## 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 59

Side ix

Whence may be inferred that the three angles of every triangle are not less than

two

has been extended and rigidly adhered to , for the express purpose of protesting

...

Whence may be inferred that the three angles of every triangle are not less than

two

**right angles**; and Euclid's Axion . The formula of generalization ( see p . 5 )has been extended and rigidly adhered to , for the express purpose of protesting

...

Side 5

For example , it is shown in the sequel , that if one angle of a triangle is greater

than a

converse of which is , that if two angles of a triangle are less than

the ...

For example , it is shown in the sequel , that if one angle of a triangle is greater

than a

**right angle**, the other two are necessarily less than**right angles**. Theconverse of which is , that if two angles of a triangle are less than

**right angles**,the ...

Side 51

But whenever the contrary is not expressed , it is always the direct angle that is

meant . XXXVII . When a straight line standing on another straight line makes the

adjacent angles equal to one another , each of the angles is called a

But whenever the contrary is not expressed , it is always the direct angle that is

meant . XXXVII . 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**. Side 52

A triangle which has a

the

called the base and perpendicular . XLIX . A triangle which has an obtuse angle ,

is ...

A triangle which has a

**right angle**, is called**right**-**angled**. The side opposite tothe

**right angle**is called the hypotenuse . The other two sides are sometimescalled the base and perpendicular . XLIX . A triangle which has an obtuse angle ,

is ...

Side 62

Cor.2 . the anles BAF and ABF are * equal to one another , and AF and BF meet

in F , the angles BAF and ABF are respectively less than ... To draw a straight line

at

Cor.2 . the anles BAF and ABF are * equal to one another , and AF and BF meet

in F , the angles BAF and ABF are respectively less than ... To draw a straight line

at

**right angles**to an assigned straight line , from an assigned point in the same .### Hva folk mener - Skriv en omtale

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### Andre utgaver - Vis alle

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.