## 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 361

... in the figure it is made to fall upon the

likewise supposed in the demonstration . Commandine seems to have been

aware of this ; for in this figure he marks one and the same

letters V ...

... in the figure it is made to fall upon the

**point**2**a**different**point**from V , which islikewise supposed in the demonstration . Commandine seems to have been

aware of this ; for in this figure he marks one and the same

**point**with the twoletters V ...

Page 389

IF a straight line be drawn to a

makes a given angle with it ; that straight line is given in position . Bb 23. 1 . Let

AB be a straight line given in position , and C a

IF a straight line be drawn to a

**given point**in a straight line given in position , andmakes a given angle with it ; that straight line is given in position . Bb 23. 1 . Let

AB be a straight line given in position , and C a

**given point**in it , the straight line ... Page 390

BC , EF , the angle EADc is equal to the angle ADC ; and ADC is given ,

wherefore also the angle EAD is given : therefore , because the straight line DA is

drawn to the

with it a ...

BC , EF , the angle EADc is equal to the angle ADC ; and ADC is given ,

wherefore also the angle EAD is given : therefore , because the straight line DA is

drawn to the

**given point**A in the straight line EF given in position , and makeswith it a ...

Page 393

1 . a to the given angle ADC ; HG is given in position b ; but it is b 32. dat . given

also in magnitude , because it is equal to ... EAF , which is drawn through the

31 ...

1 . a to the given angle ADC ; HG is given in position b ; but it is b 32. dat . given

also in magnitude , because it is equal to ... EAF , which is drawn through the

**given point**H parallel to WC given in position , is therefore given e in position . e31 ...

Page 455

because the straight line DC is drawn to the

given in position in the given angle BDC , DC is given c in position : -and the

circumference ABC is given c 32. dar . in position , therefored the point C is given

. d ...

because the straight line DC is drawn to the

**given point**D in the straight line BDgiven in position in the given angle BDC , DC is given c in position : -and the

circumference ABC is given c 32. dar . in position , therefored the point C is given

. d ...

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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.