## 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 18

Side x

The latest innovation has been the assertion , that an angle ( or the

of under that term by geometers whether they knew it or not , ) is a plane surface ;

an alteration which will probably be considered as among the most violent in ...

The latest innovation has been the assertion , that an angle ( or the

**thing**spokenof under that term by geometers whether they knew it or not , ) is a plane surface ;

an alteration which will probably be considered as among the most violent in ...

Side xi

NOMENCLATURE . 1. AFTER a

obvious to the senses , and either by speech , writing , pictorial representation , or

examination in its proper substance , has been made sufficiently the subject of ...

NOMENCLATURE . 1. AFTER a

**thing**, or a class of**things**, has been renderedobvious to the senses , and either by speech , writing , pictorial representation , or

examination in its proper substance , has been made sufficiently the subject of ...

Side 2

When a

being so and so , makes part of the original supposition or statement of the

question in hand . Thus , if the proposition is , that if two magnitudes be equal ,

some ...

When a

**thing**is said to be so and so by the hypothesis , the meaning is , that itsbeing so and so , makes part of the original supposition or statement of the

question in hand . Thus , if the proposition is , that if two magnitudes be equal ,

some ...

Side 3

When a

at some previous period of the operations in hand , been made to be what it is

said to be . Thus , if in the course of the operations in hand , some magnitude has

...

When a

**thing**is said to be so and so by construction , the meaning is , that it hasat some previous period of the operations in hand , been made to be what it is

said to be . Thus , if in the course of the operations in hand , some magnitude has

...

Side 5

For example , if the original proposition is , that if of equals one be greater than

some

this proposition is , that if of equals one be not greater than some

For example , if the original proposition is , that if of equals one be greater than

some

**thing**else , the rest are severally greater than the same ; the negative ofthis proposition is , that if of equals one be not greater than some

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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.