## 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 20

... and likewise those which are terminated in the other extremity ,

... and likewise those which are terminated in the other extremity ,

**Q. E. D. PROP**. VIII . THEOR . IF two triangles have two sides of the one equal to two sides of the other , each to each , and have like . wise their bases equal ... Page 21

**Q. E. D. PROP**. IX . PROB . TO bisect a given rectilineal angle , that is , to di . vide it into two equal angles . Let BAC be the given rectilineal angle ; it is required to bisect it . Take any point D in AB , and from AC cut a off AE ... Page 24

**Q. E. D. PROP**. XIV . THEOR . IF , at a point in a straight line , two other straight lines , upon the opposite sides of it , make the adjacent angles together equal to two right angles , these two straight lines shall be in one and the ... Page 25

And , in like manner , it may be demonstrated , that no other can be in the same straight line with it but BD , which therefore is in the same straight line with CB . Wherefore , if at a point , & c .

And , in like manner , it may be demonstrated , that no other can be in the same straight line with it but BD , which therefore is in the same straight line with CB . Wherefore , if at a point , & c .

**Q. E. D. PROP**. XV . THEOR . Page 26

**Q. E. D. PROP**. XVII . THEOR . ANY two angles of a triangle are together less than two right angles . A Let ABC be any triangle ; any two of its angles together are less than two right angles . Produce BC to D ; and because ACD is the ...### 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.