## 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 6-10 av 100

Side 21

Let ABC be a triangle of which the A side AC is greater than the side AB ; the

angle ABC is also greater than the angle BCA . D From AC , which is greater than

AB , cut off ( 3. 1. ) AD equal to AB , and

...

Let ABC be a triangle of which the A side AC is greater than the side AB ; the

angle ABC is also greater than the angle BCA . D From AC , which is greater than

AB , cut off ( 3. 1. ) AD equal to AB , and

**join**BD : and because ADB is the exterior...

Side 24

another circle HLK ; and

three straight lines , A , B , C. Because the point F is the centre of the circle DKI ,

FD is equal ( 11 . Def . ) to FK ; but FD is equal to the straight line A ; therefore FK

...

another circle HLK ; and

**join**KF , KG ; the triangle KFG has its sides equal to thethree straight lines , A , B , C. Because the point F is the centre of the circle DKI ,

FD is equal ( 11 . Def . ) to FK ; but FD is equal to the straight line A ; therefore FK

...

Side 26

Let AB be the greater of the two , and make BG equal to DE , and

therefore , because BG is equal to DE , and BC to EF , the two sides GB , BC are

equal to the two , DE , EF , each to each ; and the angle GBC is equal to the

angle DEF ...

Let AB be the greater of the two , and make BG equal to DE , and

**join**GC ;therefore , because BG is equal to DE , and BC to EF , the two sides GB , BC are

equal to the two , DE , EF , each to each ; and the angle GBC is equal to the

angle DEF ...

Side 31

... or of one right angle . SCHOLIUM . When ( Cor . 1. ) is applied to polygons ,

which have re - entrant angles , as ABC each re - entrant angle must be regarded

as greater than two right angles . B. And , by

.

... or of one right angle . SCHOLIUM . When ( Cor . 1. ) is applied to polygons ,

which have re - entrant angles , as ABC each re - entrant angle must be regarded

as greater than two right angles . B. And , by

**joining**BD , BE , BF OF GEOMETRY.

Side 32

B. And , by

contain eight right angles ; that is , as many ... The straight lines which

extremities of two equal and parallel straight lines , towards the same parts , are

also ...

B. And , by

**joining**BD , BE , BF , the figure is divided into four triangles , whichcontain eight right angles ; that is , as many ... The straight lines which

**join**theextremities of two equal and parallel straight lines , towards the same parts , are

also ...

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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.