## 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 28

Side ix

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

protesting against the unfortunate use which has been made of the term abstract

as

...

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

protesting against the unfortunate use which has been made of the term abstract

as

**applied**to what ought to have been called universal propositions ; than which...

Side 1

But besides this , there is an imaginary coincidence frequently appealed to by

geometers ; which is , when it can be shown that coincidence would take place , if

the objects in question could be

But besides this , there is an imaginary coincidence frequently appealed to by

geometers ; which is , when it can be shown that coincidence would take place , if

the objects in question could be

**applied**to one another without bar of corporeal ... Side 3

Thus , if it has been shown that because two particular magnitudes are each

equal to a third magnitude they are equal to one another ; and if the same steps

can be

reasoning ...

Thus , if it has been shown that because two particular magnitudes are each

equal to a third magnitude they are equal to one another ; and if the same steps

can be

**applied**in any other instance ; it may be avouched that by parity ofreasoning ...

Side 4

When all the instances to which a proposition may be

included under one specification or one construction , the proposition is said to

divide itself into two or more Cases ; which may in fact be considered as so many

distinct ...

When all the instances to which a proposition may be

**applied**, cannot beincluded under one specification or one construction , the proposition is said to

divide itself into two or more Cases ; which may in fact be considered as so many

distinct ...

Side 6

B * I. NomenFor because A is equal * to C , if their boundclature 14 . aries were

of doing so , by a different arrangement of parts . And because B is equal to C , in

...

B * I. NomenFor because A is equal * to C , if their boundclature 14 . aries were

**applied**to one another A and C would coincide ; or else might be made capableof doing so , by a different arrangement of parts . And because B is equal to C , in

...

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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.