## Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added, Elements of Plane and Spherical Trigonometry |

### Inni boken

Resultat 1-5 av 66

Side 15

than d the angle ACB ; but it is not ; therefore B the side AC is not less than AB ;

and it has been

PROP . XIII . THEOR . Any two sides of a triangle are together greater than the ...

than d the angle ACB ; but it is not ; therefore B the side AC is not less than AB ;

and it has been

**shewn**that it is not equal to AB ; therefore AC is greater than AB .PROP . XIII . THEOR . Any two sides of a triangle are together greater than the ...

Side 16

... if DB be added to each , the sides CE , EB , will be greater than CD , DB ; but it

has been

AC greater than BD , DC . Again , because the exterior angle of a triangle ( 9. 1. )

...

... if DB be added to each , the sides CE , EB , will be greater than CD , DB ; but it

has been

**shewn**that BA , AC are greater than BE , EC ; much more then are BA ,AC greater than BD , DC . Again , because the exterior angle of a triangle ( 9. 1. )

...

Side 17

... therefore the angle BAC is not equal to the angle EDF ; neither is it less ;

because then the base BC would be less ( 15. 1. ) than the base EF ; but it is not ;

therefore the angle B C BAC is not less than the angle EDF : and it was

that it ...

... therefore the angle BAC is not equal to the angle EDF ; neither is it less ;

because then the base BC would be less ( 15. 1. ) than the base EF ; but it is not ;

therefore the angle B C BAC is not less than the angle EDF : and it was

**shewn**that it ...

Side 22

to the angle GKD ; and it was

GHF ; therefore also AGK is equal to GKD ; and they are alternate angles ;

therefore AB is parallel ( 19. 1. ) to CD . K С D PROP . XXIV . THEOR . Two

angles are ...

to the angle GKD ; and it was

**shewn**that the angle AGK is equal to the angleGHF ; therefore also AGK is equal to GKD ; and they are alternate angles ;

therefore AB is parallel ( 19. 1. ) to CD . K С D PROP . XXIV . THEOR . Two

angles are ...

Side 23

Again , because AB is parallel to CE , and BD B С D falls upon them , the exterior

angle ECD is equal to the interior and opposite angle ABC , but the angle ACE

was

ACD ...

Again , because AB is parallel to CE , and BD B С D falls upon them , the exterior

angle ECD is equal to the interior and opposite angle ABC , but the angle ACE

was

**shewn**to be equal to the angle BAC ; therefore the whole exterior angleACD ...

### Hva folk mener - Skriv en omtale

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

### Andre utgaver - Vis alle

Elements of Geometry: Containing the First Six Books of Euclid with a ... John Playfair Uten tilgangsbegrensning - 1855 |

Elements of Geometry: Containing the First Six Books of Euclid, with a ... Euclid,John Playfair Uten tilgangsbegrensning - 1853 |

Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1847 |

### Vanlige uttrykk og setninger

ABCD altitude angle ABC angle BAC base bisected Book called centre chord circle circumference coincide common consequently construction cosine cylinder definition demonstrated described diameter difference distance divided double draw drawn equal equal angles equiangular equilateral Euclid exterior angle extremities fall fore four fourth given given straight line greater half Hence inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism Prob produced PROP proportional proposition proved radius ratio reason rectangle contained rectilineal figure remaining right angles segment shewn sides similar sine solid square straight line taken tangent THEOR third touch triangle ABC wherefore whole