which contains it . And in like manner two lines or points may actually

touch one another and coincide . But besides this , there is an imaginary

coincidence ...

Thus there is coincidence between the

**surface**of a cast and the**surface**of themould which contains it . And in like manner two lines or points may actually

touch one another and coincide . But besides this , there is an imaginary

coincidence ...

Side 13

Any solid ,

any two points , in it ; such point or points remaining unmoved . For it is supposed

to be represented on a hard body which may be so turned . PROPOSITION III .

Any solid ,

**surface**, line , or figure , may be turned about any one point , or aboutany two points , in it ; such point or points remaining unmoved . For it is supposed

to be represented on a hard body which may be so turned . PROPOSITION III .

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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.