## 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 100

Side 14

to AF , the less , and

two sides FA , AC are equal to the two GA , AB , each to each ; and they contain

the angle FAG common to the two triangles , AFC , AGB ; therefore the base FC ...

to AF , the less , and

**join**FC , GB . Because AF is equal to AĞ , and AB to AC , thetwo sides FA , AC are equal to the two GA , AB , each to each ; and they contain

the angle FAG common to the two triangles , AFC , AGB ; therefore the base FC ...

Side 15

off DB equal to AC the less , and

DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC

are equal to the two AC , CB , each to each ; but the angle DBC is also equal to ...

off DB equal to AC the less , and

**join**DC ; therefore , because in the tri D anglesDBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC

are equal to the two AC , CB , each to each ; but the angle DBC is also equal to ...

Side 17

... it into two equal angles . Let BAC be the given rectilineal angle , it is required to

bisect it . Take any point D in AB , and from AC cut ( 3. 1. ) off AE equal to AD ;

...

... it into two equal angles . Let BAC be the given rectilineal angle , it is required to

bisect it . Take any point D in AB , and from AC cut ( 3. 1. ) off AE equal to AD ;

**join**DE , and upon A it describe ( 1.1 . ) an equilateral triangle DEF ; then**join**AF...

Side 18

the equilateral F triangle DFE , and

given point C , is at right angles to the given straight line AB . Because DC is

equal to CE , and FC common to the two triangles DCF , ECF , the two sides DC ,

CF ...

the equilateral F triangle DFE , and

**join**FC ; the straight line FC , drawn from thegiven point C , is at right angles to the given straight line AB . Because DC is

equal to CE , and FC common to the two triangles DCF , ECF , the two sides DC ,

CF ...

Side 20

AC in E ,

and produce AC to G. Because AĚ is equal to EC , and BE to EF ; AE , EB are

equal to CE , EF , each to each ; and the angle AEB is equal ( 15. 1. ) to the angle

CEF ...

AC in E ,

**join**BE and produce it to F , and make EF equal to BE ;**join**also FC ,and produce AC to G. Because AĚ is equal to EC , and BE to EF ; AE , EB are

equal to CE , EF , each to each ; and the angle AEB is equal ( 15. 1. ) to the angle

CEF ...

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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.