## 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 |

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Side

There are , however , a few others , which , though

may in some degree facilitate the study of the Elements . Such are those made on

the definitions in the first Book , and particularly on that of a straight line .

There are , however , a few others , which , though

**less**considerable , it is hopedmay in some degree facilitate the study of the Elements . Such are those made on

the definitions in the first Book , and particularly on that of a straight line .

Side 5

An acute angle is that which is

enclosed by one or more boundaries . The word area denotes the quantity of

space contained in a figure , without any reference to the nature of the line or

lines ...

An acute angle is that which is

**less**than a right angle . 10. A figure is that which isenclosed by one or more boundaries . The word area denotes the quantity of

space contained in a figure , without any reference to the nature of the line or

lines ...

Side 11

A For , if AB be not equal to AC , one of them is greater than the other : Let AB be

the greater , and from it cut off DB equal to AC the

because in the triangles DBC , D ACB , DB is equal to AC , and BC common to ...

A For , if AB be not equal to AC , one of them is greater than the other : Let AB be

the greater , and from it cut off DB equal to AC the

**less**, and join DC ; therefore ,because in the triangles DBC , D ACB , DB is equal to AC , and BC common to ...

Side 13

Ax . ) to the remaining angle ABD , the

therefore BE is not in the same straight line with BC . And in like manner , it may

be demonstrated , that no other can be in the same straight line with it but BD ...

Ax . ) to the remaining angle ABD , the

**less**to the greater , which is impossible ;therefore BE is not in the same straight line with BC . And in like manner , it may

be demonstrated , that no other can be in the same straight line with it but BD ...

Side 14

Any two angles of a triangle are together

any triangle ; any two of its angles together are

Produce BC to D ; and because ACD is the exterior angle of the triangle ABC ,

ACD is ...

Any two angles of a triangle are together

**less**than two right angles . Let ABC beany triangle ; any two of its angles together are

**less**than two right angles .Produce BC to D ; and because ACD is the exterior angle of the triangle ABC ,

ACD is ...

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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