## 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 - Trigonometry - 518 pages |

### From inside the book

Page 126

See N. IF the first of four magnitudes has the same ratio to the second which the

third hath to the fourth , then any

have the same ratio to any

See N. IF the first of four magnitudes has the same ratio to the second which the

third hath to the fourth , then any

**equimultiples**whatever of the first and third shallhave the same ratio to any

**equimultiples**of the second and fourth , viz . the ... Page 127

Book V. cond and fourth : and in like manner , the first and the third have the

same ratio to any

have to B the second the same ratio which the third C has to the fourth D , and of

A ...

Book V. cond and fourth : and in like manner , the first and the third have the

same ratio to any

**equimultiples**whatever of the second and fourth . Let A the firsthave to B the second the same ratio which the third C has to the fourth D , and of

A ...

Page 135

Let A have to C a greater ratio than B has to C : A is greater than B : for , because

A has a greater ratio to C than B bas to C , there are a some

and B , and a 7. def . some multiple of C such that the multiple of A is greater than

...

Let A have to C a greater ratio than B has to C : A is greater than B : for , because

A has a greater ratio to C than B bas to C , there are a some

**equimultiples**of Aand B , and a 7. def . some multiple of C such that the multiple of A is greater than

...

Page 137

K are

G be greater than L , H is greater than M ... if there be any number of magnitudes

K are

**equimultiples**of A , C , E , and L , M , N**equimultiples**of Book V. B , D , F ; ifG be greater than L , H is greater than M ... if there be any number of magnitudes

**equimultiples**of as many , each of each , whatever multiple one of them is of its ... Page 142

NI F + Book V. multiples KO , NP : and because KO , NP are

DF ; and that KH , NM are

BE , be greater than KH , which is a multiple of the same BE , NP , likewise the ...

NI F + Book V. multiples KO , NP : and because KO , NP are

**equimultiples**of BE ,DF ; and that KH , NM are

**equimultiples**likewise of BE , DF , if KO , the multiple ofBE , be greater than KH , which is a multiple of the same BE , NP , likewise the ...

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The Elements of Euclid, Viz: The Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid No preview available - 2018 |

The Elements of Euclid, Viz: The Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid No preview available - 2015 |

The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid No preview available - 2018 |

### Common terms and phrases

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

### Popular passages

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

Page 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.

Page 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...

Page 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.

Page 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.

Page 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.

Page 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.

Page 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.

Page 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.

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