## 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

Results 1-5 of 7

Page 300

13 , book 1. This part must therefore have been

of some proposition betwixt the 5th and 13th , but none of these stand in need of

it except the 7th proposition , on account of which it has been

13 , book 1. This part must therefore have been

**added**to prop . 5 , upon accountof some proposition betwixt the 5th and 13th , but none of these stand in need of

it except the 7th proposition , on account of which it has been

**added**: besides ... Page 340

In the Greek , as also in the Latin translation , the words á stums , “ any whatever ,

” are left out in the demonstration of both parts of the proposition , and are now

In the Greek , as also in the Latin translation , the words á stums , “ any whatever ,

” are left out in the demonstration of both parts of the proposition , and are now

**added**as quite necessary ; and in the demonstration of the second part , where ... Page 369

The limitation within the inverted commas is not in the Greek text , but is now

necessarily

the book which depend upon this second proposition , where it is not expressly ...

The limitation within the inverted commas is not in the Greek text , but is now

necessarily

**added**; and the same must be understood in all the propositions ofthe book which depend upon this second proposition , where it is not expressly ...

Page 465

... magnitudes E , Z , C , a fourth proportional A may be found ; but this cannot

always be done by the Elements of Euclid ; from which it is plain Euclid must

have understood the proposition under the limitation which is now

text .

... magnitudes E , Z , C , a fourth proportional A may be found ; but this cannot

always be done by the Elements of Euclid ; from which it is plain Euclid must

have understood the proposition under the limitation which is now

**added**to histext .

Page 468

Each of these has a determination , which is now

change in their demonstrations . PROP . XXXVII , XXXIX , XL , XLI . The 35th and

36th propositions in the Greek text are joined into one , which makes the 39th in

this ...

Each of these has a determination , which is now

**added**, which occasions achange in their demonstrations . PROP . XXXVII , XXXIX , XL , XLI . The 35th and

36th propositions in the Greek text are joined into one , which makes the 39th in

this ...

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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.