## 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 9

Page 48

1.

BA is equal to с AD ; therefore the four straight lines BA , AD , DE , EB are equal

to one another , and the parallelogram ADEB is equilateral , likewise all its ...

1.

**fore**ADEB is a parallelogram : whence AB is equal a to DE , and AD to BE : butBA is equal to с AD ; therefore the four straight lines BA , AD , DE , EB are equal

to one another , and the parallelogram ADEB is equilateral , likewise all its ...

Page 125

... and so , if there be more parts in EF , GH equal to A , C : because , there

E A B G C D

third GL is of the fourth D , and that the fifth KF is the same multiple of the second

B , which ...

... and so , if there be more parts in EF , GH equal to A , C : because , there

E A B G C D

**fore**, the first EK is the same multiple of the second B , which thethird GL is of the fourth D , and that the fifth KF is the same multiple of the second

B , which ...

Page 233

... base AB G D K to the base LQ , so O Q the base CD to the B base LQ , as

before was proved : thereC L

the solid CF to the solid LR ; and therefore the solid AE is equal e to the solid CF.

e 9.

... base AB G D K to the base LQ , so O Q the base CD to the B base LQ , as

before was proved : thereC L

**fore**as the solid AE to the solid LR , so A S Η Τ isthe solid CF to the solid LR ; and therefore the solid AE is equal e to the solid CF.

e 9.

Page 235

Where- 1 29. or

THEOR . SOLID parallelepipeds which have the same alti . See N. tude , are to

one another as their bases . Let AB , CD be solid parallelepipeds of the same ...

Where- 1 29. or

**fore**, solid parallelepipeds , & c . Q. E. D. 30.11 . PROP . XXXII .THEOR . SOLID parallelepipeds which have the same alti . See N. tude , are to

one another as their bases . Let AB , CD be solid parallelepipeds of the same ...

Page 281

Where- 5 .

cylinders upon equal bases are to one another as their altitudes . Let the

cylinders EB , FD be upon the equal bases AB , CD : as the cylinder EB to the

cylinder FD ...

Where- 5 .

**fore**, if a cylinder , & c . R. E. D. PROP . XIV . THEOR . CONES andcylinders upon equal bases are to one another as their altitudes . Let the

cylinders EB , FD be upon the equal bases AB , CD : as the cylinder EB to the

cylinder FD ...

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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.