## 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 7

A plane angle is the inclination of two lines to one another See N. “ in a plane , which

A plane angle is the inclination of two lines to one another See N. “ in a plane , which

**meet**together , but are not in the same “ direction . ” IX . A plane rectilineal angle is the inclination of two straight lines to one another ... Page 8

... of which the letter that is ' at the vertex of the angle , that is , at the point in which the • straight lines that contain the angle

... of which the letter that is ' at the vertex of the angle , that is , at the point in which the • straight lines that contain the angle

**meet**one another , is put between the other two letters , and one of these two is somewhere upon ... Page 13

Parallel straight lines are such as are in the same plane , and which being produced ever so far both ways , do not

Parallel straight lines are such as are in the same plane , and which being produced ever so far both ways , do not

**meet**. POSTULATES . I. LET it be granted that a straight line may be drawn from any one point to any other point . II . Page 14

If a straight line

If a straight line

**meets**two straight lines , so as to make the “ two interior angles on the same side of it taken together “ less than two right angles , these straight lines being con“ tinually produced , shall at length**meet**upon ... Page 34

For , if it be not parallel , AB and CD being produced shall

For , if it be not parallel , AB and CD being produced shall

**meet**either towards B , D , or towards A , C ; let them be produced and**meet**towards B , D , in the point G ; therefore GEF a 16. 1. is a triangle , and its exterior angle AEF ...### What people are saying - Write a review

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### Other editions - View all

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

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 radius reason rectangle rectangle contained rectilineal figure 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.