## 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 119

Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other . V. The first of four magnitudes is said to have the same ratio to the second , which the third has to the

Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other . V. The first of four magnitudes is said to have the same ratio to the second , which the third has to the

**fourth**, when any ... Page 120

Book V. the first be greater than that of the second , the multiple of the third is also greater than that of the

Book V. the first be greater than that of the second , the multiple of the third is also greater than that of the

**fourth**. VI . Magnitudes which have the same ratio are called proportionals . N. B. When four magnitudes are proportionals ... Page 121

Permutando , or alternando , by permutation , or alternately ; this word is used when there are four proportionals , and it is See N. inferred , that the first has the same ratio to the third , which the second has to the

Permutando , or alternando , by permutation , or alternately ; this word is used when there are four proportionals , and it is See N. inferred , that the first has the same ratio to the third , which the second has to the

**fourth**; or ... Page 122

Book V. second , as the third to its excess above the

Book V. second , as the third to its excess above the

**fourth**. Prop . E , book 5 . XVIII . Ex æquali ( sc . distantia ) , or ex æquo , from equality of distance ; when there is any number of magnitudes more than two , and as many uthers ... Page 124

IF the first magnitude be the same multiple of the second that the third is of the

IF the first magnitude be the same multiple of the second that the third is of the

**fourth**, and the fifth the same multiple of the second that the sixth is of the**fourth**; then shall the first together with the fifth be the same ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### 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.