## 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 5

Side 210

Therefore , the

and since they are equilateral , the fides about the equal angles are proportionals

; the

Therefore , the

**polygons**ABCDEF and GHIKLM are equiangular to one another ;and since they are equilateral , the fides about the equal angles are proportionals

; the

**polygon**d 1. def , 6. ABCD is therefore similar to the**polygon**GHIKLM d . Side 212

And in the same manner , by joining the centre and the other angular points of

the inscribed

the sides of which will each be equal to KL , and will be equal in number to the ...

And in the same manner , by joining the centre and the other angular points of

the inscribed

**polygon**, an equilateral**polygon**may be described about the circle ,the sides of which will each be equal to KL , and will be equal in number to the ...

Side 214

Supplement of CF , that is , to the square of AF 5 , as the

above the

the circle ABC is greater than the equilateral

Supplement of CF , that is , to the square of AF 5 , as the

**polygon**M to its excessabove the

**polygon**N. But the square of AC , that is , the square described aboutthe circle ABC is greater than the equilateral

**polygon**of eight fides described ... Side 216

1. rectangle contained by DG and the half of EF c ; and as the fame is true of all

the other equal triangles having their vertices in D , which make up the

described about the circle ; therefore , the whole

...

1. rectangle contained by DG and the half of EF c ; and as the fame is true of all

the other equal triangles having their vertices in D , which make up the

**polygon**described about the circle ; therefore , the whole

**polygon**is equal to the rectangle...

Side 217

Hence , a

exceed the circumference of thie circle by a line that is less than any given line .

Let NO be the given line . Take in NO the part NP less than its half , and less also

...

Hence , a

**polygon**may be described about a circle , the perimeter of which shallexceed the circumference of thie circle by a line that is less than any given line .

Let NO be the given line . Take in NO the part NP less than its half , and less also

...

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Elements of Geometry;: Containing the First Six Books of Euclid, with a ... Formerly Chairman Department of Immunology John Playfair Ingen forhåndsvisning tilgjengelig - 2016 |

Elements of Geometry: Containing the First Six Books of Euclid, With Two ... Formerly Chairman Department of Immunology John Playfair,John Playfair Ingen forhåndsvisning tilgjengelig - 2017 |

Elements of Geometry: Containing the First Six Books of Euclid with a ... Euclid,Formerly Chairman Department of Immunology John Playfair,John Playfair Ingen forhåndsvisning tilgjengelig - 2015 |

### Vanlige uttrykk og setninger

ABCD alſo altitude angle ABC angle BAC arch baſe becauſe biſected Book called caſe centre circle circle ABC circumference coincide common cylinder definition demonſtrated deſcribed diameter difference divided draw drawn equal equal angles equiangular Euclid extremity fall fame fides firſt folid fore four fourth given given ſtraight line greater half inſcribed join leſs Let ABC magnitudes meet multiple muſt oppoſite parallel parallelogram perpendicular plane polygon priſm produced PROP proportionals propoſition proved radius rectangle contained remaining right angles ſame ſame ratio ſecond ſegment ſhall ſides ſimilar ſin ſolid ſpherical ſquare ſtraight line ſuch ſum taken tangent THEOR theſe third thoſe touches triangle triangle ABC wherefore whole

### Populære avsnitt

Side 27 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...

Side 172 - 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 42 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.

Side 84 - The diameter is the greatest straight line in a circle; and of all others, that which is nearer to the centre is always greater than one more remote; and the greater is nearer to the centre than the less. Let ABCD be a circle, of which...

Side 106 - IF from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle be equal to the square of the line which meets it, the line which meets shall touch the circle.

Side 22 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it. Let ABC be a triangle, of which the angle ABC is greater than the angle BCA : the side AC is likewise greater than the side AB. For, if it be not greater, AC must...

Side 64 - If then the sides of it, BE, ED are equal to one another, it is a square, and what was required is now done: But if they are not equal, produce one of them BE to F, and make EF equal to ED, and bisect BF in G : and from the centre G, at the distance GB, or GF, describe the semicircle...

Side 166 - IN a right angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another. Let ABC be a right angled triangle, having the right angle BAC ; and from the point A let AD be drawn perpendicular to the base BC : the triangles ABD, ADC are similar to the whole triangle ABC, and to one another.

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...

Side 2 - 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.