## 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 24

Side 34

6 . about F and G

the surface of both ; they will * cut one another in a Cor . self - rejoining line

passing through B , or else touch in B only . But whichever of these they do ...

6 . about F and G

**aret**equal but do not coincide , and the point B Interc.11 . is inthe surface of both ; they will * cut one another in a Cor . self - rejoining line

passing through B , or else touch in B only . But whichever of these they do ...

Side 54

And DA , DB , parts of them ,

equal to the remainder BG . Cor . 7 . But it has been shown that BC is equal to BG

; wherefore AL and BC are each of them equal to BG . And things which are ...

And DA , DB , parts of them ,

**aret**equal ; Interc . 1. therefore the remainder AL istequal to the remainder BG . Cor . 7 . But it has been shown that BC is equal to BG

; wherefore AL and BC are each of them equal to BG . And things which are ...

Side 56

... which is impossible , + Hyp . for they

AC is equal Hyp . to DF , the point C would coincide with the point F. But the point

B coincides with the point E ; wherefore ( the point B coin* INTERC , 12 . ciding ...

... which is impossible , + Hyp . for they

**aret**equal . And because the straight lineAC is equal Hyp . to DF , the point C would coincide with the point F. But the point

B coincides with the point E ; wherefore ( the point B coin* INTERC , 12 . ciding ...

Side 58

1. equal to the angle B ; therefore the angles A and C

And since the angles A and C are also equal to B , the angles A , B , C are all

equal to one another . PROPOSITION VI . | 1.3 . THEOREM . — If two angles of a

...

1. equal to the angle B ; therefore the angles A and C

**aret**equal to one another .And since the angles A and C are also equal to B , the angles A , B , C are all

equal to one another . PROPOSITION VI . | 1.3 . THEOREM . — If two angles of a

...

Side 63

6 . to H ; and because ABC is * a right angle , ABC and ABG

. Nom.37 . to one another ; and in like manner the angles DEF and DEHare equal

to one another . Let now the straight line CBG be applied to the straight line ...

6 . to H ; and because ABC is * a right angle , ABC and ABG

**aret**equal * Hyp . +1. Nom.37 . to one another ; and in like manner the angles DEF and DEHare equal

to one another . Let now the straight line CBG be applied to the straight line ...

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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.