## 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 3

The Co - efficient of a quantity is the number prefixed to it : thus , 2AB signifies

that the line AB is to be taken 2 times ; JAB signifies the

Division , or the ratio of one quantity to another , is usually denoted by placing

one of ...

The Co - efficient of a quantity is the number prefixed to it : thus , 2AB signifies

that the line AB is to be taken 2 times ; JAB signifies the

**half**of the line AB . 25.Division , or the ratio of one quantity to another , is usually denoted by placing

one of ...

Side 28

it ; and the triangle DBC is the

diameter DC bisects it ; and the halves of equal things are equal ( 7. Ax . ) ;

therefore the triangle ABC is equal to the triangle DBC . PROP . XXXII . THEOR .

Triangles ...

it ; and the triangle DBC is the

**half**of the parallelogram DBCF , because thediameter DC bisects it ; and the halves of equal things are equal ( 7. Ax . ) ;

therefore the triangle ABC is equal to the triangle DBC . PROP . XXXII . THEOR .

Triangles ...

Side 47

If a straight line be divided into two equal parts , and also into two unequal parts ;

the rectangle contained by the unequal parts , together with the square of the line

between the points of section , is equal to the square of

If a straight line be divided into two equal parts , and also into two unequal parts ;

the rectangle contained by the unequal parts , together with the square of the line

between the points of section , is equal to the square of

**half**the line . Let the ... Side 48

If a straight line be bisected , and produced to any point ; the rectangle contained

by the whole line thus produced , and the part of it produced , together with the

square of

...

If a straight line be bisected , and produced to any point ; the rectangle contained

by the whole line thus produced , and the part of it produced , together with the

square of

**half**the line bisected , is equal to the square of the straight line which is...

Side 50

From the demonstration it is manifest , that since the square “ of CD is quadruple

of the square of CB , the square of any druple of the square of

SCHOLIUM . In this proposition , let the line AB be denoted by a , and the parts

AC ...

From the demonstration it is manifest , that since the square “ of CD is quadruple

of the square of CB , the square of any druple of the square of

**half**that line . ”SCHOLIUM . In this proposition , let the line AB be denoted by a , and the parts

AC ...

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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