## 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 57

Side 3

The Elements of EvCLID , however , in

editors during the decline of science , had suffered some diminution of their

excellence , and much skill and learning have been employed by the modern ...

The Elements of EvCLID , however , in

**passing**through the hands of the ancienteditors during the decline of science , had suffered some diminution of their

excellence , and much skill and learning have been employed by the modern ...

Side 37

Let ABCD be a parallelogram of which the diameter is AC ; let EH , FG be the

parallelograms about AC , that is , through which AC

the other parallelograms , which make up the whole figure ABCD , A H D and are

...

Let ABCD be a parallelogram of which the diameter is AC ; let EH , FG be the

parallelograms about AC , that is , through which AC

**passes**, and let BK , KŌ bethe other parallelograms , which make up the whole figure ABCD , A H D and are

...

Side 63

Cor . Every point , moreover , in the production of AB , is farther from the centre

than the circumference . PROP . III . THEOR . If a straight line drawn through the

centre of a circle bisect a straight line in the circle , which does not

the ...

Cor . Every point , moreover , in the production of AB , is farther from the centre

than the circumference . PROP . III . THEOR . If a straight line drawn through the

centre of a circle bisect a straight line in the circle , which does not

**pass**throughthe ...

Side 64

bisecting AB , which does not

Hence , the perpendicular through the middle of a chord ,

centre ; for this perpendicular is the same as the one let fall from the centre on the

...

bisecting AB , which does not

**pass**through the centre , cuts AB at right angles . ...Hence , the perpendicular through the middle of a chord ,

**passes**through thecentre ; for this perpendicular is the same as the one let fall from the centre on the

...

Side 65

... which is nearer to the line

one more remote from it ; And from the same point there can be drawn only two

straight lines that are equal to one another , one upon each side of the shortest

line .

... which is nearer to the line

**passing**through the centre is always greater thanone more remote from it ; And from the same point there can be drawn only two

straight lines that are equal to one another , one upon each side of the shortest

line .

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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 - 1839 |

### Vanlige uttrykk og setninger

ABCD altitude angle ABC angle BAC base bisected Book called centre chord circle circle ABC circumference coincide common consequently construction 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 right angles segment shewn sides similar sine solid spherical square straight line taken tangent THEOR third touch triangle ABC wherefore whole

### Populære avsnitt

Side 53 - 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 18 - If two triangles have two sides of the one equal to two sides of the...

Side 54 - 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 on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.

Side 82 - 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 31 - Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles.

Side 11 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.

Side 21 - 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 shall either be two right angles, or shall together be equal to two right angles. For...

Side 101 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.

Side 58 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.

Side 298 - 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.