## 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 - 518 pages |

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**greater**. It is required to cut off from AB , the**greater**, a part equal to C , the less . D C B a 2. 1 . A b 3. Post . From the point A draw a the straight line AD equal to C ; and from the centre A , and at the dis- tance AD ... Page 19

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**greater**, and from it cut a off DB a 3. 1 . equal to AC , the less , and join DC ; there- A D fore , because in the ...**greater**than the angle BCD ; therefore the A angle ADC is**greater**also than BCD ; B much more then is the angle ... Page 20

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**greater**than BCD ; much more then is the angle BDC**greater**than the angle BCD . Again , because CB is equal to DB , the angle BDC is equal a to the angle BCD ; but BDC has been proved to be A**greater**than the same BCD ; which is ... Page 26

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**greater**than the angle ECF ; therefore the angle ACD is**greater**than BAE : in the same manner , if the side BC be bisected , it may be demonstrated that the angle BCG , d 15. 1. that is d , the angle ACD , is**greater**than the angle ABC ... Page 27

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**greater**than the angles ABC , ACB ; but ACD , ACB are to- gether equal to two right angles ; therefore the angles ...**greater**side of every triangle is opposite to the**greater**angle . Let ABC be a triangle , of which the side AC is ...### Other editions - View all

### Common terms and phrases

altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given point given ratio given straight line gnomon greater join less Let ABC meet multiple opposite parallel parallelogram parallelogram AC perpendicular point F polygon prism proposition pyramid Q. E. D. PROP radius rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelepipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore

### Popular passages

Page 28 - Any two sides of a triangle are together greater than the third side.

Page 62 - 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 28 - 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 57 - 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 26 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.

Page 163 - 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 17 - 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 189 - 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 37 - 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 178 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.