## 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 14

Side 11

... and over ] so as at length to become greater than AB ; for on each doubling is

added a

of C. Let C be doubled successively till the result , as DG , is greater than AB .

... and over ] so as at length to become greater than AB ; for on each doubling is

added a

**portion**as great or greater than the**portion**added by the simple additionof C. Let C be doubled successively till the result , as DG , is greater than AB .

Side 17

Let then the sphere whose centre is A , be turnedt about A , till the

surface which was originally in the ... and because the spheres will still coincide

in CEGDHF and not elsewhere , the

Let then the sphere whose centre is A , be turnedt about A , till the

**portion**of itssurface which was originally in the ... and because the spheres will still coincide

in CEGDHF and not elsewhere , the

**portion**CESF of IESF will coincide with the ... Side 18

... E and F only , and their

so posited , that if the

other line , the

... E and F only , and their

**portions**which are on different sides of those points areso posited , that if the

**portion**EKF of the one line lie above the**portion**EIF of theother line , the

**portion**ETF of the first also lies above the**portion**ESF of Fig . 2 . Side 23

In the surface of the sphere A , in that

described about B , let any point be taken , as D. But when the point A ( in the

process of describing a sphere about B as above ) was made to describe a line ,

the ...

In the surface of the sphere A , in that

**portion**of it which is within the sphere sodescribed about B , let any point be taken , as D. But when the point A ( in the

process of describing a sphere about B as above ) was made to describe a line ,

the ...

Side 27

Any

turned about its extreme points , every point in it is without change of place ;

every

...

Any

**portion**of a straight line is also a straight line . For inasmuch as when it isturned about its extreme points , every point in it is without change of place ;

every

**portion**of it is at the same time turned about its own extreme points without...

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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.