## 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 ix

If a tessera [or

sides are equal to one another and make equal interior angles with a side

between them which shall be called the base] has the angles at the base !ess

than right ...

If a tessera [or

**quadrilateral**rectilinear plane figure of which two of the oppositesides are equal to one another and make equal interior angles with a side

between them which shall be called the base] has the angles at the base !ess

than right ...

Side 51

Those contained by four straight lines, are called

contained by more than four, are called polygons. Figures in which a number of

sides is specified or intimated, are always understood to be rectilinear, when the

...

Those contained by four straight lines, are called

**quadrilateral**. XLV. Thosecontained by more than four, are called polygons. Figures in which a number of

sides is specified or intimated, are always understood to be rectilinear, when the

...

Side 52

The nomenclature of the various kinds of

propriety be given, till these figures have been shown to be capable of

possessing certain properties from which their distinctions are derived. It is

therefore to be found ...

The nomenclature of the various kinds of

**quadrilateral**figures cannot withpropriety be given, till these figures have been shown to be capable of

possessing certain properties from which their distinctions are derived. It is

therefore to be found ...

Side 84

... but the two equal straight lines do not meet; and the extremities of the two

equal straight lines be joined ; there shall be formed a

side of the base on mhich are the angles each less than the sum of two right

angles; ...

... but the two equal straight lines do not meet; and the extremities of the two

equal straight lines be joined ; there shall be formed a

**quadrilateral**figure, on thatside of the base on mhich are the angles each less than the sum of two right

angles; ...

Side 85

There shall be formed a

are the angles BAD and ABC; of which the angles ADC, BCD, which are opposite

to AB, shall be equal to one another, and each less than the sum of two right ...

There shall be formed a

**quadrilateral**figure ABCD, on the side of AB on whichare the angles BAD and ABC; of which the angles ADC, BCD, which are opposite

to AB, shall be equal to one another, and each less than the sum of two right ...

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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.