## 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 28

Side xii

A surface ,

thickness , it would not be the boundary , but part of the solid . VI . That which

bounds a surface , is called a line . A line ,

A surface ,

**consequently**, has length and breadth , but not thickness . For if it hadthickness , it would not be the boundary , but part of the solid . VI . That which

bounds a surface , is called a line . A line ,

**consequently**, has length , but not ... Side 11

For if not , there would be a magnitude which they cannot pass ; and

26 . one another . Which cannot be , for they are equal . The assumption

therefore cannot be ...

For if not , there would be a magnitude which they cannot pass ; and

**consequently**( by Cor . 16 ) the magnitudes would not be all equal to + 1.Nom .26 . one another . Which cannot be , for they are equal . The assumption

therefore cannot be ...

Side 14

Wherefore the point A can be applied to every point in the described surface , the

point B remaining at rest ;

B , are equally distant | with A and B , or all the points in * 1.Nom.12 . the ...

Wherefore the point A can be applied to every point in the described surface , the

point B remaining at rest ;

**consequently**each point in the surface 11. Nom.ll. andB , are equally distant | with A and B , or all the points in * 1.Nom.12 . the ...

Side 27

... time turned about its own extreme points without change * Interc . 9. of place ,

and

equidistant points , are equal . And the extremities of equal straight lines are

equidistant .

... time turned about its own extreme points without change * Interc . 9. of place ,

and

**consequently**is a * straight line . CoR . 3. The straight lines betweenequidistant points , are equal . And the extremities of equal straight lines are

equidistant .

Side 30

[ The other half of CD is supposed to be on the other side the spheres , and

where but in CD , For if this be disputed , First Case ; let it be assumed that they ...

[ The other half of CD is supposed to be on the other side the spheres , and

**consequently**is not represented . ] The surfaces of the spheres shall coincide nowhere but in CD , For if this be disputed , First Case ; let it be assumed that they ...

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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.