## 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 58

Side vi

... on the whole being turned about 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

... on the whole being turned about 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. Side viii

On the whole therefore it may be an interesting question in what place a

geometer would be warranted in saying, ' I could have

, but it would have been necessary to disturb the order which directs that lines be

...

On the whole therefore it may be an interesting question in what place a

geometer would be warranted in saying, ' I could have

**proved**these preliminaries, but it would have been necessary to disturb the order which directs that lines be

...

Side 6

... the like may be

magnitudes which are equal to the same, are equal to one another. Which was to

be demonstrated. CoRollARY 1. If of equals, one be equal to some thing else, the

rest ...

... the like may be

**proved**in every other instance. Wherefore, universally,magnitudes which are equal to the same, are equal to one another. Which was to

be demonstrated. CoRollARY 1. If of equals, one be equal to some thing else, the

rest ...

Side 7

than C; therefore (as has been

is less than A. And in a similar manner if C were greater than B. CoR. 3.

Magnitudes which are equal to equals, are equal to one another. Let A be equal

to B, and ...

than C; therefore (as has been

**proved**above) A also is greater than C; that is, Cis less than A. And in a similar manner if C were greater than B. CoR. 3.

Magnitudes which are equal to equals, are equal to one another. Let A be equal

to B, and ...

Side 10

If the same is to be

are to be taken two, three, &c. magnitudes, equal to it. CoR. 15. If there be two

unequal magnitudes, and from the double of the greater be taken the double of ...

If the same is to be

**proved**of the trebles, quadruples, &c., then to each magnitudeare to be taken two, three, &c. magnitudes, equal to it. CoR. 15. If there be two

unequal magnitudes, and from the double of the greater be taken the double of ...

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### Andre utgaver - Vis alle

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.