## 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 56

If two triangles have two sides of the one, equal to two sides of the other

respectively; and have also the angles belneen those sides, equal to one another

; they shall have ... AB to DE, and AC to DF; and the

angle EDF.

If two triangles have two sides of the one, equal to two sides of the other

respectively; and have also the angles belneen those sides, equal to one another

; they shall have ... AB to DE, and AC to DF; and the

**angle BAC**equal to theangle EDF.

Side 57

In any isoskeles triangle, the

another. Let

The

...

In any isoskeles triangle, the

**angles**opposite to two equal sides are equal to oneanother. Let

**BAC**be an isoskeles triangle, of which the side AB is equal to AC.The

**angles**ACB and ABC shall be equal to one another. - Prolong* AB and AC to...

Side 58

THEOREM.–If two

opposite to the two equal

triangle having the

the side CA.

THEOREM.–If two

**angles**of a triangle are equal to one another, the sidesopposite to the two equal

**angles**are equal to one another. A Let**BAC**be atriangle having the

**angle**ACB D equal to the**angle**ABC ; the side BA is equal tothe side CA.

Side 61

... of the other; and the two triangles shall be equal; and their other

be equal respectively, viz. those to mhich equal sides are opposite. Let

be two triangles, D. G. having the two sides BA, AC, equal to A the two sides DE,

...

... of the other; and the two triangles shall be equal; and their other

**angles**shallbe equal respectively, viz. those to mhich equal sides are opposite. Let

**BAC**, EDFbe two triangles, D. G. having the two sides BA, AC, equal to A the two sides DE,

...

Side 68

To bisect a given

given

two A right

To bisect a given

**angle**. [That is, to divide it into tno equal**angles**.] Let**BAC**be thegiven

**angle**. It is required G to bisect it. First Case; if**BAC**is less than the sum oftwo A right

**angles**. Take any point D in AB, and from AC cut off” AE equal to AD.### Hva folk mener - Skriv en omtale

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### 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.