## The synoptical Euclid; being the first four books of Euclid's Elements of geometry, with exercises, by S.A. Good |

### Inni boken

Resultat 1-5 av 29

Side 3

A circle is a plane figure contained by one line , which is called the cir .

cumference , and is such that all straight lines drawn from a certain point within

the figure to the

called the ...

A circle is a plane figure contained by one line , which is called the cir .

cumference , and is such that all straight lines drawn from a certain point within

the figure to the

**circumference**are equal to one another . XVI . And this point iscalled the ...

Side 64

I. Equal circles are those of which the diameters are equal , or from the centres of

which the straight lines to the

but a theorem , the truth of which is evident ; for , if the circles be applied to one ...

I. Equal circles are those of which the diameters are equal , or from the centres of

which the straight lines to the

**circumferences**are equal . “ This is not a definitionbut a theorem , the truth of which is evident ; for , if the circles be applied to one ...

Side 65

A segment of a circle is the figure contained by a straight line and the

by the straight line and the

angle ...

A segment of a circle is the figure contained by a straight line and the

**circumference**it cuts off . VII . “ The angle of a segment is that which is containedby the straight line and the

**circumference**. ” VIII . An angle in a segment is theangle ...

Side 67

Let ABC be a circle , and A , B , any two points in the

line drawn from A to B shall fall within the circle . с E B For if AB do not fall within

the circle , let it fall , if possible , without , as AEB ; find ( III . 1. ) D the centre of the

...

Let ABC be a circle , and A , B , any two points in the

**circumference**; the straightline drawn from A to B shall fall within the circle . с E B For if AB do not fall within

the circle , let it fall , if possible , without , as AEB ; find ( III . 1. ) D the centre of the

...

Side 70

VII . -THEOREM . If any point be taken in the diameter of a circle , which is not the

centre , of all the straight lines which can be drawn from it to the

the greatest is that in which the centre is , and the other part of that diameter is ...

VII . -THEOREM . If any point be taken in the diameter of a circle , which is not the

centre , of all the straight lines which can be drawn from it to the

**circumference**,the greatest is that in which the centre is , and the other part of that diameter is ...

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### Andre utgaver - Vis alle

The Synoptical Euclid; Being the First Four Books of Euclid's Elements of ... Uten tilgangsbegrensning - 1854 |

### Vanlige uttrykk og setninger

ABCD AC is equal AF is equal angle ABC angle ACB angle BAC angle BCD angle equal base base BC bisected centre circle ABC circumference coincide common cuts the circle demonstrated describe diameter distance divided double draw equal angles exterior angle extremity fall figure four given circle given point given straight line given triangle greater impossible inscribed join less Let ABC likewise manner meet opposite angles parallel parallelogram pass pentagon perpendicular point F PROBLEM produced Q.E.D. PROP reason rectangle contained rectilineal figure remaining angle required to describe right angles segment semicircle shown sides square of AC straight line AC THEOREM touches the circle triangle ABC twice the rectangle wherefore whole

### Populære avsnitt

Side 26 - 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 22 - If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle.

Side 32 - 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 1 - A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. vm. "A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same direction.

Side 97 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Side 7 - AB; but things which are equal to the same are equal to one another...

Side 14 - To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts.

Side 53 - IF a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part.

Side 41 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Side 52 - 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...