## 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 87

UPON the same straight line , and upon the same see N. side of it , there cannot

be two similar

is similar to the

UPON the same straight line , and upon the same see N. side of it , there cannot

be two similar

**segments**of circles not ... DA : and because A B the**segment**ACBis similar to the

**segment**ADB , and that similar**segments**of circles contain b ... Page 88

Book III . because AB is equal to CD : therefore , the straight line AB coinciding

with CD , the

therefore is equal to it . Wherefore , similar

Book III . because AB is equal to CD : therefore , the straight line AB coinciding

with CD , the

**segment**AEB must a coincide with the a 23. 3.**segment**CFD , andtherefore is equal to it . Wherefore , similar

**segments**, & c . Q. E. D. PROP . XXV . Page 89

From the centre E , at the distance of a any of the three AE , EB , EC , describe a

circle ; this shall pass d 9.3 . through the other points ; and the circle of which

ABC is a

...

From the centre E , at the distance of a any of the three AE , EB , EC , describe a

circle ; this shall pass d 9.3 . through the other points ; and the circle of which

ABC is a

**segment**is described : and it is evident , that if the angle ABD be greater...

Page 93

IN a circle , the angle in a semicircle is a right angle ; but the angle in a

greater than a semicircle is less than a ... Let ABCD be a circle , of which the

diameter is BC , and centre E ; and draw CA dividing the circle into the

...

IN a circle , the angle in a semicircle is a right angle ; but the angle in a

**segment**greater than a semicircle is less than a ... Let ABCD be a circle , of which the

diameter is BC , and centre E ; and draw CA dividing the circle into the

**segments**...

Page 96

3 . angle DAB is equal to the F angle in the alternate

but the angle DAB is equal to the angle C , therefore G also the angle C is equal

to the E angle in the

...

3 . angle DAB is equal to the F angle in the alternate

**segment**B g 32. 3. AHB 8 :but the angle DAB is equal to the angle C , therefore G also the angle C is equal

to the E angle in the

**segment**AHB : D wherefore , upon the given straight line AB...

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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 |

The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Robert Simson No preview available - 2017 |

### 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.