## The Elements of Euclid |

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Side 63

F . - - r Let ABCD be a circle , of which the diaAB meter is AD , and the centre E ;

and let BC be nearer to the centre than FG ; AD is greater F . than any straight

line BC which is not a

EH ...

F . - - r Let ABCD be a circle , of which the diaAB meter is AD , and the centre E ;

and let BC be nearer to the centre than FG ; AD is greater F . than any straight

line BC which is not a

**diameter**, and BC greater than FG . From the centre drawEH ...

Side 145

If two similar parallelograms have a common angle , and be similarly situated ,

they are about the same

similar and similarly situated , and have the angle DAB common : ABCD and

AEFG ...

If two similar parallelograms have a common angle , and be similarly situated ,

they are about the same

**diameter**. В Let the parallelograms ABCD , AEFG besimilar and similarly situated , and have the angle DAB common : ABCD and

AEFG ...

Side 232

sphere BCDE has to the

divided into the same number of pyramids , and in the same order , the pyramids

shall be similar to one another each to each ; because they have the solid angles

...

sphere BCDE has to the

**diameter**of the other sphere ; for if these two solids bedivided into the same number of pyramids , and in the same order , the pyramids

shall be similar to one another each to each ; because they have the solid angles

...

Side 354

milarly placed ; therefore EF is given in speG HF cies , and is about the same

therefore , because the figure EF given in species is described upon the given ...

milarly placed ; therefore EF is given in speG HF cies , and is about the same

**diameter**( 26 . 6 . ) with DL ; let BCG be the**diameter**, and construct the figure ;therefore , because the figure EF given in species is described upon the given ...

Side 368

If from a given point in the

and from that point a straight line be drawn at right angles to the first , and from

the point in ...

If from a given point in the

**diameter**of a circle given in position , or in the**diameter**produced , a straight line be drawn to any point in the circumference ,and from that point a straight line be drawn at right angles to the first , and from

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.