## 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 37

Side 22

... imbedded in one continuous hard body , let the * INTERC . 2. whole be turned

* about B , in such sort that the sphere A shall be moved to a new situation having

no 14 а IN PROP . VII . 23 B. part in

... imbedded in one continuous hard body , let the * INTERC . 2. whole be turned

* about B , in such sort that the sphere A shall be moved to a new situation having

no 14 а IN PROP . VII . 23 B. part in

**common**with 22 INTERCALARY BOOK . Side 23

23 B. part in

whose centre is C ; and let the line then described by the point A from A to C , be

afterwards turned about B in various * Interc.3 . directions as called for , till a ...

23 B. part in

**common**with the old , as for instance to the situation of the spherewhose centre is C ; and let the line then described by the point A from A to C , be

afterwards turned about B in various * Interc.3 . directions as called for , till a ...

Side 30

... the lines HOPLNM and IOPKNM are now traced on a

inclosed by them will coincide throughout . Also if on the one sphere the points M

, N ...

... the lines HOPLNM and IOPKNM are now traced on a

**common**surface by a**common**point N , these lines will coincide with one another , and the surfacesinclosed by them will coincide throughout . Also if on the one sphere the points M

, N ...

Side 31

26 . and the

will continue to coincide throughout . Which having been done , let the spheres

be returned to their original situation . Wherefore the two surfaces HOPLNM and

...

26 . and the

**common**centre A , and the whole surfaces HOPLNM and IOPKNMwill continue to coincide throughout . Which having been done , let the spheres

be returned to their original situation . Wherefore the two surfaces HOPLNM and

...

Side 32

If two equal spheres with different centres , have a point in their surfaces in

that point , or else touch one another externally in that point only . For their

surfaces ...

If two equal spheres with different centres , have a point in their surfaces in

**common**, they will cut one another in one self - rejoining line passing throughthat point , or else touch one another externally in that point only . For their

surfaces ...

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### 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.