## 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 viii

... better that they should be adopted without proof.” In labouring to get rid of

Axioms, the object has been to assail the belief in the existence of such things as

self-evident truths. Nothing is self-evident, except perhaps an identical

... better that they should be adopted without proof.” In labouring to get rid of

Axioms, the object has been to assail the belief in the existence of such things as

self-evident truths. Nothing is self-evident, except perhaps an identical

**proposition**. Side ix

The Axiom which declared the whole to be greater than its part, has been omitted

as amounting, after the explanation of the terms 'greater' and “less introduced

from Euclid's Book of Data, to no more than the

The Axiom which declared the whole to be greater than its part, has been omitted

as amounting, after the explanation of the terms 'greater' and “less introduced

from Euclid's Book of Data, to no more than the

**proposition**that ' the greatest is ... Side x

No

subsequently cited ; with the exception of the concluding one, and of a small

number the application of which in the following Books of Euclid, or other reason

for insertion, ...

No

**Proposition**or Corollary has been admitted throughout, which is notsubsequently cited ; with the exception of the concluding one, and of a small

number the application of which in the following Books of Euclid, or other reason

for insertion, ...

Side xi

F I R S T B O O K. (In the marginal references, the Roman numerals express the

Book; and the Arabic ones next following, the

expressed by INTERc.) NOMENCLATURE. I. AFTER a thing, or a class of things ...

F I R S T B O O K. (In the marginal references, the Roman numerals express the

Book; and the Arabic ones next following, the

**Proposition**. The Intercalary Book isexpressed by INTERc.) NOMENCLATURE. I. AFTER a thing, or a class of things ...

Side 2

An assertion which it is proposed to show to be true, is called a Theorem. An

operation which it is proposed to show how to perform, is called a Problem. And

both are called by the title of

...

An assertion which it is proposed to show to be true, is called a Theorem. An

operation which it is proposed to show how to perform, is called a Problem. And

both are called by the title of

**Propositions**. XIX. A**Proposition**dependent on some...

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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.