## 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 100

Side ix

If a tessera ( or quadrilateral rectilinear plane figure of which two of the opposite

sides are

between them which shall be called the base ] has the angles at the base less

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 sidebetween them which shall be called the base ] has the angles at the base less

than ...

Side 1

... to coincide , may three , or any other number . X. Points which do not coincide ,

are said to be distant . XI . Two points A and B are said to be equally distant with

two others C and D , or to be at a distance

... to coincide , may three , or any other number . X. Points which do not coincide ,

are said to be distant . XI . Two points A and B are said to be equally distant with

two others C and D , or to be at a distance

**equal**to the distance of C and ... Side 2

Magnitudes are said to be given , when

, if the proposition is , that if two magnitudes be

shall follow , as , for instance , that the sum of them shall be

Magnitudes are said to be given , when

**equals**to them can be assigned . ... Thus, if the proposition is , that if two magnitudes be

**equal**, some particular resultshall follow , as , for instance , that the sum of them shall be

**equal**to some third ... Side 3

Thus , if in the course of the operations in hand , some magnitude has been cut

off

afterwards be avouched to be

specially ...

Thus , if in the course of the operations in hand , some magnitude has been cut

off

**equal**to another magnitude ; these two magnitudes may at any timeafterwards be avouched to be

**equal**by construction . For one of them has beenspecially ...

Side 5

For example , if the original proposition is , that magnitudes which are

the same , are

magnitudes which are

is ...

For example , if the original proposition is , that magnitudes which are

**equal**tothe same , are

**equal**to one another ; the converse of this proposition is , thatmagnitudes which are

**equal**to one another , are**equal**to the same . XXXI . Whatis ...

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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.