## 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 33

Side 53

To describe an equilateral

straight line. ... 9 instance C) drawf the straight lines CA, CB, to the points A and

Or. - e B.

To describe an equilateral

**triangle**upon a given straight line. Let AB be the givenstraight line. ... 9 instance C) drawf the straight lines CA, CB, to the points A and

Or. - e B.

**ABC**shall be an equilateral**triangle**. Because the point A is the centre ... Side 56

If two

respectively; and have also the angles ... to which the equal sides are opposite,

shall be equal respectively, viz. the angle

ACB to the ...

If two

**triangles**have two sides of the one, equal to two sides of the otherrespectively; and have also the angles ... to which the equal sides are opposite,

shall be equal respectively, viz. the angle

**ABC**to the angle DEF, and the angleACB to the ...

Side 57

In any isoskeles

another. Let BAC be an isoskeles

The angles ACB and

...

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

BCF and CBG, are also equal; it follows that the remainders are” equal, viz. the

angle ACB equal to the angle

proved in every other instance. Wherefore, universally, in an isoskeles

the ...

BCF and CBG, are also equal; it follows that the remainders are” equal, viz. the

angle ACB equal to the angle

**ABC**. And by parity of reasoning, the like may beproved in every other instance. Wherefore, universally, in an isoskeles

**triangle**the ...

Side 59

Every equiangular

the angles are equal to one another, then because the angles A and B are equal,

the side CB (by Prop. VI above) is equal to the side CA. Again, because the ...

Every equiangular

**triangle**is also equilateral. For if**ABC**be a**triangle**of which allthe angles are equal to one another, then because the angles A and B are equal,

the side CB (by Prop. VI above) is equal to the side CA. Again, because the ...

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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.