## 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 41

Side 26

... pass; the two points are said to be joined. If to a straight line addition is made at

either end, in such manner that the whole continues to be a straight line, the

original straight line is said to See Note: be

called ...

... pass; the two points are said to be joined. If to a straight line addition is made at

either end, in such manner that the whole continues to be a straight line, the

original straight line is said to See Note: be

**prolonged**, and the part added iscalled ...

Side 36

A terminated straight line may be

by Cor. 5 above) it may be multiplied [that is to say, straight lines equal to it may

be added one to another] any number of times, and the whole be one straight line

.

A terminated straight line may be

**prolonged**to any length in a straight line. For (by Cor. 5 above) it may be multiplied [that is to say, straight lines equal to it may

be added one to another] any number of times, and the whole be one straight line

.

Side 37

That is to say, the straight line BC being

łINTERc.10. Cor. 6. {INTERC.10. Cor. 4 *INTERC. 5. #INTERC. 9. Cor. :INTERC.

10. Cor. 7. *INTERC.10. Cor. 4. the surface. PROPOSITION XIII. PROBLEM.

That is to say, the straight line BC being

**prolonged**before the first turning, cutsłINTERc.10. Cor. 6. {INTERC.10. Cor. 4 *INTERC. 5. #INTERC. 9. Cor. :INTERC.

10. Cor. 7. *INTERC.10. Cor. 4. the surface. PROPOSITION XIII. PROBLEM.

Side 38

and let CF bef

spheres BFGH and AFIH be united as one #INTERc. 9, body, and together with

the straight line CL be turned round; the Nom. straight line AB which remains at

rest.

and let CF bef

**prolonged**to an unlimited length on the side " of L. Let then thespheres BFGH and AFIH be united as one #INTERc. 9, body, and together with

the straight line CL be turned round; the Nom. straight line AB which remains at

rest.

Side 42

And if from M be drawn a straight line to any other point in MQCP, and

to an unlimited length, in like manner may be shown that every point in this

straight line or in its prolongation either way, is in the surface described by CL.

And if from M be drawn a straight line to any other point in MQCP, and

**prolonged**to an unlimited length, in like manner may be shown that every point in this

straight line or in its prolongation either way, is in the surface described by CL.

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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.