## 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 ... |

### Inni boken

Resultat 1-5 av 25

Side ix

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 side

between them which shall be called the

than ...

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 side

between them which shall be called the

**base**] has the angles at the**base**lessthan ...

Side 52

The other two sides are sometimes called the

triangle which has an obtuse angle , is called obtuse - angled . L. A triangle

which has all its angles acute , is called acule - angled . LI . A triangle which has

all its ...

The other two sides are sometimes called the

**base**and perpendicular . XLIX . Atriangle which has an obtuse angle , is called obtuse - angled . L. A triangle

which has all its angles acute , is called acule - angled . LI . A triangle which has

all its ...

Side 84

If from the ends of a given straight line [ which shall for distinction be called the

making equal interior angles at the

If from the ends of a given straight line [ which shall for distinction be called the

**base**) , two straight lines equal to one another be drawn towards the same side ,making equal interior angles at the

**base**, each less than the sum of two right ... Side 86

The side of the quadrilateral figure which is opposite to the

right angles by the perpendicular drawn from the middle of the

parallel to the

Constr .

The side of the quadrilateral figure which is opposite to the

**base**, is bisected atright angles by the perpendicular drawn from the middle of the

**base**; and isparallel to the

**base**. For it has been shown that EF bisects DC at right angles .Constr .

Side 88

Again , because at the ends of the • Hyp .

lines AB , CE , making with + Hyp . AC the equalt angles CAB , ACE , each of

which is less than the sum of two right angles ; BACE is a tessera , and the

angles ...

Again , because at the ends of the • Hyp .

**base**AC are drawn * two equal straightlines AB , CE , making with + Hyp . AC the equalt angles CAB , ACE , each of

which is less than the sum of two right angles ; BACE is a tessera , and the

angles ...

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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ... Thomas Perronet Thompson 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 added alternate angle ABC angle BAC applied aret assigned axis base bisected body Book called centre change of place circle coincide common consequently Constr continually demonstrated described distance double drawn equal Euclid exterior angle extremities fall figure follows formed four right angles Geometry given straight line greater half impossible instance INTERC interior join kind less magnitude manner meet moved Note opposite parallel parallelogram parity of reasoning pass perpendicular plane portion prolonged proof Prop PROPOSITION proved radius remaining angle respectively rest right angles Second self-rejoining line shown situation space sphere sphere whose centre square straight line succession surface taken terminated thing third side touch triangle triangle ABC true turned unequal universally Wherefore whole

### 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.