## 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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Side vi

A solid may be described, all the points in whose surface shall be equidistant

from a given point within ; such a solid is

turned in any manner whatsoever about its centre, without change of place.

A solid may be described, all the points in whose surface shall be equidistant

from a given point within ; such a solid is

**called**a sphere. A sphere may beturned in any manner whatsoever about its centre, without change of place.

Side ix

If a tessera [or quadrilateral rectilinear plane figure of which two of the opposite

sides are equal to one another and make equal interior angles with a side

between them which shall be

than right ...

If a tessera [or quadrilateral rectilinear plane figure of which two of the opposite

sides are equal to one another and make equal interior angles with a side

between them which shall be

**called**the base] has the angles at the base !essthan right ...

Side xi

science, is

, is

at least by any force there is question of employing; is

science, is

**called**Nomenclature. II. Anything that can be made the object of touch, is

**called**a body. III. A body whose particles are immoveable among themselves,at least by any force there is question of employing; is

**called**a hard body. IV. Side xii

V. That which bounds a solid, is

length and breadth, but not thickness. For if it had thickness, it would not be the

boundary, but part of the solid. VI. That which bounds a surface, is

V. That which bounds a solid, is

**called**a surface. A surface, consequently, haslength and breadth, but not thickness. For if it had thickness, it would not be the

boundary, but part of the solid. VI. That which bounds a surface, is

**called**a line. Side 1

are

one another, would coincide; or might be made capable of doing so, by a

different arrangement of parts; are

See ...

are

**called**magnitudes. XIV. Magnitudes which if their boundaries were applied toone another, would coincide; or might be made capable of doing so, by a

different arrangement of parts; are

**called**equal. See Note. See Note. See Note,See ...

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Geometry Without Axioms Or the First Book Euclid's Elements: With ... 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 adjacent angles alternate angles angle ABC angle ACB angle BAC angular points aret equal assigned point axis base BC bisected called CEGDHF central distances change of place circle coincide throughout Constr demonstrated double equal straight lines equal to AC equal to EF equilateral triangle Euclid exterior angle extremities four right angles Geometry given straight line greater hard body inclose a space instance INTERC Intercalary Book ist equal join line AC magnitude manner meet opposite angles parallelogram parity of reasoning pass perpendicular prolonged Prop PROPOSITION proved quadrilateral radii radius rectilinear figure remain unmoved remaining angle remains at rest respectively Scholium self-rejoining line shown side BC side opposite situation sphere whose centre straight line BC tessera THEOREM.–If third side triangle ABC tryo turned unlimited length Wherefore willf

### 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.