## 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 6-10 av 10

Side 37

Thomas Perronet Thompson. •

of place , the straight line BCG which cuts the surface of the sphere after the last

turning , cuts also the surface as it was before the first turning . That is to say , the

...

Thomas Perronet Thompson. •

**INTERC**. 4. about the centre is * without changeof place , the straight line BCG which cuts the surface of the sphere after the last

turning , cuts also the surface as it was before the first turning . That is to say , the

...

Side 54

B В G *

, and upon it describet the equilateral triangle

the straight lines DA and DB , to E and F ; Cor . 6 . *

in ...

B В G *

**INTERC**. 9 . From the point A to B draw * the straight line Cor . +1 . 1 . AB, and upon it describet the equilateral triangle

**INTERC**. 12. DAB , and prolongthe straight lines DA and DB , to E and F ; Cor . 6 . *

**INTERC**.13 . which will * bein ...

Side 67

... wherefore if it be moved till it also pass #

straight line DE willf coincide with Cor . 1 . such unlimited straight line to the

extent of the length that is common to both , and its prolongation will also be in

the same ...

... wherefore if it be moved till it also pass #

**Interc**.12 . through the point E , thestraight line DE willf coincide with Cor . 1 . such unlimited straight line to the

extent of the length that is common to both , and its prolongation will also be in

the same ...

Side 91

+

. is equal to CAZ . Wherefore the straight line LV will lie between the two straight

lines LU , LA , and being prolonged will 1.13.Cor.5 . cuts the perimeter of the ...

+

**INTERC**. 1. is less than CAZ ; ILA ist less than CAZ , and than ILV which Cor . 2. is equal to CAZ . Wherefore the straight line LV will lie between the two straight

lines LU , LA , and being prolonged will 1.13.Cor.5 . cuts the perimeter of the ...

Side 99

CAB and ACD aret together less than two right angles , they are + Hyp . į

. less than CAF and ACD . Wherefore , by taking away the Cor . 2 . *

**Interc**. I , and ACD are * together equal to two right angles . And because Cor . 1 .CAB and ACD aret together less than two right angles , they are + Hyp . į

**Interc**. 1. less than CAF and ACD . Wherefore , by taking away the Cor . 2 . *

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Geometry Without Axioms Or the First Book Euclid's Elements: With ... 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.