## 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 58

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

, viz. the

triangle be prolonged, the two

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. ... If two equal sides of any isoskelestriangle be prolonged, the two

**angles exterior**to the third side shall be equal. Side 69

For any other would divide the angle BAC into two angles, one greater than the

half and the other less; which cannot be equal. ... If one side of a triangle be

prolonged, the

For any other would divide the angle BAC into two angles, one greater than the

half and the other less; which cannot be equal. ... If one side of a triangle be

prolonged, the

**exterior angle**is greater than either of the interior opposite angles. Side 70

2. the remaining angles of the triangle AEB are equal to the remaining angles of

the triangle CEF respectively, viz. those to which the ... And in the same way may

be shown that any other

...

2. the remaining angles of the triangle AEB are equal to the remaining angles of

the triangle CEF respectively, viz. those to which the ... And in the same way may

be shown that any other

**exterior angle**made by prolonging a side of the triangle...

Side 71

The angle ABC is greater than the angle ACB. Since AC is greater than AB, make

" AD B C equal to AB; and join BD. Because ADB is the

triangle BDC, it ist greater than the interior opposite angle DCB. But because AD

is: ...

The angle ABC is greater than the angle ACB. Since AC is greater than AB, make

" AD B C equal to AB; and join BD. Because ADB is the

**exterior angle**of thetriangle BDC, it ist greater than the interior opposite angle DCB. But because AD

is: ...

Side 73

Again, because the

opposite angle, the

angle EAB. And for the same reason the

is greater ...

Again, because the

**exterior angle**of a triangle is" greater than the interioropposite angle, the

**exterior angle**DEC of the triangle EAB is greater than theangle EAB. And for the same reason the

**exterior angle**BDC of the triangle DECis greater ...

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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.