## 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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Page 38

Book I. the preceding proposition , all the angles of these triangles are equal to

twice as many

the figure ; and the same angles are equal to the angles of the figure , together

with ...

Book I. the preceding proposition , all the angles of these triangles are equal to

twice as many

**right angles**as there are triangles , that is , as there are sides ofthe figure ; and the same angles are equal to the angles of the figure , together

with ...

Page 48

From the point A draw a AC at

to AB , and through the point D draw DE o 31. 1. parallel c to AB , and through B

draw BE parallel to AD ; thered 34. 1. fore ADEB is a parallelogram : whence AB

...

From the point A draw a AC at

**right angles**10 AB ; and b 3. 1 . make b'AD equalto AB , and through the point D draw DE o 31. 1. parallel c to AB , and through B

draw BE parallel to AD ; thered 34. 1. fore ADEB is a parallelogram : whence AB

...

Page 93

IN a circle , the angle in a semicircle is a

greater than a semicircle is less than a

less than a semicircle is greater than a

which ...

IN a circle , the angle in a semicircle is a

**right angle**; but the angle in a segmentgreater than a semicircle is less than a

**right angle**; and the angle in a segmentless than a semicircle is greater than a

**right angle**. Let ABCD be a circle , ofwhich ...

Page 201

equal to EH , and AG to BH : and because AE is equal to EB , Book XI . and FE

common and at

proved equal to the base FC ; therefore the angle FAD is equal d to the angle d

8.1 .

equal to EH , and AG to BH : and because AE is equal to EB , Book XI . and FE

common and at

**right angles**to them ... each to each ; and the base DF was Fproved equal to the base FC ; therefore the angle FAD is equal d to the angle d

8.1 .

Page 204

Let AB , CD be two parallel straight lines , and let one of them AB be at

meet the plane in the points B , D , and join BD : 87.11 . therefore & AB , CD , BD

are ...

Let AB , CD be two parallel straight lines , and let one of them AB be at

**right****angles**to a plane ; the other CD is at**right angles**to the same plane . Let AB , CDmeet the plane in the points B , D , and join BD : 87.11 . therefore & AB , CD , BD

are ...

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The Elements of Euclid, Viz: The Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid No preview available - 2018 |

The Elements of Euclid, Viz: The Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid No preview available - 2015 |

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### 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 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 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.