## 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 32

Side vi

... the two centres of the spheres , will describe a surface in which any two points

being

may be proved to lie wholly in that surface . A surface of this kind is called a plane

.

... the two centres of the spheres , will describe a surface in which any two points

being

**taken**, the straight line between them , with its prolongation either way ,may be proved to lie wholly in that surface . A surface of this kind is called a plane

.

Side xii

When a point is directed to be

extremity , it may be imagined to be determined by causing See Note . the line to

terminate at that point . See Note . VIII . Anything that has boundaries which are

fixed ...

When a point is directed to be

**taken**in some part of a line which is not theextremity , it may be imagined to be determined by causing See Note . the line to

terminate at that point . See Note . VIII . Anything that has boundaries which are

fixed ...

Side 2

To which is Added an Appendix ... Thomas Perronet Thompson. See Note . See

Note . XV . A magnitude is said to be greater than another by a certain magnitude

, when this last - mentioned magnitude being

To which is Added an Appendix ... Thomas Perronet Thompson. See Note . See

Note . XV . A magnitude is said to be greater than another by a certain magnitude

, when this last - mentioned magnitude being

**taken**from the first , the remainder ... Side 4

For example , a cooper knows that in every instance where he has tried it , the

distance that went exactly round the rim of his cask at six times , was the distance

to be

For example , a cooper knows that in every instance where he has tried it , the

distance that went exactly round the rim of his cask at six times , was the distance

to be

**taken**in his compasses in order to describe the head that would fit . But he ... Side 5

its separate enunciation , specification , construction , & c . , the which ,

together , amount to the establishment of the universal proposition . XXX . What is

called the converse of a proposition is , when the premises and the conclusion

are ...

its separate enunciation , specification , construction , & c . , the which ,

**taken**together , amount to the establishment of the universal proposition . XXX . What is

called the converse of a proposition is , when the premises and the conclusion

are ...

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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.