## 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

Results 1-5 of 12

Page 93

IN a circle , the angle in a semicircle is a right angle ; but the angle in a segment

greater than a semicircle is

which ...

IN a circle , the angle in a semicircle is a right angle ; but 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 . Let ABCD be a circle , ofwhich ...

Page 119

I. A

the

number of times exactly in the greater . ' II . A greater magnitude is said to be a ...

I. A

**LESS**magnitude is said to be a part of a greater magnitude , Book V. whenthe

**less**measures the greater , that is , when the**less**is • contained a certainnumber of times exactly in the greater . ' II . A greater magnitude is said to be a ...

Page 129

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

which the third has to the fourth ; then , if the first be greater than the second , the

third is also greater than the fourth ; and , if equal , equal ; if

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

which the third has to the fourth ; then , if the first be greater than the second , the

third is also greater than the fourth ; and , if equal , equal ; if

**less**,**less**. Page 193

... if

BC , EF , and the two sectors BGC , EHF , and of the circumference BC , and

sector BGC , the circumference BL and sector BGL are any equal multiples

whatever ...

... if

**less**,**less**: since , then , there are four magnitudes , the two circumferencesBC , EF , and the two sectors BGC , EHF , and of the circumference BC , and

sector BGC , the circumference BL and sector BGL are any equal multiples

whatever ...

Page 217

4 . either be within the triangle , or in one of its sides , or without it . First , let the

centre X be within the triangle , and join LX , MX , NX : AB is greater than LX : if

not , AB must either be equal to , or

because ...

4 . either be within the triangle , or in one of its sides , or without it . First , let the

centre X be within the triangle , and join LX , MX , NX : AB is greater than LX : if

not , AB must either be equal to , or

**less**than LX ; first , let it be equal : thenbecause ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

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 No preview available - 2017 |

### 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.