## Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement on the Quadrature of the Circle and the Geometry of Solids ... |

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Side 71

With a Supplement on the Quadrature of the Circle and the Geometry of Solids ...

John Playfair. straight lines FB , FC , FG , & c . that can be drawn from F to the

the ...

With a Supplement on the Quadrature of the Circle and the Geometry of Solids ...

John Playfair. straight lines FB , FC , FG , & c . that can be drawn from F to the

**circumference**, F , is the greatest , and FD , the other part of the diameter AD , isthe ...

Side 169

Now , DA is the semidiameter of the circle ABC , and AH the half of its

( 1. 6. ) , and because by this proposition , DA.AH = the area of the circle , of

which DA ...

Now , DA is the semidiameter of the circle ABC , and AH the half of its

**circumference**. Therefore , & c . Q. E. D. Cor . 1. Because DA : AH :: DA ? : DA.AH( 1. 6. ) , and because by this proposition , DA.AH = the area of the circle , of

which DA ...

Side 175

It is evident , that the arches BD , ' BE are each of them one - sixth of the

between AH ...

It is evident , that the arches BD , ' BE are each of them one - sixth of the

**circumference**( Cor . 15. 4. ) , and that therefore the arch DBE is one - third of the**circumference**. Wherefore , the line ( 8. 1. Sup . ) CG is a mean proportionalbetween AH ...

Side 177

722 It remains to demonstrate , that the part by which the

exceeds the diameter is greater than of the diameter . 71 It was before shewn ,

that CG2 = 750000 ; wherefore CG = 866 . 02545 , because ( 866.02545 ) 2 is

greater ...

722 It remains to demonstrate , that the part by which the

**circumference**10exceeds the diameter is greater than of the diameter . 71 It was before shewn ,

that CG2 = 750000 ; wherefore CG = 866 . 02545 , because ( 866.02545 ) 2 is

greater ...

Side 222

But ABD is a right angle , and therefore four times the arch AD is equal to the

whole

different circles stand on arches which have the same ratio to their

But ABD is a right angle , and therefore four times the arch AD is equal to the

whole

**circumference**ACF ; therefore , the angle ... Equal angles at the centres ofdifferent circles stand on arches which have the same ratio to their

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Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1824 |

Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1819 |

### Vanlige uttrykk og setninger

ABCD altitude angle ABC angle BAC arch base bisected Book called centre circle circle ABC circumference coincide common cosine cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular Euclid exterior extremity fall fore four fourth given given straight line greater half inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism produced PROP proportionals proposition proved Q. E. D. PROP radius ratio reason rectangle contained rectilineal figure right angles segment shewn sides similar sine solid square straight line taken tangent THEOR thing third touches triangle ABC wherefore whole

### Populære avsnitt

Side 153 - If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle...

Side 19 - 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 33 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.

Side 292 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...

Side 308 - 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 36 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.

Side 18 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.

Side 78 - To draw a straight line from a given point, either without or in the circumference, which shall touch a given circle. First, let A be a given point without the given circle BCD : it is required to draw a straight line from A which shall touch the circle.

Side 77 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...

Side 39 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the too interior angles upon the same side together equal to two right angles.