## The Elements of Euclid |

### Inni boken

Resultat 1-5 av 6

Side 311

in it ; the straight line drawn to C , which makes a given angle with CB , is

this be the angle at D : at the given A point C , in the given straight line AB ...

in it ; the straight line drawn to C , which makes a given angle with CB , is

**given in****position**. Because the angle is given , one equal to it can be found ( 1 . def . ) ; letthis be the angle at D : at the given A point C , in the given straight line AB ...

Side 312

If therefore D be equal to AE , AE B E C is the straight line given in magnitude ,

drawn from the given point A to BC : and it is evident that AE is

( 33 . dat . ) , because it is drawn from the given point A to BC , which is

If therefore D be equal to AE , AE B E C is the straight line given in magnitude ,

drawn from the given point A to BC : and it is evident that AE is

**given in position**,( 33 . dat . ) , because it is drawn from the given point A to BC , which is

**given in**... Side 314

Let the straight line AD given in magnitude be drawn from the point A to the

straight line BC , given in posi - E A H F tion , in the given angle ADC : the straight

line EAF drawn through A parallel to BC is

...

Let the straight line AD given in magnitude be drawn from the point A to the

straight line BC , given in posi - E A H F tion , in the given angle ADC : the straight

line EAF drawn through A parallel to BC is

**given in position**. In BC take the given...

Side 315

From the given point A , let the straight line AED be drawn to the two parallel

straight lines FG , BC , and let the ratio of the segments AE , AD be given ; if one

of the parallels BC be

From the given point A , let the straight line AED be drawn to the two parallel

straight lines FG , BC , and let the ratio of the segments AE , AD be given ; if one

of the parallels BC be

**given in position**, the other FG is also**given in position**. Side 368

If from any point in the circumference of a circle

lines be drawn meeting the circumference , and containing a given angle ; if the

point in which one of them meets the circumference again be given , the point in ...

If from any point in the circumference of a circle

**given in position**, two straightlines be drawn meeting the circumference , and containing a given angle ; if the

point in which one of them meets the circumference again be given , the point in ...

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added altitude angle ABC angle BAC base BC is given centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples Euclid excess fore four fourth given angle given in magnitude given in position given in species given magnitude given ratio given straight line gles greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid Q. E. D. PROP reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid sphere square square of BC taken THEOR third triangle ABC wherefore whole

### Populære avsnitt

Side 36 - 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. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.

Side 145 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.

Side 65 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.

Side 248 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.

Side 11 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.

Side 121 - 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 21 - 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 14 - To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third (20.

Side 80 - 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 133 - ... rectilineal figures are to one another in the duplicate ratio of their homologous sides.