## The Elements of Euclid |

### Inni boken

Resultat 1-5 av 9

Side 87

It is also equiangular ; because the circumference AB is equal to the

circumference DE : if to each be

whole EDCB : and the angle AED stands on the circumference ABCD , and the

angle BAE on ...

It is also equiangular ; because the circumference AB is equal to the

circumference DE : if to each be

**added**BCD , the whole ABCD is equal to thewhole EDCB : and the angle AED stands on the circumference ABCD , and the

angle BAE on ...

Side 240

13 , book 1 . This part must therefore have been

of some proposition betwixt the 5th and 13th , but none of these stand in need of

it except the 7th proposition , on account of which it has been

13 , book 1 . This part must therefore have been

**added**to prop . 5 , upon accountof some proposition betwixt the 5th and 13th , but none of these stand in need of

it except the 7th proposition , on account of which it has been

**added**: besides ... Side 241

B . I . 1 To this is

greater than the other ; " that is , take that side of the two DE , DF , which is not

greater than the other , in order to make with it the angle EDG equal to BAC ,

because ...

B . I . 1 To this is

**added**, “ of the two sides DE DF , let DE be that which is notgreater than the other ; " that is , take that side of the two DE , DF , which is not

greater than the other , in order to make with it the angle EDG equal to BAC ,

because ...

Side 250

... and defend it against the captious objections of those who attack it . " To this

citation from Dr . Barrow I have nothing to add , except that I fully believe the 3d

and 8th definitions are not Euclid ' s , but

.

... and defend it against the captious objections of those who attack it . " To this

citation from Dr . Barrow I have nothing to add , except that I fully believe the 3d

and 8th definitions are not Euclid ' s , but

**added**by some unskilful editor . DEF . XI.

Side 252

The demonstration of the other case is now

also the 5th proposition , are necessary to the demonstration of the 18th

proposition of this book . The translation from the Arabic gives both cases briefly .

PROP .

The demonstration of the other case is now

**added**, because both of them , asalso the 5th proposition , are necessary to the demonstration of the 18th

proposition of this book . The translation from the Arabic gives both cases briefly .

PROP .

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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.