## 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 |

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Page 16

Ax . therefore the remainder AL is equal to the remainder f BG : but it has been

Ax . therefore the remainder AL is equal to the remainder f BG : but it has been

**shown**, that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ... Page 28

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

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 . Page 29

... DB ; but it has been

... DB ; but it has been

**shown**that BA , AC are greater than BE , EC ; much more then are BA , AC B C greater than BD , DC . Again , because the exterior angle of a triangle is greater than the interior and opposite angle , the exterior ... Page 32

1. be less b than the B C E F base EF ; but it is not ; therefore the angle BAC is not less than the angle EDF ; and it was

1. be less b than the B C E F base EF ; but it is not ; therefore the angle BAC is not less than the angle EDF ; and it was

**shown**that it is not equal to it ; therefore the angle BAC is greater than the angle EDF . Page 37

... but the angle ACE was

... but the angle ACE was

**shown**to be equal to the angle BAC ; therefore the whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC ; to these equals add the angle ACB , and the angles ACD , ACB are equal to ...### What people are saying - Write a review

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

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Robert Simson,Robert Euclid No preview available - 2016 |

### Common terms and phrases

added altitude angle ABC angle BAC base Book centre circle circle ABCD 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 26 - Any two sides of a triangle are together greater than the third side.

Page 60 - 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 26 - 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 55 - 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 24 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.

Page 161 - 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 15 - 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 187 - 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 35 - 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 176 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.