## 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 ... |

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Resultat 1-5 av 50

Side 3

When the parity of reasoning is extended to all instances to which the proposition

is capable of being applied , ( or in other words , to all which come under its terms

) , the proposition is said to be established

When the parity of reasoning is extended to all instances to which the proposition

is capable of being applied , ( or in other words , to all which come under its terms

) , the proposition is said to be established

**universally**. And a proposition so ... Side 6

...

another . Which was to be demonstrated . COROLLARY 1. If of equals , one be

equal to some thing else , the rest are severally equal to the same . Let A and B

be equal ...

...

**universally**, magnitudes which are equal to the same , are equal to oneanother . Which was to be demonstrated . COROLLARY 1. If of equals , one be

equal to some thing else , the rest are severally equal to the same . Let A and B

be equal ...

Side 13

Wherefore ,

to be demonstrated . Cor . Any solid , surface , line , or figure , may be turned

about any one point , or about any two points , in it ; such point or points

remaining ...

Wherefore ,

**universally**, a hard body may be See Note . turned & c . Which wasto be demonstrated . Cor . Any solid , surface , line , or figure , may be turned

about any one point , or about any two points , in it ; such point or points

remaining ...

Side 16

Wherefore ,

demonstrated . INT PROPOSITION V. THEOREM . - If two spheres touch one

another externally , they touch only in a point . Let there be two spheres whose

centres are A and ...

Wherefore ,

**universally**, if a sphere be turned & c . Which was to bedemonstrated . INT PROPOSITION V. THEOREM . - If two spheres touch one

another externally , they touch only in a point . Let there be two spheres whose

centres are A and ...

Side 21

... in any line , nor in any insulated points more than one at a time ; they can touch

only in a point . And by parity of reasoning , the like may be proved of any other

spheres . Wherefore ,

... in any line , nor in any insulated points more than one at a time ; they can touch

only in a point . And by parity of reasoning , the like may be proved of any other

spheres . Wherefore ,

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### Andre utgaver - Vis alle

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.