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

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Resultat 1-5 av 13

Side 2

... 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

. XII .

... 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 . XI . An obtuse angle is that which is greater than a right angle. XII .

Side 16

To draw a straight line

length , from a given point without it . Let AB be the given straight line , which may

be produced to any length both ways , and let C be a point without it . It is

required to ...

To draw a straight line

**perpendicular**to a given straight line of an unlimitedlength , from a given point without it . Let AB be the given straight line , which may

be produced to any length both ways , and let C be a point without it . It is

required to ...

Side 60

In obtuse - angled triangles , if a

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 ...

In obtuse - angled triangles , if a

**perpendicular**be drawn from either of the acuteangles 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 ...

Side 61

the

angle B , is less than the squares of CB , BA , by twice the rectangle CB , BD .

A B D First , let AD fall within the triangle ABC ; and because the straight line CB

is ...

the

**perpendicular**AD from the opposite angle : the square of AC opposite to theangle B , is less than the squares of CB , BA , by twice the rectangle CB , BD .

A B D First , let AD fall within the triangle ABC ; and because the straight line CB

is ...

Side 62

Lastly , let the side AC be

between the

) The squares of AB , BC , are equal to the square of AC , and twice the square ...

Lastly , let the side AC be

**perpendicular**to BC . B C Then BC is the straight linebetween the

**perpendicular**and the acute angle at B ; and it is manifest that ( I. 47.) The squares of AB , BC , are equal to the square of AC , and twice the square ...

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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...