## 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 4

and , as this

now thrown out of the Elements , and another , which , without doubt , Euclid had

given , is put in its proper place among the

and , as this

**definition**did much embarrass beginners , and is quite useless , it isnow thrown out of the Elements , and another , which , without doubt , Euclid had

given , is put in its proper place among the

**definitions**of the 5th book , by which ... Page 313

To this citation from Dr. Barrow I have nothing to add , except that I fully believe

the 3d and 8th

continual ” before “ pro“ portionals ” in this

33d prop ...

To this citation from Dr. Barrow I have nothing to add , except that I fully believe

the 3d and 8th

**definitions**are not ... B. V. It was necessary to add the word "continual ” before “ pro“ portionals ” in this

**definition**; and thus it is cited in the33d prop ...

Page 328

Nothing is usually reckoned more difficult in the elements of geometry by learners

, than the doctrine of compound ratio , which Theon has rendered absurd and

ungeometrical , by substituting the 5th

Nothing is usually reckoned more difficult in the elements of geometry by learners

, than the doctrine of compound ratio , which Theon has rendered absurd and

ungeometrical , by substituting the 5th

**definition**of the 6th book in place of the ... Page 329

and of the ratio of L to M. ” This

useless and absurd ; for that Theon brought it into the Elements can scarce be

doubted ; as it is to be found in his Commentary upon Ptolomy's Meyvan

Eustažus ...

and of the ratio of L to M. ” This

**definition**therefore of Book VI . Theon is quiteuseless and absurd ; for that Theon brought it into the Elements can scarce be

doubted ; as it is to be found in his Commentary upon Ptolomy's Meyvan

Eustažus ...

Page 341

THE similitude of plane figures is

the proportionality of the sides about the ... that are neither similar nor equal , as

shall be demonstrated after the notes on the 10th

...

THE similitude of plane figures is

**defined**from the equality of their angles , andthe proportionality of the sides about the ... that are neither similar nor equal , as

shall be demonstrated after the notes on the 10th

**definition**: upon this account it...

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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.