## 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

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**double**of the same are equal to one another . VII . Things which are halves of the same are equal to one another . VIII . Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one ... Page 40

1. parallelograms is

1. parallelograms is

**double**a of the triangle BDC ; and they are therefore equal to one another . But , if the sides AD , EF , opposite B B с to the base BC of the parallelograms ABCD ... Page 43

IF a parallelogram and triangle be upon the same base , and between the same parallels ; the parallelogram shall be

IF a parallelogram and triangle be upon the same base , and between the same parallels ; the parallelogram shall be

**double**of the triangle . Book I. Let the parallelogram ABCD and the triangle EBC OF EUCLID . 43. Page 44

But the parallelogram ABCD is

But the parallelogram ABCD is

**double**b of the triangle ABC , because the diameter AC divides it into two equal parts ; wherefore ABCD is also**double**of the B с triangle EBC . Therefore , if a parallelogram , & c . Q. E. D. PROP . XLII . Page 49

1 . gle ABD to the triangle FBC : now the parallelogram BL is

1 . gle ABD to the triangle FBC : now the parallelogram BL is

**double**8 of the triangle ABD , because they are upon the såme g 41. 1 . base BD , and between the same parallels , BD , AL ; and the square GB is**double**of the triangle FBC ...### 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

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.