## 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 104

PROPOSITION XXXIII. THEOREM.–The opposite sides and angles of every

it into trvo equal parts]. Let ACDB be a

diagonal.

PROPOSITION XXXIII. THEOREM.–The opposite sides and angles of every

**parallelogram**are equal to one another; and a diagonal bisects it [that is, dividesit into trvo equal parts]. Let ACDB be a

**parallelogram**, of which BC A B is adiagonal.

Side 105

And in the same way, if the angular points A and D were joined, might be shown

that the opposite sides and angles of the

diagonal from A to D likewise bisects the

And in the same way, if the angular points A and D were joined, might be shown

that the opposite sides and angles of the

**parallelogram**were equal, and that thediagonal from A to D likewise bisects the

**parallelogram**. And by parity of ... Side 106

DGH is" greater than DGI; and GI, which ist parallel to DE Hoor.l. and also lies

between GH and GD, being prolonged willf meet EH floor.o. between E and H, as

in I. Because DGIE is a

...

DGH is" greater than DGI; and GI, which ist parallel to DE Hoor.l. and also lies

between GH and GD, being prolonged willf meet EH floor.o. between E and H, as

in I. Because DGIE is a

**parallelogram**, + or. GI ist equal to DE, and consequentlyi...

Side 107

Which was to be demonstrated. PROPOSITION XXXIV bis. THEOREM.–Every

quadrilateral rectilinear figure, of nhich the See Note. opposite sides are equal to

one another, is a

figure, ...

Which was to be demonstrated. PROPOSITION XXXIV bis. THEOREM.–Every

quadrilateral rectilinear figure, of nhich the See Note. opposite sides are equal to

one another, is a

**parallelogram**. Let ACDB be a quadrilateral rectilinear A Bfigure, ...

Side 108

For, because the quadrilateral figure (by the Prop. above) is a

opposite angles are" equal to one another; wherefore if one of the angles be a

right angle, the angle opposite to it will also be a right angle, and the two together

...

For, because the quadrilateral figure (by the Prop. above) is a

**parallelogram**, theopposite angles are" equal to one another; wherefore if one of the angles be a

right angle, the angle opposite to it will also be a right angle, and the two together

...

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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.