## 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

Side 99

FG to GE ; in the same manner , it may be

of them equal to FG or GE ; thereA E D fore the four straight lines GE , GF , GH ,

GK , are equal to one another ; and the circle described from the centre G , at the

...

FG to GE ; in the same manner , it may be

**demonstrated**, that GH , GK , are eachof them equal to FG or GE ; thereA E D fore the four straight lines GE , GF , GH ,

GK , are equal to one another ; and the circle described from the centre G , at the

...

Side 103

... and the angle FKC to the angle FLC : and because KC is equal to CL , KL is

double of KC : in the same manner , it may be shown that HK is double of BK :

and because BK is equal to KC , as was

and ...

... and the angle FKC to the angle FLC : and because KC is equal to CL , KL is

double of KC : in the same manner , it may be shown that HK is double of BK :

and because BK is equal to KC , as was

**demonstrated**, and KL is double of KC ,and ...

Side 298

Alexandrinus in the 3d Book of his Mathematical Collections , but the

sufficient vindication of Euclid for having

which some affect to ...

Alexandrinus in the 3d Book of his Mathematical Collections , but the

**demonstration**is of a kind that does not belong to ... This proposition is asufficient vindication of Euclid for having

**demonstrated**the 21st proposition ,which some affect to ...

Side 300

In order to

a straight line meet two straight “ lines ... proof , that , as Proclus has observed ,

the converse of it is a proposition thai confessedly requires to be

In order to

**demonstrate**this proposition , Euclid assumed it as an Axiom , that “ ifa straight line meet two straight “ lines ... proof , that , as Proclus has observed ,

the converse of it is a proposition thai confessedly requires to be

**demonstrated**. Side 301

... in the first edition of his Elements It is however a faulty definition , for it conceals

an Axiom in it , and takes for granted a property of straight lines , that ought either

to be laid down as self - evident , or

... in the first edition of his Elements It is however a faulty definition , for it conceals

an Axiom in it , and takes for granted a property of straight lines , that ought either

to be laid down as self - evident , or

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

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

### Vanlige uttrykk og setninger

ABCD altitude angle ABC angle BAC arch base bisected Book called centre circle circle ABC circumference coincide common contained 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 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 56 - 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 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 62 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...

Side 62 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle...

Side 130 - 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 76 - 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 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 55 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.