## 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

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Page 92

Take a K , L , the centres of the circles , and join BK , KC , EL , LF : and because

the

circles ...

Take a K , L , the centres of the circles , and join BK , KC , EL , LF : and because

the

**circumference**BGC is equal to the a 1. 3 . A D K L B C'E G H b 27. 3.**circumference**EHF , the angle BKC is equal o to the angle ELF : and because thecircles ...

Page 191

Take any number of

whatever FM , MN each equal to EF ... KGL are also all equal a : therefore what

multiple soever the circum - a 27.3 ference BL is of the

Take any number of

**circumferences**CK , KL , each equal to BC , and any numberwhatever FM , MN each equal to EF ... KGL are also all equal a : therefore what

multiple soever the circum - a 27.3 ference BL is of the

**circumference**BC , the ... Page 192

Book VI . and if the

angle BGL is also equal a to the angle ... being then four magnitudes , the two

...

Book VI . and if the

**circumference**BL be equal to the**circumference**LEN , theangle BGL is also equal a to the angle ... being then four magnitudes , the two

**circumferences**BC , EF , and the two angles BGC , EHF ; of the**circumference**BC...

Page 193

Therefore b , as the cir- b5.def.5 . cumference BC is to the

is the sector BGC to the sector EHF . Wherefore , in equal circles , & c . Q. E. D.

Book VI . PROP . B. THEOR . See N. 2 B OF EUCLID . 193 and they are upon ...

Therefore b , as the cir- b5.def.5 . cumference BC is to the

**circumference**EF , sois the sector BGC to the sector EHF . Wherefore , in equal circles , & c . Q. E. D.

Book VI . PROP . B. THEOR . See N. 2 B OF EUCLID . 193 and they are upon ...

Page 273

12 . scribed pyramid ; therefore the pyramid of which the base is the square

EFGH , and its vertex the same with that of the cone , is greater than half of the

cone : divide the

the ...

12 . scribed pyramid ; therefore the pyramid of which the base is the square

EFGH , and its vertex the same with that of the cone , is greater than half of the

cone : divide the

**circumferences**EF , FG , GH , HE , each into two equal parts inthe ...

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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 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.