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

### Inni boken

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

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 . Side 5

I. Let it be granted that a straight line may be

I. Let it be granted that a straight line may be

**drawn**from any one point to any other point . II . That a terminated straight line may be produced straight line . any length in a III . And that a circle may be described from any centre ... Side 7

the circle BCD ; and from the centre B , at the distance BA , describe the circle ACE ; and from the point C , in which the circles cut one another ,

the circle BCD ; and from the centre B , at the distance BA , describe the circle ACE ; and from the point C , in which the circles cut one another ,

**draw**( Post . 1. ) the straight lines CA , CB , to the points 4 , B ; ABC shall be an ... Side 8

Wherefore from the given point A a straight line AL has been

Wherefore from the given point A a straight line AL has been

**drawn**equal to the given straight line BC . Which was to be done . PROP . III . PROBLEM . From the greater of two given straight lines to cut off a part equal to the less . Side 14

To

To

**draw**a straight line at right angles to a given straight line , from a given point in the same . Let AB be a given straight line , and C a point given in it ; it is required to**draw**a straight line from the point C , at right angles ...### Hva folk mener - Skriv en omtale

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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...