## 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 quadrilateral rectilinear plane figure of which two of the

sides are equal to one another and make equal interior

between them which shall be called the base] has the

than right ...

If a tessera [or quadrilateral rectilinear plane figure of which two of the

**opposite**sides are equal to one another and make equal interior

**angles**with a sidebetween them which shall be called the base] has the

**angles**at the base !essthan right ...

Side 52

The side opposite to the right angle is called the hypotenuse. The other two sides

are ... For brevity, quadrilateral figures may be named by the letters at two of their

The side opposite to the right angle is called the hypotenuse. The other two sides

are ... For brevity, quadrilateral figures may be named by the letters at two of their

**opposite angles**, when no obscurity arises therefrom. LIV. Of polygons, such as ... Side 56

AB to DE, and AC to DF; and the

side BC shall be equal to the third side EF, and the triangle BAC to the triangle

EDF; and the other

...

AB to DE, and AC to DF; and the

**angle**BAC equal to the**angle**EDF. The thirdside BC shall be equal to the third side EF, and the triangle BAC to the triangle

EDF; and the other

**angles**, to which the equal sides are**opposite**, shall be equal...

Side 57

In any isoskeles triangle, the

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

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

Hyp. # I.4. BCF and CBG, are also equal; it follows that the remainders are” equal

, viz. the

isoskeles triangle the

another.

Hyp. # I.4. BCF and CBG, are also equal; it follows that the remainders are” equal

, viz. the

**angle**ACB equal to the**angle**ABC. ... Wherefore, universally, in anisoskeles triangle the

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

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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.