## The Elements of Euclid: The Errors by which Theon, Or Others, Have Long Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also the Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfth |

### Inni boken

Side 43

+1 Ax . F E square ;

therefore A C B the side BC is equal * to the side CG : but CB is equal * also to

GK , and CG II to BK ;

+1 Ax . F E square ;

**wherefore**the angle CGB is equal to the angle CBG ; andtherefore A C B the side BC is equal * to the side CG : but CB is equal * also to

GK , and CG II to BK ;

**wherefore**the figure CGKB ist equilateral : it is likewise ... Side 141

one angle of the one equal to one angle of the other , and the sides about the

equal angles proportionals , the triangles shall be equiangular , and shall have

those ...

**Wherefore**, if the sides , & c . Q. E. D. PROP . VI . THEOR . If two triangles haveone angle of the one equal to one angle of the other , and the sides about the

equal angles proportionals , the triangles shall be equiangular , and shall have

those ...

Side 348

And because as DC to DB , so is AD to DE , AC is * to EB , as DC to DB ; and the

ratio of DC to DB is given ;

because the ratio of EB to AC is given , and that AE is given , therefore EB the

excess of ...

And because as DC to DB , so is AD to DE , AC is * to EB , as DC to DB ; and the

ratio of DC to DB is given ;

**wherefore**the ratio of AC to EB , is given ; andbecause the ratio of EB to AC is given , and that AE is given , therefore EB the

excess of ...

Side 367

In like manner EF also is given in position ;

the points D , E are given ; therefore each of the straight lines DE , EF , FD is

given * in magnitude ;

and ...

In like manner EF also is given in position ;

**wherefore**the point F is given : andthe points D , E are given ; therefore each of the straight lines DE , EF , FD is

given * in magnitude ;

**wherefore**the triangle DEF is • 29 Dat . given in species * ;and ...

Side 421

4 . and because the triangle ABC is similar * to A EB , as AC to CB , so is AB to

BE ; therefore the rectangle AC , BE , is equal to AB , BC ; and the rectangle AB ,

BC , is given ,

of ...

4 . and because the triangle ABC is similar * to A EB , as AC to CB , so is AB to

BE ; therefore the rectangle AC , BE , is equal to AB , BC ; and the rectangle AB ,

BC , is given ,

**wherefore**AC , BE , is given : and because the sum of the squaresof ...

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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ... Robert Simson Uten tilgangsbegrensning - 1775 |

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1762 |

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1781 |

### Vanlige uttrykk og setninger

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

### Populære avsnitt

Side 141 - 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 40 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...

Side 26 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another, and the exterior angle equal to the interior and opposite upon the same side, and also the two interior angles upon the same side together equal to two right angles.

Side 46 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Side 28 - Cor. angles; that is * together with four right angles. There1s, 1. fore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 21 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.

Side 12 - IF two triangles have two sides of the one equal to two sides of the other, each to each, and have likewise their bases equal; the angle. which is contained by the two sides...

Side 169 - 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 5 - LET it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3. And that a circle may be described from any centre, at any distance from that centre.

Side 97 - 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.