## 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 18

Side vii

These results , together with the proofs offered of what have usually been termed

the Axioms and Postulates , have been

view to facilitate their postponement in the case of students beginning geometry ...

These results , together with the proofs offered of what have usually been termed

the Axioms and Postulates , have been

**formed**into an Intercalary Book , with aview to facilitate their postponement in the case of students beginning geometry ...

Side ix

And this because , if a number of such figures are placed side by side , a straight

line of unlimited length which shall travel continuously from one of the angular

points in the series of bases , along the straight line

...

And this because , if a number of such figures are placed side by side , a straight

line of unlimited length which shall travel continuously from one of the angular

points in the series of bases , along the straight line

**formed**by the junction of two...

Side 14

... equal to the distance of any two points that shall have been assigned . For it

may be done as in Cor . 1 above . Cor . 3. When a sphere is described as above ,

the interior sphere , and the hollow one

... equal to the distance of any two points that shall have been assigned . For it

may be done as in Cor . 1 above . Cor . 3. When a sphere is described as above ,

the interior sphere , and the hollow one

**formed**by the substance out of which + 1. Side 23

... if the space about B were filled with some yielding substance like plaster , out

of which a sphere was to be

possible quantity of matter by the turning of the sphere A in different directions

about ...

... if the space about B were filled with some yielding substance like plaster , out

of which a sphere was to be

**formed**through the scraping away of the greatestpossible quantity of matter by the turning of the sphere A in different directions

about ...

Side 36

... on the contrary it shall without further notice be considered as prolonged to any

extent a motive may ever arise for desiring . Cor . 7. Any three points ( which are

not in the same straight line ) being joined , there shall be

...

... on the contrary it shall without further notice be considered as prolonged to any

extent a motive may ever arise for desiring . Cor . 7. Any three points ( which are

not in the same straight line ) being joined , there shall be

**formed**a three - sided...

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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.