## 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 49

Side 7

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

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

Side 35

... triangle ABC is the

bisects ( 34 . 1 . ) it ; and the triangle DBC is the

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

... triangle ABC is the

**half**of the parallelogram EBCA , because the diameter ABbisects ( 34 . 1 . ) it ; and the triangle DBC is the

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

Side 51

If a straight line le 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 le 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 52

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 54

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

of the square of CB , the square of any line is qua“ druple of the square of

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

...

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

of the square of CB , the square of any line is qua“ druple of the square of

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

...

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### Andre utgaver - Vis alle

Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1840 |

Elements of Geometry: Containing the First Six Books of Euclid, with a ... Euclid,John Playfair Uten tilgangsbegrensning - 1845 |

Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1852 |

### Vanlige uttrykk og setninger

ABCD altitude angle ABC angle BAC base bisected Book called centre chord circle circle ABC circumference coincide common consequently construction contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equilateral Euclid exterior angle extremity 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

### Populære avsnitt

Side 51 - 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.

Side 12 - AB; but things which are equal to the same are equal to one another...

Side 80 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.

Side 288 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 35 - Parallelograms upon the same base and between the same parallels, are equal to one another.

Side 81 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by this line with the line which touches the circle, shall be equal to the angles in the alternate segments of the circle.

Side 52 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.

Side 127 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Side 23 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle.

Side 19 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it the angles CBA, ABD ; these are either two right angles, or are together equal to two right angles. For, if the angle CBA be equal to ABD, each of them is a right angle (Def.