## 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

The alterations made are chiefly in the First and Third Books ; the arrangement of

those Books is

Trigonometry . As the properties of the sections of straight lines are easily derived

...

The alterations made are chiefly in the First and Third Books ; the arrangement of

those Books is

**similar**to that of LEGENDRE , in his Elements of Geometry andTrigonometry . As the properties of the sections of straight lines are easily derived

...

Side 42

3 A square may be thus formed that shall be equivalent to the sum of any number

of squares ; for a

reduce three of them to two , and these two to one , and so of others . PROP . XX .

3 A square may be thus formed that shall be equivalent to the sum of any number

of squares ; for a

**similar**construction which reduces two of them to one , willreduce three of them to two , and these two to one , and so of others . PROP . XX .

Side 56

The sector of a circle is the figure contained by two straight lines drawn from the

centre , and the arc of the circumference between them . 12.

a circle , are those in which the angles are equal , or which contain equal angles .

The sector of a circle is the figure contained by two straight lines drawn from the

centre , and the arc of the circumference between them . 12.

**Similar**segments ofa circle , are those in which the angles are equal , or which contain equal angles .

Side 62

For

equally distant from the point F , and consequently lie in the circumference of the

circle , whose centre is F , and radius FA . A It is obvious , that besides this , no

other ...

For

**similar**reasons FB , FC , are equal ; hence the points A , B , C , are all Dequally distant from the point F , and consequently lie in the circumference of the

circle , whose centre is F , and radius FA . A It is obvious , that besides this , no

other ...

Side 72

THEOR Upon the same straight line , and upon the same side of it , there cannot

be two

possible , let the two

same ...

THEOR Upon the same straight line , and upon the same side of it , there cannot

be two

**similar**segments of circles , not coinciding with one another . If it bepossible , let the two

**similar**segments of circles viz . ACB , ADB , be upon thesame ...

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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