## 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 54

Side 1

An Axiom , or Maxim , is a self - evident proposition , requiring no formal

demonstration to

proposition ; in which some property ir asserted , and the truth of it required to be

An Axiom , or Maxim , is a self - evident proposition , requiring no formal

demonstration to

**prove**the truth of it ; but is ... A Theorem is a demonstrativeproposition ; in which some property ir asserted , and the truth of it required to be

**proved**. Side 20

The angles AGH , GHD therefore are not unequal , that is , they are equal to one

another . Now , the angle EGB is equal to AGH ( 8. 1. ) ; and AGH is

equal to GHD ; therefore EGB is likewise equal to GHD ; add to each of these the

...

The angles AGH , GHD therefore are not unequal , that is , they are equal to one

another . Now , the angle EGB is equal to AGH ( 8. 1. ) ; and AGH is

**proved**to beequal to GHD ; therefore EGB is likewise equal to GHD ; add to each of these the

...

Side 32

Because the point A is the centre of the circle BCD , AC is equal ( 11. Def . ) to AB

; and because the point B is the centre of the circle ACE , BC is equal to AB : But it

has been

Because the point A is the centre of the circle BCD , AC is equal ( 11. Def . ) to AB

; and because the point B is the centre of the circle ACE , BC is equal to AB : But it

has been

**proved**that CA is equal to AB ; therefore CA , CB are each of them ... Side 76

to two right angles , are equal to the angles BAD , BCD ; and DBF has been

BCD in the alternate segment of the circle . F PROP . XXXI . THEOR . If two

straight ...

to two right angles , are equal to the angles BAD , BCD ; and DBF has been

**proved**equal to BAD ; therefore the remaining angle DBE is equal to the angleBCD in the alternate segment of the circle . F PROP . XXXI . THEOR . If two

straight ...

Side 84

Join AR , BR , and at their respective points of bisection , M , N , erect the

perpendicular MO , NO to AR , BR ; they will intersect at 0 , the centre of the circle

. That OA = OR = OB , is

or MN ...

Join AR , BR , and at their respective points of bisection , M , N , erect the

perpendicular MO , NO to AR , BR ; they will intersect at 0 , the centre of the circle

. That OA = OR = OB , is

**proved**as before . The joints between the arch - stones ,or MN ...

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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