## 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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Resultat 1-5 av 12

Side 27

Two straight lines cannot

there would be two different straightlines. Which (by the Proposition above)

cannot be. CoR. 2. Any portion of a straight line is also a straight line. For

inasmuch as ...

Two straight lines cannot

**inclose a space**. For if they did, between two pointsthere would be two different straightlines. Which (by the Proposition above)

cannot be. CoR. 2. Any portion of a straight line is also a straight line. For

inasmuch as ...

Side 34

For, First : If they fail to coincide betnyeen the points, two INTERC.10: straight

lines must

afterwards fail to coincide beyond the points, to the extent of the length common

to both ...

For, First : If they fail to coincide betnyeen the points, two INTERC.10: straight

lines must

**inclose a space**; which ist impossible. Cor. 1. Secondly; If theyafterwards fail to coincide beyond the points, to the extent of the length common

to both ...

Side 45

... coincide in all that is nvithin the figure, then from two points [among the points

in which the planes coincide], may be drawn two straight lines [one in each of the

planes, in the parts where they do not coincidel, which shall

... coincide in all that is nvithin the figure, then from two points [among the points

in which the planes coincide], may be drawn two straight lines [one in each of the

planes, in the parts where they do not coincidel, which shall

**inclose a space**. Side 48

Two straight lines cannot

straight line. Two straight lines, which are not in one and the same line, cannot

have a common segment. If any two points in one straight line coincide with two ...

Two straight lines cannot

**inclose a space**. Any portion of a straight line is also astraight line. Two straight lines, which are not in one and the same line, cannot

have a common segment. If any two points in one straight line coincide with two ...

Side 67

... two straightlines would

which is E.; that is, on which is the angle that is less than the sum of two right

angles. CoR. 4. If any number of straight lines be added one to another in

succession ...

... two straightlines would

**inclose a space**. Therefore it shall pass on the side onwhich is E.; that is, on which is the angle that is less than the sum of two right

angles. CoR. 4. If any number of straight lines be added one to another in

succession ...

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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.