## 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

Side 1

Geometry is a science which has for its object the measurement of

height or thickness . 2. In Geometry there are several general terms or principles

...

Geometry is a science which has for its object the measurement of

**magnitudes**. .**Magnitudes**may be considered under three dimensions , -length , breadth ,height or thickness . 2. In Geometry there are several general terms or principles

...

Side 8

7. Things which are halves of the same thing , are equal to one another . 8. Two

other , they coincide throughout their whole extent . They then fill the same space

. 9.

7. Things which are halves of the same thing , are equal to one another . 8. Two

**magnitudes**, lines , surfaces , or solids , are equal , if , when applied to eachother , they coincide throughout their whole extent . They then fill the same space

. 9.

Side 100

It is to be observed , that in speaking of the

in reality , those which these letters are ... When a number , or a letter denoting a

number , is written close to “ another letter denoting a

It is to be observed , that in speaking of the

**magnitudes**A , B , C , & c . , we mean ,in reality , those which these letters are ... When a number , or a letter denoting a

number , is written close to “ another letter denoting a

**magnitude**of any kind , it ... Side 101

as to exceed the greater ; and it is only such

ratio to one another . 5. If there be four

**Magnitudes**are said to be of the same kind , when the less can be multiplied soas to exceed the greater ; and it is only such

**magnitudes**that are said to have aratio to one another . 5. If there be four

**magnitudes**, and if any equimultiples ... Side 102

If three

said to be duplicate of the ratio of the first to the second . Thus , if A be to B as B to

C , the ratio of A to C is said to be duplicate “ of the ratio of A to B. Hence , since ...

If three

**magnitudes**are continual proportionals , the ratio of the first to the third issaid to be duplicate of the ratio of the first to the second . Thus , if A be to B as B to

C , the ratio of A to C is said to be duplicate “ of the ratio of A to B. Hence , since ...

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Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1819 |

Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1854 |

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

### 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 spherical square straight line taken tangent THEOR third touch triangle ABC wherefore whole