## 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 72

Side xii

... be

be represented. Nevertheless the application of one object to another will, when

required, be imagined to take place without bar of corporeal substance;—that is ...

... be

**shown**to be practicable with the hard body on which they are understood tobe represented. Nevertheless the application of one object to another will, when

required, be imagined to take place without bar of corporeal substance;—that is ...

Side 1

But besides this, there is an imaginary coincidence frequently appealed to by

geometers; which is, when it can be

the objects in question could be applied to one another without bar of corporeal ...

But besides this, there is an imaginary coincidence frequently appealed to by

geometers; which is, when it can be

**shown**that coincidence would take place, ifthe objects in question could be applied to one another without bar of corporeal ...

Side 3

When a thing is said to be so and so by parity of reasoning, the meaning is, that

what has been

same steps be

two ...

When a thing is said to be so and so by parity of reasoning, the meaning is, that

what has been

**shown**to be true in some previous instance, may by taking thesame steps be

**shown**to be true in this. Thus, if it has been**shown**that becausetwo ...

Side 5

For example, it is

than a right angle, the other two are necessarily less than right angles. The

converse of which is, that if two angles of a triangle are less than right angles, the

other is ...

For example, it is

**shown**in the sequel, that if one angle of a triangle is greaterthan a right angle, the other two are necessarily less than right angles. The

converse of which is, that if two angles of a triangle are less than right angles, the

other is ...

Side 17

... exhibited are hardt bodies. The assumption", therefore, which involves this

impossible consequence, cannot be true; or the two spheres cannot coincide in

the surface CEGDHF. And in like manner may be

coincide in ...

... exhibited are hardt bodies. The assumption", therefore, which involves this

impossible consequence, cannot be true; or the two spheres cannot coincide in

the surface CEGDHF. And in like manner may be

**shown**that they cannotcoincide in ...

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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.