## 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 |

### Inni boken

Side 28

Book I. but it is not ; therefore the side AC is not less than AB ; and it has been

shown that it is not equal to AB ; therefore AC is

Book I. but it is not ; therefore the side AC is not less than AB ; and it has been

shown that it is not equal to AB ; therefore AC is

**greater**than AB . Wherefore , the**greater**angle , & c . Q. E. D. PROP . XX . THEOR . See N. ANY two sides of a ... Side 134

Let A , B have each of them the same ratio to C : A is equal to B : for , if they are

not equal , one of them is

what was shown in the preceding proposition , there are some equimultiples of A

...

Let A , B have each of them the same ratio to C : A is equal to B : for , if they are

not equal , one of them is

**greater**than the other ; let A be the**greater**; then , bywhat was shown in the preceding proposition , there are some equimultiples of A

...

Side 138

Book V. of A and C , M and G are equimultiples ; and of B and D , N and K are

equimultiples ; if M be

, equal ; and if less , less b ; but G is

...

Book V. of A and C , M and G are equimultiples ; and of B and D , N and K are

equimultiples ; if M be

**greater**than N , G is**greater**b 5.def.5 . than K ; and if equal, equal ; and if less , less b ; but G is

**greater**than K , therefore M is**greater**than N...

Side 344

Book XI . together : of the three A , B , C , let A be that which is not less than either

of the two B and C : and first let B and C together be not less than A : therefore B ,

C , D together are

Book XI . together : of the three A , B , C , let A be that which is not less than either

of the two B and C : and first let B and C together be not less than A : therefore B ,

C , D together are

**greater**than A ; and because A is not less than B ; A , C , D ... Side 345

C above D : and because , by the hypothesis , the three B , C , D are together

above B : therefore a magnitude may be taken which is less than C and D

together , but ...

C above D : and because , by the hypothesis , the three B , C , D are together

**greater**than the fourth A ; C and D together are**greater**than the excess of Aabove B : therefore a magnitude may be taken which is less than C and D

together , but ...

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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,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |

### 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.