## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago 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 twelfthMathew Carey, and sold by J. Conrad & Company, S. F. Bradford, Birch & Small, and Samuel Etheridge. Printed by T. & G. Palmer, 116, High-Street., 1806 - 518 sider |

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Resultat 6-10 av 12

Side 460

And because the

the circle ABC

: and GF is equal lo 'Jo. dat. y^rjj wherefore the rectangle AD, EF is

And because the

**straight line**F.FG is drawn from a piven point F without or withinthe circle ABC

**given**in position, d 'J5. or therefore d the rectangle EF, FG is**given**: and GF is equal lo 'Jo. dat. y^rjj wherefore the rectangle AD, EF is

**given**. Side 463

4. is thus : “ Points , lines , spaces , " and angles are said to be

which have always « the same ... But from the things here

which ...

4. is thus : “ Points , lines , spaces , " and angles are said to be

**given**in positionwhich have always « the same ... But from the things here

**given**, neither the**straight line**BD nor the point can be found by the help of E Elements only , bywhich ...

Side 465

... a given angle , and B another an А B A gle to which A has a given ratio , for

instance , the ratio of the

found an angle C equal to A , how can the angle a be found to which C has the

same ...

... a given angle , and B another an А B A gle to which A has a given ratio , for

instance , the ratio of the

**given straight line**E to the given one Z ; then , havingfound an angle C equal to A , how can the angle a be found to which C has the

same ...

Side 473

Let EFG be equal to the

that the ratio of he rectangle B , BC to ...

to BA is the next thing said to be

Let EFG be equal to the

**given**angle ABC , and because in the analysis it is saidthat the ratio of he rectangle B , BC to ...

**straight**“**line**GL to FE , which ratio of DBto BA is the next thing said to be

**given**in the analysis ; from this it is plain that ... Side 475

Let AB be the first straight line , CD the second , and EF the third ; and because

the ratio of AB to CD is given , and that if a

the ratio of the remainder to EF is given ; therefore a the excess of the first AB a

24.

Let AB be the first straight line , CD the second , and EF the third ; and because

the ratio of AB to CD is given , and that if a

**given straight line**be taken from CD ,the ratio of the remainder to EF is given ; therefore a the excess of the first AB a

24.

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The Elements of Euclid, Viz: The Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2018 |

The Elements of Euclid, Viz: The Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2015 |

The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Robert Simson Ingen forhåndsvisning tilgjengelig - 2017 |

### Vanlige uttrykk og setninger

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

### Populære avsnitt

Side 30 - Any two sides of a triangle are together greater than the third side.

Side 64 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.

Side 30 - IF, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle. Let...

Side 59 - PROP. VIII. THEOR. IF a straight line be divided into any two parts, tour 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 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.

Side 165 - 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 19 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.

Side 191 - In right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar, and similarly described figures upon the sides containing the right angle.

Side 39 - 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 sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.

Side 180 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.