## 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 36

STRAIGHT lines which are

another . Let AB , CD be each of them

Let the straight line GHK cut AB , EF , CD ; and because GHK cuts the

STRAIGHT lines which are

**parallel**to the same straight line are**parallel**to oneanother . Let AB , CD be each of them

**parallel**to EF ; AB is also**parallel**to CD .Let the straight line GHK cut AB , EF , CD ; and because GHK cuts the

**parallel**... Page 43

ABC is equal b to the triangle EBC , because it is upon the same Book 1 . base

BC , and between the same

demonstrated that no other line but AD is

ABC is equal b to the triangle EBC , because it is upon the same Book 1 . base

BC , and between the same

**parallels**BC ... In the same manner , it can bedemonstrated that no other line but AD is

**parallel**to BC ; AD is B с therefore**parallel**to it . Page 205

TWO straight lines which are each of them

not in the same plane with it , are

them

TWO straight lines which are each of them

**parallel**to the same straight line , andnot in the same plane with it , are

**parallel**to one another . Let AB , CD be each ofthem

**parallel**to EF , and not in the same plane with it ; AB shall be**parallel**to ... Page 210

See N. IF two

with it are

and let their common sections with it be EF , GH : EF is

not ...

See N. IF two

**parallel**planes be cut by another plane , their common sectionswith it are

**parallels**. Let the**parallel**planes AB , CD be cut by the plane EFHG ,and let their common sections with it be EF , GH : EF is

**parallel**to GH . For , if it isnot ...

Page 224

See N. IF a solid be contained by six planes , two and two of which are

the opposite planes are similar and equal parallelograms . Let the solid CDGH

be contained by the

planes ...

See N. IF a solid be contained by six planes , two and two of which are

**parallel**;the opposite planes are similar and equal parallelograms . Let the solid CDGH

be contained by the

**parallel**planes AC , GF ; BG , CE ; FB , AE : its oppositeplanes ...

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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.