## The Elements of Euclid |

### Inni boken

Resultat 1-5 av 13

Side 216

+ Vertex is put in the place of altitude , which is in the

pyramid , in what follows , is supposed to be circumscribed about the cone , and

so must have the same vertex . And the same change is made in some places

following ...

+ Vertex is put in the place of altitude , which is in the

**Greek**, because thepyramid , in what follows , is supposed to be circumscribed about the cone , and

so must have the same vertex . And the same change is made in some places

following ...

Side 238

B . I . Instead of this definition as it is in the

given from a property of a plane superficies , which is manifestly supposed in the

Elements , viz . that a straight line drawn from any point in a plane to any other in

...

B . I . Instead of this definition as it is in the

**Greek**copies , a more distinct one isgiven from a property of a plane superficies , which is manifestly supposed in the

Elements , viz . that a straight line drawn from any point in a plane to any other in

...

Side 249

in the 1st , 2d , 3d , and 6th definitions in Commandine ' s translation , “ tangit , ”

must be read instead of a contingit ; " and in the 2d and 3d definitions of book 3 ,

the same change must be made : but in the

...

in the 1st , 2d , 3d , and 6th definitions in Commandine ' s translation , “ tangit , ”

must be read instead of a contingit ; " and in the 2d and 3d definitions of book 3 ,

the same change must be made : but in the

**Greek**text of propositions 11th , 12th...

Side 252

B . V . There are two cases of this proposition , of which only the first and simplest

is demonstrated in the

give this one , since he was to make use of neither of them in his mutilated ...

B . V . There are two cases of this proposition , of which only the first and simplest

is demonstrated in the

**Greek**: and it is probable Theon thought it was sufficient togive this one , since he was to make use of neither of them in his mutilated ...

Side 257

... not evidently possible ; for a certain conclusion can never be deduced by the

means of an uncertain proposition : upon this account , we have given a

legitimate demonstration of this proposition instead of that in the

editions ...

... not evidently possible ; for a certain conclusion can never be deduced by the

means of an uncertain proposition : upon this account , we have given a

legitimate demonstration of this proposition instead of that in the

**Greek**and othereditions ...

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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.